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Hyper-3DG: Text-to-3D Gaussian Generation via Hypergraph (2403.09236v2)
Published 14 Mar 2024 in cs.CV
Abstract: Text-to-3D generation represents an exciting field that has seen rapid advancements, facilitating the transformation of textual descriptions into detailed 3D models. However, current progress often neglects the intricate high-order correlation of geometry and texture within 3D objects, leading to challenges such as over-smoothness, over-saturation and the Janus problem. In this work, we propose a method named 3D Gaussian Generation via Hypergraph (Hyper-3DG)'', designed to capture the sophisticated high-order correlations present within 3D objects. Our framework is anchored by a well-established mainflow and an essential module, namedGeometry and Texture Hypergraph Refiner (HGRefiner)''. This module not only refines the representation of 3D Gaussians but also accelerates the update process of these 3D Gaussians by conducting the Patch-3DGS Hypergraph Learning on both explicit attributes and latent visual features. Our framework allows for the production of finely generated 3D objects within a cohesive optimization, effectively circumventing degradation. Extensive experimentation has shown that our proposed method significantly enhances the quality of 3D generation while incurring no additional computational overhead for the underlying framework. (Project code: https://github.com/yjhboy/Hyper3DG)
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[2023] Kerbl, B., Kopanas, G., Leimkühler, T., Drettakis, G.: 3d gaussian splatting for real-time radiance field rendering. ACM Trans. Graph. 42(4) (2023) Tang et al. [2023] Tang, J., Ren, J., Zhou, H., Liu, Z., Zeng, G.: Dreamgaussian: Generative gaussian splatting for efficient 3d content creation. arXiv preprint arXiv:2309.16653 (2023) Fridovich-Keil et al. [2022] Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yu, Y., Zhu, S., Qin, H., Li, H.: BoostDream: Efficient Refining for High-Quality Text-to-3D Generation from Multi-View Diffusion (2024) Huang et al. [2023] Huang, Y., Wang, J., Zeng, A., Cao, H., Qi, X., Shi, Y., Zha, Z.-J., Zhang, L.: DreamWaltz: Make a Scene with Complex 3D Animatable Avatars (2023) Sun et al. [2024] Sun, J., Zhang, B., Shao, R., Wang, L., Liu, W., Xie, Z., Liu, Y.: Dreamcraft3d: Hierarchical 3d generation with bootstrapped diffusion prior. Int. Conf. Learn. Represent. (2024) Poole et al. [2023] Poole, B., Jain, A., Barron, J.T., Mildenhall, B.: Dreamfusion: Text-to-3d using 2d diffusion. Int. Conf. Learn. Represent. (2023) Wang et al. [2024] Wang, Z., Lu, C., Wang, Y., Bao, F., Li, C., Su, H., Zhu, J.: Prolificdreamer: High-fidelity and diverse text-to-3d generation with variational score distillation. Adv. Neural Inform. Process. Syst. 36 (2024) Yi et al. [2023] Yi, T., Fang, J., Wu, G., Xie, L., Zhang, X., Liu, W., Tian, Q., Wang, X.: Gaussiandreamer: Fast generation from text to 3d gaussian splatting with point cloud priors. arXiv preprint arXiv:2310.08529 (2023) Zhang [2019] Zhang, H.: 3d model generation on architectural plan and section training through machine learning. Technologies 7(4), 82 (2019) Hong et al. [2024] Hong, S., Ahn, D., Kim, S.: Debiasing scores and prompts of 2d diffusion for view-consistent text-to-3d generation. Adv. Neural Inform. Process. Syst. 36 (2024) Armandpour et al. [2023] Armandpour, M., Zheng, H., Sadeghian, A., Sadeghian, A., Zhou, M.: Re-imagine the negative prompt algorithm: Transform 2d diffusion into 3d, alleviate janus problem and beyond. arXiv preprint arXiv:2304.04968 (2023) Chen et al. [2023] Chen, Z., Wang, F., Liu, H.: Text-to-3d using gaussian splatting. arXiv preprint arXiv:2309.16585 (2023) Liu et al. [2023] Liu, R., Wu, R., Van Hoorick, B., Tokmakov, P., Zakharov, S., Vondrick, C.: Zero-1-to-3: Zero-shot one image to 3d object. In: Int. Conf. Comput. Vis., pp. 9298–9309 (2023) Ho et al. [2020] Ho, J., Jain, A., Abbeel, P.: Denoising diffusion probabilistic models. Adv. Neural Inform. Process. Syst. 33, 6840–6851 (2020) Song et al. [2020] Song, Y., Sohl-Dickstein, J., Kingma, D.P., Kumar, A., Ermon, S., Poole, B.: Score-based generative modeling through stochastic differential equations. arXiv preprint arXiv:2011.13456 (2020) Nichol et al. [2022] Nichol, A., Jun, H., Dhariwal, P., Mishkin, P., Chen, M.: Point-e: A system for generating 3d point clouds from complex prompts. arXiv preprint arXiv:2212.08751 (2022) Jun and Nichol [2023] Jun, H., Nichol, A.: Shap-e: Generating conditional 3d implicit functions. arXiv preprint arXiv:2305.02463 (2023) Peebles and Xie [2023] Peebles, W., Xie, S.: Scalable diffusion models with transformers. In: Int. Conf. Comput. Vis., pp. 4195–4205 (2023) He et al. [2016] He, K., Zhang, X., Ren, S., Sun, J.: Deep residual learning for image recognition. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 770–778 (2016) Xie et al. [2017] Xie, S., Girshick, R., Dollár, P., Tu, Z., He, K.: Aggregated residual transformations for deep neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 1492–1500 (2017) Dosovitskiy et al. [2021] Dosovitskiy, A., Beyer, L., Kolesnikov, A., Weissenborn, D., Zhai, X., Unterthiner, T., Dehghani, M., Minderer, M., Heigold, G., Gelly, S., Uszkoreit, J., Houlsby, N.: An image is worth 16x16 words: Transformers for image recognition at scale. In: Int. Conf. Learn. Represent. (2021) Liu et al. [2021] Liu, Z., Lin, Y., Cao, Y., Hu, H., Wei, Y., Zhang, Z., Lin, S., Guo, B.: Swin transformer: Hierarchical vision transformer using shifted windows. In: Int. Conf. Comput. Vis., pp. 10012–10022 (2021) Caron et al. [2021] Caron, M., Touvron, H., Misra, I., Jégou, H., Mairal, J., Bojanowski, P., Joulin, A.: Emerging properties in self-supervised vision transformers. In: Int. Conf. Comput. Vis., pp. 9650–9660 (2021) Feng et al. [2019] Feng, Y., You, H., Zhang, Z., Ji, R., Gao, Y.: Hypergraph neural networks. In: AAAI Conf. on Artificial Intell., vol. 33, pp. 3558–3565 (2019) Gao et al. [2022] Gao, Y., Feng, Y., Ji, S., Ji, R.: Hgnn+: General hypergraph neural networks. IEEE Trans. Pattern Anal. Mach. Intell. 45(3), 3181–3199 (2022) Liang et al. [2023] Liang, Y., Yang, X., Lin, J., Li, H., Xu, X., Chen, Y.: Luciddreamer: Towards high-fidelity text-to-3d generation via interval score matching. arXiv preprint arXiv:2311.11284 (2023) Radford et al. [2021] Radford, A., Kim, J.W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., Sastry, G., Askell, A., Mishkin, P., Clark, J., et al.: Learning transferable visual models from natural language supervision. In: Int. Conf. on Mach. Learn., pp. 8748–8763 (2021). PMLR Long et al. [2023] Long, X., Guo, Y.-C., Lin, C., Liu, Y., Dou, Z., Liu, L., Ma, Y., Zhang, S.-H., Habermann, M., Theobalt, C., et al.: Wonder3d: Single image to 3d using cross-domain diffusion. arXiv preprint arXiv:2310.15008 (2023) Mildenhall et al. [2020] Mildenhall, B., Srinivasan, P.P., Tancik, M., Barron, J.T., Ramamoorthi, R., Ng, R.: Nerf: Representing scenes as neural radiance fields for view synthesis. In: Eur. Conf. Comput. Vis. (2020) Wang et al. [2021] Wang, P., Liu, L., Liu, Y., Theobalt, C., Komura, T., Wang, W.: Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. Adv. Neural Inform. Process. Syst. (2021) Wang et al. [2023] Wang, H., Du, X., Li, J., Yeh, R.A., Shakhnarovich, G.: Score jacobian chaining: Lifting pretrained 2d diffusion models for 3d generation. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 12619–12629 (2023) Kerbl et al. [2023] Kerbl, B., Kopanas, G., Leimkühler, T., Drettakis, G.: 3d gaussian splatting for real-time radiance field rendering. ACM Trans. Graph. 42(4) (2023) Tang et al. [2023] Tang, J., Ren, J., Zhou, H., Liu, Z., Zeng, G.: Dreamgaussian: Generative gaussian splatting for efficient 3d content creation. arXiv preprint arXiv:2309.16653 (2023) Fridovich-Keil et al. [2022] Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. 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[2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Caron, M., Touvron, H., Misra, I., Jégou, H., Mairal, J., Bojanowski, P., Joulin, A.: Emerging properties in self-supervised vision transformers. In: Int. Conf. Comput. Vis., pp. 9650–9660 (2021) Feng et al. [2019] Feng, Y., You, H., Zhang, Z., Ji, R., Gao, Y.: Hypergraph neural networks. In: AAAI Conf. on Artificial Intell., vol. 33, pp. 3558–3565 (2019) Gao et al. [2022] Gao, Y., Feng, Y., Ji, S., Ji, R.: Hgnn+: General hypergraph neural networks. IEEE Trans. Pattern Anal. Mach. Intell. 45(3), 3181–3199 (2022) Liang et al. [2023] Liang, Y., Yang, X., Lin, J., Li, H., Xu, X., Chen, Y.: Luciddreamer: Towards high-fidelity text-to-3d generation via interval score matching. arXiv preprint arXiv:2311.11284 (2023) Radford et al. 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[2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Feng, Y., You, H., Zhang, Z., Ji, R., Gao, Y.: Hypergraph neural networks. In: AAAI Conf. on Artificial Intell., vol. 33, pp. 3558–3565 (2019) Gao et al. [2022] Gao, Y., Feng, Y., Ji, S., Ji, R.: Hgnn+: General hypergraph neural networks. IEEE Trans. Pattern Anal. Mach. Intell. 45(3), 3181–3199 (2022) Liang et al. [2023] Liang, Y., Yang, X., Lin, J., Li, H., Xu, X., Chen, Y.: Luciddreamer: Towards high-fidelity text-to-3d generation via interval score matching. arXiv preprint arXiv:2311.11284 (2023) Radford et al. [2021] Radford, A., Kim, J.W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., Sastry, G., Askell, A., Mishkin, P., Clark, J., et al.: Learning transferable visual models from natural language supervision. In: Int. Conf. on Mach. Learn., pp. 8748–8763 (2021). 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[1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. 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[2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. 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[2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. 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[2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. 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[2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. 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[2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. 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Syst. 34, 6087–6101 (2021) Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. 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[2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. 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[2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. 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Syst. 34, 6087–6101 (2021) Xie, S., Girshick, R., Dollár, P., Tu, Z., He, K.: Aggregated residual transformations for deep neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 1492–1500 (2017) Dosovitskiy et al. [2021] Dosovitskiy, A., Beyer, L., Kolesnikov, A., Weissenborn, D., Zhai, X., Unterthiner, T., Dehghani, M., Minderer, M., Heigold, G., Gelly, S., Uszkoreit, J., Houlsby, N.: An image is worth 16x16 words: Transformers for image recognition at scale. In: Int. Conf. Learn. Represent. (2021) Liu et al. [2021] Liu, Z., Lin, Y., Cao, Y., Hu, H., Wei, Y., Zhang, Z., Lin, S., Guo, B.: Swin transformer: Hierarchical vision transformer using shifted windows. In: Int. Conf. Comput. Vis., pp. 10012–10022 (2021) Caron et al. [2021] Caron, M., Touvron, H., Misra, I., Jégou, H., Mairal, J., Bojanowski, P., Joulin, A.: Emerging properties in self-supervised vision transformers. In: Int. Conf. Comput. Vis., pp. 9650–9660 (2021) Feng et al. 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[2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. 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Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. 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[1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. 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[2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. 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[2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. 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In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. 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[2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. 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IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. 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[2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 770–778 (2016) Xie et al. [2017] Xie, S., Girshick, R., Dollár, P., Tu, Z., He, K.: Aggregated residual transformations for deep neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 1492–1500 (2017) Dosovitskiy et al. [2021] Dosovitskiy, A., Beyer, L., Kolesnikov, A., Weissenborn, D., Zhai, X., Unterthiner, T., Dehghani, M., Minderer, M., Heigold, G., Gelly, S., Uszkoreit, J., Houlsby, N.: An image is worth 16x16 words: Transformers for image recognition at scale. In: Int. Conf. Learn. Represent. (2021) Liu et al. [2021] Liu, Z., Lin, Y., Cao, Y., Hu, H., Wei, Y., Zhang, Z., Lin, S., Guo, B.: Swin transformer: Hierarchical vision transformer using shifted windows. In: Int. Conf. Comput. Vis., pp. 10012–10022 (2021) Caron et al. [2021] Caron, M., Touvron, H., Misra, I., Jégou, H., Mairal, J., Bojanowski, P., Joulin, A.: Emerging properties in self-supervised vision transformers. In: Int. Conf. Comput. 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[2023] Long, X., Guo, Y.-C., Lin, C., Liu, Y., Dou, Z., Liu, L., Ma, Y., Zhang, S.-H., Habermann, M., Theobalt, C., et al.: Wonder3d: Single image to 3d using cross-domain diffusion. arXiv preprint arXiv:2310.15008 (2023) Mildenhall et al. [2020] Mildenhall, B., Srinivasan, P.P., Tancik, M., Barron, J.T., Ramamoorthi, R., Ng, R.: Nerf: Representing scenes as neural radiance fields for view synthesis. In: Eur. Conf. Comput. Vis. (2020) Wang et al. [2021] Wang, P., Liu, L., Liu, Y., Theobalt, C., Komura, T., Wang, W.: Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. Adv. Neural Inform. Process. Syst. (2021) Wang et al. [2023] Wang, H., Du, X., Li, J., Yeh, R.A., Shakhnarovich, G.: Score jacobian chaining: Lifting pretrained 2d diffusion models for 3d generation. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 12619–12629 (2023) Kerbl et al. [2023] Kerbl, B., Kopanas, G., Leimkühler, T., Drettakis, G.: 3d gaussian splatting for real-time radiance field rendering. ACM Trans. Graph. 42(4) (2023) Tang et al. [2023] Tang, J., Ren, J., Zhou, H., Liu, Z., Zeng, G.: Dreamgaussian: Generative gaussian splatting for efficient 3d content creation. arXiv preprint arXiv:2309.16653 (2023) Fridovich-Keil et al. [2022] Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. 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[2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. 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[2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. 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Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. 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Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. 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Syst. 34, 6087–6101 (2021) Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. 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[2023] Kerbl, B., Kopanas, G., Leimkühler, T., Drettakis, G.: 3d gaussian splatting for real-time radiance field rendering. ACM Trans. Graph. 42(4) (2023) Tang et al. [2023] Tang, J., Ren, J., Zhou, H., Liu, Z., Zeng, G.: Dreamgaussian: Generative gaussian splatting for efficient 3d content creation. arXiv preprint arXiv:2309.16653 (2023) Fridovich-Keil et al. [2022] Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. 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[2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Xie, S., Girshick, R., Dollár, P., Tu, Z., He, K.: Aggregated residual transformations for deep neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 1492–1500 (2017) Dosovitskiy et al. [2021] Dosovitskiy, A., Beyer, L., Kolesnikov, A., Weissenborn, D., Zhai, X., Unterthiner, T., Dehghani, M., Minderer, M., Heigold, G., Gelly, S., Uszkoreit, J., Houlsby, N.: An image is worth 16x16 words: Transformers for image recognition at scale. In: Int. Conf. Learn. Represent. (2021) Liu et al. [2021] Liu, Z., Lin, Y., Cao, Y., Hu, H., Wei, Y., Zhang, Z., Lin, S., Guo, B.: Swin transformer: Hierarchical vision transformer using shifted windows. In: Int. Conf. Comput. Vis., pp. 10012–10022 (2021) Caron et al. [2021] Caron, M., Touvron, H., Misra, I., Jégou, H., Mairal, J., Bojanowski, P., Joulin, A.: Emerging properties in self-supervised vision transformers. In: Int. Conf. Comput. Vis., pp. 9650–9660 (2021) Feng et al. [2019] Feng, Y., You, H., Zhang, Z., Ji, R., Gao, Y.: Hypergraph neural networks. In: AAAI Conf. on Artificial Intell., vol. 33, pp. 3558–3565 (2019) Gao et al. [2022] Gao, Y., Feng, Y., Ji, S., Ji, R.: Hgnn+: General hypergraph neural networks. IEEE Trans. Pattern Anal. Mach. Intell. 45(3), 3181–3199 (2022) Liang et al. [2023] Liang, Y., Yang, X., Lin, J., Li, H., Xu, X., Chen, Y.: Luciddreamer: Towards high-fidelity text-to-3d generation via interval score matching. arXiv preprint arXiv:2311.11284 (2023) Radford et al. [2021] Radford, A., Kim, J.W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., Sastry, G., Askell, A., Mishkin, P., Clark, J., et al.: Learning transferable visual models from natural language supervision. In: Int. Conf. on Mach. Learn., pp. 8748–8763 (2021). PMLR Long et al. [2023] Long, X., Guo, Y.-C., Lin, C., Liu, Y., Dou, Z., Liu, L., Ma, Y., Zhang, S.-H., Habermann, M., Theobalt, C., et al.: Wonder3d: Single image to 3d using cross-domain diffusion. arXiv preprint arXiv:2310.15008 (2023) Mildenhall et al. [2020] Mildenhall, B., Srinivasan, P.P., Tancik, M., Barron, J.T., Ramamoorthi, R., Ng, R.: Nerf: Representing scenes as neural radiance fields for view synthesis. In: Eur. Conf. Comput. Vis. (2020) Wang et al. [2021] Wang, P., Liu, L., Liu, Y., Theobalt, C., Komura, T., Wang, W.: Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. Adv. Neural Inform. Process. Syst. (2021) Wang et al. [2023] Wang, H., Du, X., Li, J., Yeh, R.A., Shakhnarovich, G.: Score jacobian chaining: Lifting pretrained 2d diffusion models for 3d generation. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 12619–12629 (2023) Kerbl et al. [2023] Kerbl, B., Kopanas, G., Leimkühler, T., Drettakis, G.: 3d gaussian splatting for real-time radiance field rendering. ACM Trans. Graph. 42(4) (2023) Tang et al. [2023] Tang, J., Ren, J., Zhou, H., Liu, Z., Zeng, G.: Dreamgaussian: Generative gaussian splatting for efficient 3d content creation. arXiv preprint arXiv:2309.16653 (2023) Fridovich-Keil et al. [2022] Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. 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[2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Gao, Y., Feng, Y., Ji, S., Ji, R.: Hgnn+: General hypergraph neural networks. IEEE Trans. Pattern Anal. Mach. Intell. 45(3), 3181–3199 (2022) Liang et al. [2023] Liang, Y., Yang, X., Lin, J., Li, H., Xu, X., Chen, Y.: Luciddreamer: Towards high-fidelity text-to-3d generation via interval score matching. arXiv preprint arXiv:2311.11284 (2023) Radford et al. [2021] Radford, A., Kim, J.W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., Sastry, G., Askell, A., Mishkin, P., Clark, J., et al.: Learning transferable visual models from natural language supervision. In: Int. Conf. on Mach. Learn., pp. 8748–8763 (2021). PMLR Long et al. [2023] Long, X., Guo, Y.-C., Lin, C., Liu, Y., Dou, Z., Liu, L., Ma, Y., Zhang, S.-H., Habermann, M., Theobalt, C., et al.: Wonder3d: Single image to 3d using cross-domain diffusion. arXiv preprint arXiv:2310.15008 (2023) Mildenhall et al. [2020] Mildenhall, B., Srinivasan, P.P., Tancik, M., Barron, J.T., Ramamoorthi, R., Ng, R.: Nerf: Representing scenes as neural radiance fields for view synthesis. In: Eur. Conf. Comput. Vis. 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Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. 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[2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Liang, Y., Yang, X., Lin, J., Li, H., Xu, X., Chen, Y.: Luciddreamer: Towards high-fidelity text-to-3d generation via interval score matching. arXiv preprint arXiv:2311.11284 (2023) Radford et al. [2021] Radford, A., Kim, J.W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., Sastry, G., Askell, A., Mishkin, P., Clark, J., et al.: Learning transferable visual models from natural language supervision. In: Int. Conf. on Mach. Learn., pp. 8748–8763 (2021). PMLR Long et al. [2023] Long, X., Guo, Y.-C., Lin, C., Liu, Y., Dou, Z., Liu, L., Ma, Y., Zhang, S.-H., Habermann, M., Theobalt, C., et al.: Wonder3d: Single image to 3d using cross-domain diffusion. arXiv preprint arXiv:2310.15008 (2023) Mildenhall et al. [2020] Mildenhall, B., Srinivasan, P.P., Tancik, M., Barron, J.T., Ramamoorthi, R., Ng, R.: Nerf: Representing scenes as neural radiance fields for view synthesis. In: Eur. Conf. Comput. Vis. (2020) Wang et al. [2021] Wang, P., Liu, L., Liu, Y., Theobalt, C., Komura, T., Wang, W.: Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. Adv. Neural Inform. Process. Syst. (2021) Wang et al. [2023] Wang, H., Du, X., Li, J., Yeh, R.A., Shakhnarovich, G.: Score jacobian chaining: Lifting pretrained 2d diffusion models for 3d generation. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 12619–12629 (2023) Kerbl et al. [2023] Kerbl, B., Kopanas, G., Leimkühler, T., Drettakis, G.: 3d gaussian splatting for real-time radiance field rendering. ACM Trans. Graph. 42(4) (2023) Tang et al. [2023] Tang, J., Ren, J., Zhou, H., Liu, Z., Zeng, G.: Dreamgaussian: Generative gaussian splatting for efficient 3d content creation. arXiv preprint arXiv:2309.16653 (2023) Fridovich-Keil et al. [2022] Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. 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[2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Long, X., Guo, Y.-C., Lin, C., Liu, Y., Dou, Z., Liu, L., Ma, Y., Zhang, S.-H., Habermann, M., Theobalt, C., et al.: Wonder3d: Single image to 3d using cross-domain diffusion. arXiv preprint arXiv:2310.15008 (2023) Mildenhall et al. [2020] Mildenhall, B., Srinivasan, P.P., Tancik, M., Barron, J.T., Ramamoorthi, R., Ng, R.: Nerf: Representing scenes as neural radiance fields for view synthesis. In: Eur. Conf. Comput. Vis. (2020) Wang et al. [2021] Wang, P., Liu, L., Liu, Y., Theobalt, C., Komura, T., Wang, W.: Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. Adv. Neural Inform. Process. Syst. (2021) Wang et al. 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[2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. 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[2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. 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[2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. 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[1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. 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IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. 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Syst. 34, 6087–6101 (2021) Xie, S., Girshick, R., Dollár, P., Tu, Z., He, K.: Aggregated residual transformations for deep neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 1492–1500 (2017) Dosovitskiy et al. [2021] Dosovitskiy, A., Beyer, L., Kolesnikov, A., Weissenborn, D., Zhai, X., Unterthiner, T., Dehghani, M., Minderer, M., Heigold, G., Gelly, S., Uszkoreit, J., Houlsby, N.: An image is worth 16x16 words: Transformers for image recognition at scale. In: Int. Conf. Learn. Represent. (2021) Liu et al. [2021] Liu, Z., Lin, Y., Cao, Y., Hu, H., Wei, Y., Zhang, Z., Lin, S., Guo, B.: Swin transformer: Hierarchical vision transformer using shifted windows. In: Int. Conf. Comput. Vis., pp. 10012–10022 (2021) Caron et al. [2021] Caron, M., Touvron, H., Misra, I., Jégou, H., Mairal, J., Bojanowski, P., Joulin, A.: Emerging properties in self-supervised vision transformers. In: Int. Conf. Comput. Vis., pp. 9650–9660 (2021) Feng et al. 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[2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. 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IEEE Trans. Pattern Anal. Mach. Intell. 45(3), 3181–3199 (2022) Liang et al. [2023] Liang, Y., Yang, X., Lin, J., Li, H., Xu, X., Chen, Y.: Luciddreamer: Towards high-fidelity text-to-3d generation via interval score matching. arXiv preprint arXiv:2311.11284 (2023) Radford et al. [2021] Radford, A., Kim, J.W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., Sastry, G., Askell, A., Mishkin, P., Clark, J., et al.: Learning transferable visual models from natural language supervision. In: Int. Conf. on Mach. Learn., pp. 8748–8763 (2021). PMLR Long et al. [2023] Long, X., Guo, Y.-C., Lin, C., Liu, Y., Dou, Z., Liu, L., Ma, Y., Zhang, S.-H., Habermann, M., Theobalt, C., et al.: Wonder3d: Single image to 3d using cross-domain diffusion. arXiv preprint arXiv:2310.15008 (2023) Mildenhall et al. [2020] Mildenhall, B., Srinivasan, P.P., Tancik, M., Barron, J.T., Ramamoorthi, R., Ng, R.: Nerf: Representing scenes as neural radiance fields for view synthesis. In: Eur. Conf. Comput. Vis. 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Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. 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Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Liang, Y., Yang, X., Lin, J., Li, H., Xu, X., Chen, Y.: Luciddreamer: Towards high-fidelity text-to-3d generation via interval score matching. arXiv preprint arXiv:2311.11284 (2023) Radford et al. [2021] Radford, A., Kim, J.W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., Sastry, G., Askell, A., Mishkin, P., Clark, J., et al.: Learning transferable visual models from natural language supervision. In: Int. Conf. on Mach. Learn., pp. 8748–8763 (2021). PMLR Long et al. [2023] Long, X., Guo, Y.-C., Lin, C., Liu, Y., Dou, Z., Liu, L., Ma, Y., Zhang, S.-H., Habermann, M., Theobalt, C., et al.: Wonder3d: Single image to 3d using cross-domain diffusion. arXiv preprint arXiv:2310.15008 (2023) Mildenhall et al. [2020] Mildenhall, B., Srinivasan, P.P., Tancik, M., Barron, J.T., Ramamoorthi, R., Ng, R.: Nerf: Representing scenes as neural radiance fields for view synthesis. In: Eur. Conf. Comput. Vis. (2020) Wang et al. [2021] Wang, P., Liu, L., Liu, Y., Theobalt, C., Komura, T., Wang, W.: Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. Adv. Neural Inform. Process. Syst. (2021) Wang et al. [2023] Wang, H., Du, X., Li, J., Yeh, R.A., Shakhnarovich, G.: Score jacobian chaining: Lifting pretrained 2d diffusion models for 3d generation. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 12619–12629 (2023) Kerbl et al. 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[2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Long, X., Guo, Y.-C., Lin, C., Liu, Y., Dou, Z., Liu, L., Ma, Y., Zhang, S.-H., Habermann, M., Theobalt, C., et al.: Wonder3d: Single image to 3d using cross-domain diffusion. arXiv preprint arXiv:2310.15008 (2023) Mildenhall et al. [2020] Mildenhall, B., Srinivasan, P.P., Tancik, M., Barron, J.T., Ramamoorthi, R., Ng, R.: Nerf: Representing scenes as neural radiance fields for view synthesis. In: Eur. Conf. Comput. Vis. (2020) Wang et al. [2021] Wang, P., Liu, L., Liu, Y., Theobalt, C., Komura, T., Wang, W.: Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. Adv. Neural Inform. Process. Syst. (2021) Wang et al. 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[2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. 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In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. 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In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. 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[2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. 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IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. 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Syst. 34, 6087–6101 (2021) Xie, S., Girshick, R., Dollár, P., Tu, Z., He, K.: Aggregated residual transformations for deep neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 1492–1500 (2017) Dosovitskiy et al. [2021] Dosovitskiy, A., Beyer, L., Kolesnikov, A., Weissenborn, D., Zhai, X., Unterthiner, T., Dehghani, M., Minderer, M., Heigold, G., Gelly, S., Uszkoreit, J., Houlsby, N.: An image is worth 16x16 words: Transformers for image recognition at scale. In: Int. Conf. Learn. Represent. (2021) Liu et al. [2021] Liu, Z., Lin, Y., Cao, Y., Hu, H., Wei, Y., Zhang, Z., Lin, S., Guo, B.: Swin transformer: Hierarchical vision transformer using shifted windows. In: Int. Conf. Comput. Vis., pp. 10012–10022 (2021) Caron et al. [2021] Caron, M., Touvron, H., Misra, I., Jégou, H., Mairal, J., Bojanowski, P., Joulin, A.: Emerging properties in self-supervised vision transformers. In: Int. Conf. Comput. Vis., pp. 9650–9660 (2021) Feng et al. 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[2023] Kerbl, B., Kopanas, G., Leimkühler, T., Drettakis, G.: 3d gaussian splatting for real-time radiance field rendering. ACM Trans. Graph. 42(4) (2023) Tang et al. [2023] Tang, J., Ren, J., Zhou, H., Liu, Z., Zeng, G.: Dreamgaussian: Generative gaussian splatting for efficient 3d content creation. arXiv preprint arXiv:2309.16653 (2023) Fridovich-Keil et al. [2022] Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. 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[2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Dosovitskiy, A., Beyer, L., Kolesnikov, A., Weissenborn, D., Zhai, X., Unterthiner, T., Dehghani, M., Minderer, M., Heigold, G., Gelly, S., Uszkoreit, J., Houlsby, N.: An image is worth 16x16 words: Transformers for image recognition at scale. In: Int. Conf. Learn. Represent. (2021) Liu et al. [2021] Liu, Z., Lin, Y., Cao, Y., Hu, H., Wei, Y., Zhang, Z., Lin, S., Guo, B.: Swin transformer: Hierarchical vision transformer using shifted windows. In: Int. Conf. Comput. Vis., pp. 10012–10022 (2021) Caron et al. [2021] Caron, M., Touvron, H., Misra, I., Jégou, H., Mairal, J., Bojanowski, P., Joulin, A.: Emerging properties in self-supervised vision transformers. In: Int. Conf. Comput. Vis., pp. 9650–9660 (2021) Feng et al. [2019] Feng, Y., You, H., Zhang, Z., Ji, R., Gao, Y.: Hypergraph neural networks. In: AAAI Conf. on Artificial Intell., vol. 33, pp. 3558–3565 (2019) Gao et al. [2022] Gao, Y., Feng, Y., Ji, S., Ji, R.: Hgnn+: General hypergraph neural networks. IEEE Trans. Pattern Anal. Mach. Intell. 45(3), 3181–3199 (2022) Liang et al. [2023] Liang, Y., Yang, X., Lin, J., Li, H., Xu, X., Chen, Y.: Luciddreamer: Towards high-fidelity text-to-3d generation via interval score matching. arXiv preprint arXiv:2311.11284 (2023) Radford et al. [2021] Radford, A., Kim, J.W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., Sastry, G., Askell, A., Mishkin, P., Clark, J., et al.: Learning transferable visual models from natural language supervision. In: Int. Conf. on Mach. Learn., pp. 8748–8763 (2021). PMLR Long et al. [2023] Long, X., Guo, Y.-C., Lin, C., Liu, Y., Dou, Z., Liu, L., Ma, Y., Zhang, S.-H., Habermann, M., Theobalt, C., et al.: Wonder3d: Single image to 3d using cross-domain diffusion. arXiv preprint arXiv:2310.15008 (2023) Mildenhall et al. [2020] Mildenhall, B., Srinivasan, P.P., Tancik, M., Barron, J.T., Ramamoorthi, R., Ng, R.: Nerf: Representing scenes as neural radiance fields for view synthesis. In: Eur. Conf. Comput. Vis. (2020) Wang et al. [2021] Wang, P., Liu, L., Liu, Y., Theobalt, C., Komura, T., Wang, W.: Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. Adv. Neural Inform. Process. Syst. (2021) Wang et al. [2023] Wang, H., Du, X., Li, J., Yeh, R.A., Shakhnarovich, G.: Score jacobian chaining: Lifting pretrained 2d diffusion models for 3d generation. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 12619–12629 (2023) Kerbl et al. [2023] Kerbl, B., Kopanas, G., Leimkühler, T., Drettakis, G.: 3d gaussian splatting for real-time radiance field rendering. ACM Trans. Graph. 42(4) (2023) Tang et al. 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[2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. 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[2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. 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[2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Caron, M., Touvron, H., Misra, I., Jégou, H., Mairal, J., Bojanowski, P., Joulin, A.: Emerging properties in self-supervised vision transformers. In: Int. Conf. Comput. Vis., pp. 9650–9660 (2021) Feng et al. [2019] Feng, Y., You, H., Zhang, Z., Ji, R., Gao, Y.: Hypergraph neural networks. In: AAAI Conf. on Artificial Intell., vol. 33, pp. 3558–3565 (2019) Gao et al. [2022] Gao, Y., Feng, Y., Ji, S., Ji, R.: Hgnn+: General hypergraph neural networks. IEEE Trans. Pattern Anal. Mach. Intell. 45(3), 3181–3199 (2022) Liang et al. [2023] Liang, Y., Yang, X., Lin, J., Li, H., Xu, X., Chen, Y.: Luciddreamer: Towards high-fidelity text-to-3d generation via interval score matching. arXiv preprint arXiv:2311.11284 (2023) Radford et al. [2021] Radford, A., Kim, J.W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., Sastry, G., Askell, A., Mishkin, P., Clark, J., et al.: Learning transferable visual models from natural language supervision. In: Int. Conf. on Mach. Learn., pp. 8748–8763 (2021). PMLR Long et al. [2023] Long, X., Guo, Y.-C., Lin, C., Liu, Y., Dou, Z., Liu, L., Ma, Y., Zhang, S.-H., Habermann, M., Theobalt, C., et al.: Wonder3d: Single image to 3d using cross-domain diffusion. arXiv preprint arXiv:2310.15008 (2023) Mildenhall et al. [2020] Mildenhall, B., Srinivasan, P.P., Tancik, M., Barron, J.T., Ramamoorthi, R., Ng, R.: Nerf: Representing scenes as neural radiance fields for view synthesis. In: Eur. Conf. Comput. Vis. (2020) Wang et al. [2021] Wang, P., Liu, L., Liu, Y., Theobalt, C., Komura, T., Wang, W.: Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. Adv. Neural Inform. Process. Syst. (2021) Wang et al. 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[2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Feng, Y., You, H., Zhang, Z., Ji, R., Gao, Y.: Hypergraph neural networks. In: AAAI Conf. on Artificial Intell., vol. 33, pp. 3558–3565 (2019) Gao et al. [2022] Gao, Y., Feng, Y., Ji, S., Ji, R.: Hgnn+: General hypergraph neural networks. IEEE Trans. Pattern Anal. Mach. Intell. 45(3), 3181–3199 (2022) Liang et al. [2023] Liang, Y., Yang, X., Lin, J., Li, H., Xu, X., Chen, Y.: Luciddreamer: Towards high-fidelity text-to-3d generation via interval score matching. arXiv preprint arXiv:2311.11284 (2023) Radford et al. [2021] Radford, A., Kim, J.W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., Sastry, G., Askell, A., Mishkin, P., Clark, J., et al.: Learning transferable visual models from natural language supervision. In: Int. Conf. on Mach. Learn., pp. 8748–8763 (2021). PMLR Long et al. [2023] Long, X., Guo, Y.-C., Lin, C., Liu, Y., Dou, Z., Liu, L., Ma, Y., Zhang, S.-H., Habermann, M., Theobalt, C., et al.: Wonder3d: Single image to 3d using cross-domain diffusion. arXiv preprint arXiv:2310.15008 (2023) Mildenhall et al. [2020] Mildenhall, B., Srinivasan, P.P., Tancik, M., Barron, J.T., Ramamoorthi, R., Ng, R.: Nerf: Representing scenes as neural radiance fields for view synthesis. In: Eur. Conf. Comput. Vis. (2020) Wang et al. [2021] Wang, P., Liu, L., Liu, Y., Theobalt, C., Komura, T., Wang, W.: Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. Adv. Neural Inform. Process. Syst. (2021) Wang et al. [2023] Wang, H., Du, X., Li, J., Yeh, R.A., Shakhnarovich, G.: Score jacobian chaining: Lifting pretrained 2d diffusion models for 3d generation. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 12619–12629 (2023) Kerbl et al. 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Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. 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Syst. 34, 6087–6101 (2021) Wang, P., Liu, L., Liu, Y., Theobalt, C., Komura, T., Wang, W.: Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. Adv. Neural Inform. Process. Syst. (2021) Wang et al. [2023] Wang, H., Du, X., Li, J., Yeh, R.A., Shakhnarovich, G.: Score jacobian chaining: Lifting pretrained 2d diffusion models for 3d generation. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 12619–12629 (2023) Kerbl et al. [2023] Kerbl, B., Kopanas, G., Leimkühler, T., Drettakis, G.: 3d gaussian splatting for real-time radiance field rendering. ACM Trans. Graph. 42(4) (2023) Tang et al. [2023] Tang, J., Ren, J., Zhou, H., Liu, Z., Zeng, G.: Dreamgaussian: Generative gaussian splatting for efficient 3d content creation. arXiv preprint arXiv:2309.16653 (2023) Fridovich-Keil et al. [2022] Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. 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[1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Kerbl, B., Kopanas, G., Leimkühler, T., Drettakis, G.: 3d gaussian splatting for real-time radiance field rendering. ACM Trans. Graph. 42(4) (2023) Tang et al. [2023] Tang, J., Ren, J., Zhou, H., Liu, Z., Zeng, G.: Dreamgaussian: Generative gaussian splatting for efficient 3d content creation. arXiv preprint arXiv:2309.16653 (2023) Fridovich-Keil et al. [2022] Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. 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[2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Tang, J., Ren, J., Zhou, H., Liu, Z., Zeng, G.: Dreamgaussian: Generative gaussian splatting for efficient 3d content creation. arXiv preprint arXiv:2309.16653 (2023) Fridovich-Keil et al. [2022] Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. 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[1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. 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[2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. 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Syst. 34, 6087–6101 (2021) Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. 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[2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. 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Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. 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Syst. 34, 6087–6101 (2021) Xie, S., Girshick, R., Dollár, P., Tu, Z., He, K.: Aggregated residual transformations for deep neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 1492–1500 (2017) Dosovitskiy et al. [2021] Dosovitskiy, A., Beyer, L., Kolesnikov, A., Weissenborn, D., Zhai, X., Unterthiner, T., Dehghani, M., Minderer, M., Heigold, G., Gelly, S., Uszkoreit, J., Houlsby, N.: An image is worth 16x16 words: Transformers for image recognition at scale. In: Int. Conf. Learn. Represent. (2021) Liu et al. [2021] Liu, Z., Lin, Y., Cao, Y., Hu, H., Wei, Y., Zhang, Z., Lin, S., Guo, B.: Swin transformer: Hierarchical vision transformer using shifted windows. In: Int. Conf. Comput. Vis., pp. 10012–10022 (2021) Caron et al. [2021] Caron, M., Touvron, H., Misra, I., Jégou, H., Mairal, J., Bojanowski, P., Joulin, A.: Emerging properties in self-supervised vision transformers. In: Int. Conf. Comput. Vis., pp. 9650–9660 (2021) Feng et al. 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[2023] Kerbl, B., Kopanas, G., Leimkühler, T., Drettakis, G.: 3d gaussian splatting for real-time radiance field rendering. ACM Trans. Graph. 42(4) (2023) Tang et al. [2023] Tang, J., Ren, J., Zhou, H., Liu, Z., Zeng, G.: Dreamgaussian: Generative gaussian splatting for efficient 3d content creation. arXiv preprint arXiv:2309.16653 (2023) Fridovich-Keil et al. [2022] Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. 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[2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Dosovitskiy, A., Beyer, L., Kolesnikov, A., Weissenborn, D., Zhai, X., Unterthiner, T., Dehghani, M., Minderer, M., Heigold, G., Gelly, S., Uszkoreit, J., Houlsby, N.: An image is worth 16x16 words: Transformers for image recognition at scale. In: Int. Conf. Learn. Represent. (2021) Liu et al. [2021] Liu, Z., Lin, Y., Cao, Y., Hu, H., Wei, Y., Zhang, Z., Lin, S., Guo, B.: Swin transformer: Hierarchical vision transformer using shifted windows. In: Int. Conf. Comput. Vis., pp. 10012–10022 (2021) Caron et al. [2021] Caron, M., Touvron, H., Misra, I., Jégou, H., Mairal, J., Bojanowski, P., Joulin, A.: Emerging properties in self-supervised vision transformers. In: Int. Conf. Comput. Vis., pp. 9650–9660 (2021) Feng et al. [2019] Feng, Y., You, H., Zhang, Z., Ji, R., Gao, Y.: Hypergraph neural networks. In: AAAI Conf. on Artificial Intell., vol. 33, pp. 3558–3565 (2019) Gao et al. 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[2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Caron, M., Touvron, H., Misra, I., Jégou, H., Mairal, J., Bojanowski, P., Joulin, A.: Emerging properties in self-supervised vision transformers. In: Int. Conf. Comput. Vis., pp. 9650–9660 (2021) Feng et al. [2019] Feng, Y., You, H., Zhang, Z., Ji, R., Gao, Y.: Hypergraph neural networks. In: AAAI Conf. on Artificial Intell., vol. 33, pp. 3558–3565 (2019) Gao et al. [2022] Gao, Y., Feng, Y., Ji, S., Ji, R.: Hgnn+: General hypergraph neural networks. IEEE Trans. Pattern Anal. Mach. Intell. 45(3), 3181–3199 (2022) Liang et al. [2023] Liang, Y., Yang, X., Lin, J., Li, H., Xu, X., Chen, Y.: Luciddreamer: Towards high-fidelity text-to-3d generation via interval score matching. arXiv preprint arXiv:2311.11284 (2023) Radford et al. 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[2023] Wang, H., Du, X., Li, J., Yeh, R.A., Shakhnarovich, G.: Score jacobian chaining: Lifting pretrained 2d diffusion models for 3d generation. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 12619–12629 (2023) Kerbl et al. [2023] Kerbl, B., Kopanas, G., Leimkühler, T., Drettakis, G.: 3d gaussian splatting for real-time radiance field rendering. ACM Trans. Graph. 42(4) (2023) Tang et al. [2023] Tang, J., Ren, J., Zhou, H., Liu, Z., Zeng, G.: Dreamgaussian: Generative gaussian splatting for efficient 3d content creation. arXiv preprint arXiv:2309.16653 (2023) Fridovich-Keil et al. [2022] Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. 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[2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. 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Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Feng, Y., You, H., Zhang, Z., Ji, R., Gao, Y.: Hypergraph neural networks. In: AAAI Conf. on Artificial Intell., vol. 33, pp. 3558–3565 (2019) Gao et al. [2022] Gao, Y., Feng, Y., Ji, S., Ji, R.: Hgnn+: General hypergraph neural networks. IEEE Trans. Pattern Anal. Mach. Intell. 45(3), 3181–3199 (2022) Liang et al. [2023] Liang, Y., Yang, X., Lin, J., Li, H., Xu, X., Chen, Y.: Luciddreamer: Towards high-fidelity text-to-3d generation via interval score matching. arXiv preprint arXiv:2311.11284 (2023) Radford et al. [2021] Radford, A., Kim, J.W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., Sastry, G., Askell, A., Mishkin, P., Clark, J., et al.: Learning transferable visual models from natural language supervision. In: Int. Conf. on Mach. Learn., pp. 8748–8763 (2021). PMLR Long et al. [2023] Long, X., Guo, Y.-C., Lin, C., Liu, Y., Dou, Z., Liu, L., Ma, Y., Zhang, S.-H., Habermann, M., Theobalt, C., et al.: Wonder3d: Single image to 3d using cross-domain diffusion. arXiv preprint arXiv:2310.15008 (2023) Mildenhall et al. [2020] Mildenhall, B., Srinivasan, P.P., Tancik, M., Barron, J.T., Ramamoorthi, R., Ng, R.: Nerf: Representing scenes as neural radiance fields for view synthesis. In: Eur. Conf. Comput. Vis. (2020) Wang et al. [2021] Wang, P., Liu, L., Liu, Y., Theobalt, C., Komura, T., Wang, W.: Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. Adv. Neural Inform. Process. Syst. (2021) Wang et al. [2023] Wang, H., Du, X., Li, J., Yeh, R.A., Shakhnarovich, G.: Score jacobian chaining: Lifting pretrained 2d diffusion models for 3d generation. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 12619–12629 (2023) Kerbl et al. [2023] Kerbl, B., Kopanas, G., Leimkühler, T., Drettakis, G.: 3d gaussian splatting for real-time radiance field rendering. ACM Trans. Graph. 42(4) (2023) Tang et al. [2023] Tang, J., Ren, J., Zhou, H., Liu, Z., Zeng, G.: Dreamgaussian: Generative gaussian splatting for efficient 3d content creation. arXiv preprint arXiv:2309.16653 (2023) Fridovich-Keil et al. [2022] Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. 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[2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Gao, Y., Feng, Y., Ji, S., Ji, R.: Hgnn+: General hypergraph neural networks. IEEE Trans. Pattern Anal. Mach. Intell. 45(3), 3181–3199 (2022) Liang et al. [2023] Liang, Y., Yang, X., Lin, J., Li, H., Xu, X., Chen, Y.: Luciddreamer: Towards high-fidelity text-to-3d generation via interval score matching. arXiv preprint arXiv:2311.11284 (2023) Radford et al. [2021] Radford, A., Kim, J.W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., Sastry, G., Askell, A., Mishkin, P., Clark, J., et al.: Learning transferable visual models from natural language supervision. In: Int. Conf. on Mach. Learn., pp. 8748–8763 (2021). PMLR Long et al. [2023] Long, X., Guo, Y.-C., Lin, C., Liu, Y., Dou, Z., Liu, L., Ma, Y., Zhang, S.-H., Habermann, M., Theobalt, C., et al.: Wonder3d: Single image to 3d using cross-domain diffusion. arXiv preprint arXiv:2310.15008 (2023) Mildenhall et al. [2020] Mildenhall, B., Srinivasan, P.P., Tancik, M., Barron, J.T., Ramamoorthi, R., Ng, R.: Nerf: Representing scenes as neural radiance fields for view synthesis. In: Eur. Conf. Comput. Vis. 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Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Liang, Y., Yang, X., Lin, J., Li, H., Xu, X., Chen, Y.: Luciddreamer: Towards high-fidelity text-to-3d generation via interval score matching. arXiv preprint arXiv:2311.11284 (2023) Radford et al. [2021] Radford, A., Kim, J.W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., Sastry, G., Askell, A., Mishkin, P., Clark, J., et al.: Learning transferable visual models from natural language supervision. In: Int. Conf. on Mach. Learn., pp. 8748–8763 (2021). PMLR Long et al. [2023] Long, X., Guo, Y.-C., Lin, C., Liu, Y., Dou, Z., Liu, L., Ma, Y., Zhang, S.-H., Habermann, M., Theobalt, C., et al.: Wonder3d: Single image to 3d using cross-domain diffusion. arXiv preprint arXiv:2310.15008 (2023) Mildenhall et al. [2020] Mildenhall, B., Srinivasan, P.P., Tancik, M., Barron, J.T., Ramamoorthi, R., Ng, R.: Nerf: Representing scenes as neural radiance fields for view synthesis. In: Eur. Conf. Comput. Vis. (2020) Wang et al. [2021] Wang, P., Liu, L., Liu, Y., Theobalt, C., Komura, T., Wang, W.: Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. Adv. Neural Inform. Process. Syst. (2021) Wang et al. [2023] Wang, H., Du, X., Li, J., Yeh, R.A., Shakhnarovich, G.: Score jacobian chaining: Lifting pretrained 2d diffusion models for 3d generation. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 12619–12629 (2023) Kerbl et al. [2023] Kerbl, B., Kopanas, G., Leimkühler, T., Drettakis, G.: 3d gaussian splatting for real-time radiance field rendering. ACM Trans. Graph. 42(4) (2023) Tang et al. [2023] Tang, J., Ren, J., Zhou, H., Liu, Z., Zeng, G.: Dreamgaussian: Generative gaussian splatting for efficient 3d content creation. arXiv preprint arXiv:2309.16653 (2023) Fridovich-Keil et al. [2022] Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. 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Syst. 34, 6087–6101 (2021) Wang, P., Liu, L., Liu, Y., Theobalt, C., Komura, T., Wang, W.: Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. Adv. Neural Inform. Process. Syst. (2021) Wang et al. [2023] Wang, H., Du, X., Li, J., Yeh, R.A., Shakhnarovich, G.: Score jacobian chaining: Lifting pretrained 2d diffusion models for 3d generation. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 12619–12629 (2023) Kerbl et al. [2023] Kerbl, B., Kopanas, G., Leimkühler, T., Drettakis, G.: 3d gaussian splatting for real-time radiance field rendering. ACM Trans. Graph. 42(4) (2023) Tang et al. [2023] Tang, J., Ren, J., Zhou, H., Liu, Z., Zeng, G.: Dreamgaussian: Generative gaussian splatting for efficient 3d content creation. arXiv preprint arXiv:2309.16653 (2023) Fridovich-Keil et al. [2022] Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. 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Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. 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[1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. 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[2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. 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[2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. 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[1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. 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Syst. 34, 6087–6101 (2021) Dosovitskiy, A., Beyer, L., Kolesnikov, A., Weissenborn, D., Zhai, X., Unterthiner, T., Dehghani, M., Minderer, M., Heigold, G., Gelly, S., Uszkoreit, J., Houlsby, N.: An image is worth 16x16 words: Transformers for image recognition at scale. In: Int. Conf. Learn. Represent. (2021) Liu et al. [2021] Liu, Z., Lin, Y., Cao, Y., Hu, H., Wei, Y., Zhang, Z., Lin, S., Guo, B.: Swin transformer: Hierarchical vision transformer using shifted windows. In: Int. Conf. Comput. Vis., pp. 10012–10022 (2021) Caron et al. [2021] Caron, M., Touvron, H., Misra, I., Jégou, H., Mairal, J., Bojanowski, P., Joulin, A.: Emerging properties in self-supervised vision transformers. In: Int. Conf. Comput. Vis., pp. 9650–9660 (2021) Feng et al. [2019] Feng, Y., You, H., Zhang, Z., Ji, R., Gao, Y.: Hypergraph neural networks. In: AAAI Conf. on Artificial Intell., vol. 33, pp. 3558–3565 (2019) Gao et al. 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[2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Caron, M., Touvron, H., Misra, I., Jégou, H., Mairal, J., Bojanowski, P., Joulin, A.: Emerging properties in self-supervised vision transformers. In: Int. Conf. Comput. Vis., pp. 9650–9660 (2021) Feng et al. [2019] Feng, Y., You, H., Zhang, Z., Ji, R., Gao, Y.: Hypergraph neural networks. In: AAAI Conf. on Artificial Intell., vol. 33, pp. 3558–3565 (2019) Gao et al. [2022] Gao, Y., Feng, Y., Ji, S., Ji, R.: Hgnn+: General hypergraph neural networks. IEEE Trans. Pattern Anal. Mach. Intell. 45(3), 3181–3199 (2022) Liang et al. [2023] Liang, Y., Yang, X., Lin, J., Li, H., Xu, X., Chen, Y.: Luciddreamer: Towards high-fidelity text-to-3d generation via interval score matching. arXiv preprint arXiv:2311.11284 (2023) Radford et al. 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[2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Feng, Y., You, H., Zhang, Z., Ji, R., Gao, Y.: Hypergraph neural networks. In: AAAI Conf. on Artificial Intell., vol. 33, pp. 3558–3565 (2019) Gao et al. [2022] Gao, Y., Feng, Y., Ji, S., Ji, R.: Hgnn+: General hypergraph neural networks. IEEE Trans. Pattern Anal. Mach. Intell. 45(3), 3181–3199 (2022) Liang et al. [2023] Liang, Y., Yang, X., Lin, J., Li, H., Xu, X., Chen, Y.: Luciddreamer: Towards high-fidelity text-to-3d generation via interval score matching. arXiv preprint arXiv:2311.11284 (2023) Radford et al. [2021] Radford, A., Kim, J.W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., Sastry, G., Askell, A., Mishkin, P., Clark, J., et al.: Learning transferable visual models from natural language supervision. In: Int. Conf. on Mach. Learn., pp. 8748–8763 (2021). PMLR Long et al. [2023] Long, X., Guo, Y.-C., Lin, C., Liu, Y., Dou, Z., Liu, L., Ma, Y., Zhang, S.-H., Habermann, M., Theobalt, C., et al.: Wonder3d: Single image to 3d using cross-domain diffusion. arXiv preprint arXiv:2310.15008 (2023) Mildenhall et al. [2020] Mildenhall, B., Srinivasan, P.P., Tancik, M., Barron, J.T., Ramamoorthi, R., Ng, R.: Nerf: Representing scenes as neural radiance fields for view synthesis. In: Eur. Conf. Comput. Vis. (2020) Wang et al. [2021] Wang, P., Liu, L., Liu, Y., Theobalt, C., Komura, T., Wang, W.: Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. Adv. Neural Inform. Process. Syst. (2021) Wang et al. [2023] Wang, H., Du, X., Li, J., Yeh, R.A., Shakhnarovich, G.: Score jacobian chaining: Lifting pretrained 2d diffusion models for 3d generation. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 12619–12629 (2023) Kerbl et al. [2023] Kerbl, B., Kopanas, G., Leimkühler, T., Drettakis, G.: 3d gaussian splatting for real-time radiance field rendering. ACM Trans. Graph. 42(4) (2023) Tang et al. [2023] Tang, J., Ren, J., Zhou, H., Liu, Z., Zeng, G.: Dreamgaussian: Generative gaussian splatting for efficient 3d content creation. arXiv preprint arXiv:2309.16653 (2023) Fridovich-Keil et al. [2022] Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. 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[2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. 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[2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. 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[2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. 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[2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. 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Syst. 34, 6087–6101 (2021) Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. 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In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. 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[2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. 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[2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Caron, M., Touvron, H., Misra, I., Jégou, H., Mairal, J., Bojanowski, P., Joulin, A.: Emerging properties in self-supervised vision transformers. In: Int. Conf. Comput. Vis., pp. 9650–9660 (2021) Feng et al. [2019] Feng, Y., You, H., Zhang, Z., Ji, R., Gao, Y.: Hypergraph neural networks. In: AAAI Conf. on Artificial Intell., vol. 33, pp. 3558–3565 (2019) Gao et al. [2022] Gao, Y., Feng, Y., Ji, S., Ji, R.: Hgnn+: General hypergraph neural networks. IEEE Trans. Pattern Anal. Mach. Intell. 45(3), 3181–3199 (2022) Liang et al. [2023] Liang, Y., Yang, X., Lin, J., Li, H., Xu, X., Chen, Y.: Luciddreamer: Towards high-fidelity text-to-3d generation via interval score matching. arXiv preprint arXiv:2311.11284 (2023) Radford et al. 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[2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Feng, Y., You, H., Zhang, Z., Ji, R., Gao, Y.: Hypergraph neural networks. In: AAAI Conf. on Artificial Intell., vol. 33, pp. 3558–3565 (2019) Gao et al. [2022] Gao, Y., Feng, Y., Ji, S., Ji, R.: Hgnn+: General hypergraph neural networks. IEEE Trans. Pattern Anal. Mach. Intell. 45(3), 3181–3199 (2022) Liang et al. [2023] Liang, Y., Yang, X., Lin, J., Li, H., Xu, X., Chen, Y.: Luciddreamer: Towards high-fidelity text-to-3d generation via interval score matching. arXiv preprint arXiv:2311.11284 (2023) Radford et al. [2021] Radford, A., Kim, J.W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., Sastry, G., Askell, A., Mishkin, P., Clark, J., et al.: Learning transferable visual models from natural language supervision. In: Int. Conf. on Mach. Learn., pp. 8748–8763 (2021). 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[1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. 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[2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. 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[2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. 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[2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. 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[2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. 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[2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. 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Syst. 34, 6087–6101 (2021) Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. 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[2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. 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[2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. 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[2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. 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[2023] Long, X., Guo, Y.-C., Lin, C., Liu, Y., Dou, Z., Liu, L., Ma, Y., Zhang, S.-H., Habermann, M., Theobalt, C., et al.: Wonder3d: Single image to 3d using cross-domain diffusion. arXiv preprint arXiv:2310.15008 (2023) Mildenhall et al. [2020] Mildenhall, B., Srinivasan, P.P., Tancik, M., Barron, J.T., Ramamoorthi, R., Ng, R.: Nerf: Representing scenes as neural radiance fields for view synthesis. In: Eur. Conf. Comput. Vis. (2020) Wang et al. [2021] Wang, P., Liu, L., Liu, Y., Theobalt, C., Komura, T., Wang, W.: Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. Adv. Neural Inform. Process. Syst. (2021) Wang et al. [2023] Wang, H., Du, X., Li, J., Yeh, R.A., Shakhnarovich, G.: Score jacobian chaining: Lifting pretrained 2d diffusion models for 3d generation. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 12619–12629 (2023) Kerbl et al. [2023] Kerbl, B., Kopanas, G., Leimkühler, T., Drettakis, G.: 3d gaussian splatting for real-time radiance field rendering. ACM Trans. Graph. 42(4) (2023) Tang et al. [2023] Tang, J., Ren, J., Zhou, H., Liu, Z., Zeng, G.: Dreamgaussian: Generative gaussian splatting for efficient 3d content creation. arXiv preprint arXiv:2309.16653 (2023) Fridovich-Keil et al. [2022] Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. 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[2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. 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Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. 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[2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. 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Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. 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Syst. 34, 6087–6101 (2021) Dosovitskiy, A., Beyer, L., Kolesnikov, A., Weissenborn, D., Zhai, X., Unterthiner, T., Dehghani, M., Minderer, M., Heigold, G., Gelly, S., Uszkoreit, J., Houlsby, N.: An image is worth 16x16 words: Transformers for image recognition at scale. In: Int. Conf. Learn. Represent. (2021) Liu et al. [2021] Liu, Z., Lin, Y., Cao, Y., Hu, H., Wei, Y., Zhang, Z., Lin, S., Guo, B.: Swin transformer: Hierarchical vision transformer using shifted windows. In: Int. Conf. Comput. Vis., pp. 10012–10022 (2021) Caron et al. [2021] Caron, M., Touvron, H., Misra, I., Jégou, H., Mairal, J., Bojanowski, P., Joulin, A.: Emerging properties in self-supervised vision transformers. In: Int. Conf. Comput. Vis., pp. 9650–9660 (2021) Feng et al. [2019] Feng, Y., You, H., Zhang, Z., Ji, R., Gao, Y.: Hypergraph neural networks. In: AAAI Conf. on Artificial Intell., vol. 33, pp. 3558–3565 (2019) Gao et al. 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[2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Caron, M., Touvron, H., Misra, I., Jégou, H., Mairal, J., Bojanowski, P., Joulin, A.: Emerging properties in self-supervised vision transformers. In: Int. Conf. Comput. Vis., pp. 9650–9660 (2021) Feng et al. [2019] Feng, Y., You, H., Zhang, Z., Ji, R., Gao, Y.: Hypergraph neural networks. In: AAAI Conf. on Artificial Intell., vol. 33, pp. 3558–3565 (2019) Gao et al. [2022] Gao, Y., Feng, Y., Ji, S., Ji, R.: Hgnn+: General hypergraph neural networks. IEEE Trans. Pattern Anal. Mach. Intell. 45(3), 3181–3199 (2022) Liang et al. [2023] Liang, Y., Yang, X., Lin, J., Li, H., Xu, X., Chen, Y.: Luciddreamer: Towards high-fidelity text-to-3d generation via interval score matching. arXiv preprint arXiv:2311.11284 (2023) Radford et al. 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[2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Feng, Y., You, H., Zhang, Z., Ji, R., Gao, Y.: Hypergraph neural networks. In: AAAI Conf. on Artificial Intell., vol. 33, pp. 3558–3565 (2019) Gao et al. [2022] Gao, Y., Feng, Y., Ji, S., Ji, R.: Hgnn+: General hypergraph neural networks. IEEE Trans. Pattern Anal. Mach. Intell. 45(3), 3181–3199 (2022) Liang et al. [2023] Liang, Y., Yang, X., Lin, J., Li, H., Xu, X., Chen, Y.: Luciddreamer: Towards high-fidelity text-to-3d generation via interval score matching. arXiv preprint arXiv:2311.11284 (2023) Radford et al. [2021] Radford, A., Kim, J.W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., Sastry, G., Askell, A., Mishkin, P., Clark, J., et al.: Learning transferable visual models from natural language supervision. In: Int. Conf. on Mach. Learn., pp. 8748–8763 (2021). PMLR Long et al. [2023] Long, X., Guo, Y.-C., Lin, C., Liu, Y., Dou, Z., Liu, L., Ma, Y., Zhang, S.-H., Habermann, M., Theobalt, C., et al.: Wonder3d: Single image to 3d using cross-domain diffusion. arXiv preprint arXiv:2310.15008 (2023) Mildenhall et al. [2020] Mildenhall, B., Srinivasan, P.P., Tancik, M., Barron, J.T., Ramamoorthi, R., Ng, R.: Nerf: Representing scenes as neural radiance fields for view synthesis. In: Eur. Conf. Comput. Vis. (2020) Wang et al. [2021] Wang, P., Liu, L., Liu, Y., Theobalt, C., Komura, T., Wang, W.: Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. Adv. Neural Inform. Process. Syst. (2021) Wang et al. [2023] Wang, H., Du, X., Li, J., Yeh, R.A., Shakhnarovich, G.: Score jacobian chaining: Lifting pretrained 2d diffusion models for 3d generation. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 12619–12629 (2023) Kerbl et al. [2023] Kerbl, B., Kopanas, G., Leimkühler, T., Drettakis, G.: 3d gaussian splatting for real-time radiance field rendering. ACM Trans. Graph. 42(4) (2023) Tang et al. [2023] Tang, J., Ren, J., Zhou, H., Liu, Z., Zeng, G.: Dreamgaussian: Generative gaussian splatting for efficient 3d content creation. arXiv preprint arXiv:2309.16653 (2023) Fridovich-Keil et al. [2022] Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. 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[2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. 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[2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. 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[2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. 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[2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. 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Syst. 34, 6087–6101 (2021) Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. 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In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. 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[2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. 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[2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 770–778 (2016) Xie et al. [2017] Xie, S., Girshick, R., Dollár, P., Tu, Z., He, K.: Aggregated residual transformations for deep neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 1492–1500 (2017) Dosovitskiy et al. [2021] Dosovitskiy, A., Beyer, L., Kolesnikov, A., Weissenborn, D., Zhai, X., Unterthiner, T., Dehghani, M., Minderer, M., Heigold, G., Gelly, S., Uszkoreit, J., Houlsby, N.: An image is worth 16x16 words: Transformers for image recognition at scale. In: Int. Conf. Learn. Represent. (2021) Liu et al. [2021] Liu, Z., Lin, Y., Cao, Y., Hu, H., Wei, Y., Zhang, Z., Lin, S., Guo, B.: Swin transformer: Hierarchical vision transformer using shifted windows. In: Int. Conf. Comput. Vis., pp. 10012–10022 (2021) Caron et al. [2021] Caron, M., Touvron, H., Misra, I., Jégou, H., Mairal, J., Bojanowski, P., Joulin, A.: Emerging properties in self-supervised vision transformers. In: Int. Conf. Comput. 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[2023] Long, X., Guo, Y.-C., Lin, C., Liu, Y., Dou, Z., Liu, L., Ma, Y., Zhang, S.-H., Habermann, M., Theobalt, C., et al.: Wonder3d: Single image to 3d using cross-domain diffusion. arXiv preprint arXiv:2310.15008 (2023) Mildenhall et al. [2020] Mildenhall, B., Srinivasan, P.P., Tancik, M., Barron, J.T., Ramamoorthi, R., Ng, R.: Nerf: Representing scenes as neural radiance fields for view synthesis. In: Eur. Conf. Comput. Vis. (2020) Wang et al. [2021] Wang, P., Liu, L., Liu, Y., Theobalt, C., Komura, T., Wang, W.: Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. Adv. Neural Inform. Process. Syst. (2021) Wang et al. [2023] Wang, H., Du, X., Li, J., Yeh, R.A., Shakhnarovich, G.: Score jacobian chaining: Lifting pretrained 2d diffusion models for 3d generation. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 12619–12629 (2023) Kerbl et al. [2023] Kerbl, B., Kopanas, G., Leimkühler, T., Drettakis, G.: 3d gaussian splatting for real-time radiance field rendering. ACM Trans. Graph. 42(4) (2023) Tang et al. [2023] Tang, J., Ren, J., Zhou, H., Liu, Z., Zeng, G.: Dreamgaussian: Generative gaussian splatting for efficient 3d content creation. arXiv preprint arXiv:2309.16653 (2023) Fridovich-Keil et al. [2022] Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. 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[2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. 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[2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. 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Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. 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Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. 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Syst. 34, 6087–6101 (2021) Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. 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[2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Caron, M., Touvron, H., Misra, I., Jégou, H., Mairal, J., Bojanowski, P., Joulin, A.: Emerging properties in self-supervised vision transformers. In: Int. Conf. Comput. Vis., pp. 9650–9660 (2021) Feng et al. [2019] Feng, Y., You, H., Zhang, Z., Ji, R., Gao, Y.: Hypergraph neural networks. In: AAAI Conf. on Artificial Intell., vol. 33, pp. 3558–3565 (2019) Gao et al. [2022] Gao, Y., Feng, Y., Ji, S., Ji, R.: Hgnn+: General hypergraph neural networks. IEEE Trans. Pattern Anal. Mach. Intell. 45(3), 3181–3199 (2022) Liang et al. [2023] Liang, Y., Yang, X., Lin, J., Li, H., Xu, X., Chen, Y.: Luciddreamer: Towards high-fidelity text-to-3d generation via interval score matching. arXiv preprint arXiv:2311.11284 (2023) Radford et al. 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[2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Feng, Y., You, H., Zhang, Z., Ji, R., Gao, Y.: Hypergraph neural networks. In: AAAI Conf. on Artificial Intell., vol. 33, pp. 3558–3565 (2019) Gao et al. [2022] Gao, Y., Feng, Y., Ji, S., Ji, R.: Hgnn+: General hypergraph neural networks. IEEE Trans. Pattern Anal. Mach. Intell. 45(3), 3181–3199 (2022) Liang et al. [2023] Liang, Y., Yang, X., Lin, J., Li, H., Xu, X., Chen, Y.: Luciddreamer: Towards high-fidelity text-to-3d generation via interval score matching. arXiv preprint arXiv:2311.11284 (2023) Radford et al. [2021] Radford, A., Kim, J.W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., Sastry, G., Askell, A., Mishkin, P., Clark, J., et al.: Learning transferable visual models from natural language supervision. In: Int. Conf. on Mach. Learn., pp. 8748–8763 (2021). 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[1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. 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[2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. 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[2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. 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[2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. 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[2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. 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[2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. 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Syst. 34, 6087–6101 (2021) Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. 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[2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. 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[2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. 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Syst. 34, 6087–6101 (2021) Dosovitskiy, A., Beyer, L., Kolesnikov, A., Weissenborn, D., Zhai, X., Unterthiner, T., Dehghani, M., Minderer, M., Heigold, G., Gelly, S., Uszkoreit, J., Houlsby, N.: An image is worth 16x16 words: Transformers for image recognition at scale. In: Int. Conf. Learn. Represent. (2021) Liu et al. [2021] Liu, Z., Lin, Y., Cao, Y., Hu, H., Wei, Y., Zhang, Z., Lin, S., Guo, B.: Swin transformer: Hierarchical vision transformer using shifted windows. In: Int. Conf. Comput. Vis., pp. 10012–10022 (2021) Caron et al. [2021] Caron, M., Touvron, H., Misra, I., Jégou, H., Mairal, J., Bojanowski, P., Joulin, A.: Emerging properties in self-supervised vision transformers. In: Int. Conf. Comput. Vis., pp. 9650–9660 (2021) Feng et al. [2019] Feng, Y., You, H., Zhang, Z., Ji, R., Gao, Y.: Hypergraph neural networks. In: AAAI Conf. on Artificial Intell., vol. 33, pp. 3558–3565 (2019) Gao et al. 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[2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Caron, M., Touvron, H., Misra, I., Jégou, H., Mairal, J., Bojanowski, P., Joulin, A.: Emerging properties in self-supervised vision transformers. In: Int. Conf. Comput. Vis., pp. 9650–9660 (2021) Feng et al. [2019] Feng, Y., You, H., Zhang, Z., Ji, R., Gao, Y.: Hypergraph neural networks. In: AAAI Conf. on Artificial Intell., vol. 33, pp. 3558–3565 (2019) Gao et al. [2022] Gao, Y., Feng, Y., Ji, S., Ji, R.: Hgnn+: General hypergraph neural networks. IEEE Trans. Pattern Anal. Mach. Intell. 45(3), 3181–3199 (2022) Liang et al. [2023] Liang, Y., Yang, X., Lin, J., Li, H., Xu, X., Chen, Y.: Luciddreamer: Towards high-fidelity text-to-3d generation via interval score matching. arXiv preprint arXiv:2311.11284 (2023) Radford et al. 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[2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Feng, Y., You, H., Zhang, Z., Ji, R., Gao, Y.: Hypergraph neural networks. In: AAAI Conf. on Artificial Intell., vol. 33, pp. 3558–3565 (2019) Gao et al. [2022] Gao, Y., Feng, Y., Ji, S., Ji, R.: Hgnn+: General hypergraph neural networks. IEEE Trans. Pattern Anal. Mach. Intell. 45(3), 3181–3199 (2022) Liang et al. [2023] Liang, Y., Yang, X., Lin, J., Li, H., Xu, X., Chen, Y.: Luciddreamer: Towards high-fidelity text-to-3d generation via interval score matching. arXiv preprint arXiv:2311.11284 (2023) Radford et al. [2021] Radford, A., Kim, J.W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., Sastry, G., Askell, A., Mishkin, P., Clark, J., et al.: Learning transferable visual models from natural language supervision. In: Int. Conf. on Mach. Learn., pp. 8748–8763 (2021). PMLR Long et al. [2023] Long, X., Guo, Y.-C., Lin, C., Liu, Y., Dou, Z., Liu, L., Ma, Y., Zhang, S.-H., Habermann, M., Theobalt, C., et al.: Wonder3d: Single image to 3d using cross-domain diffusion. arXiv preprint arXiv:2310.15008 (2023) Mildenhall et al. [2020] Mildenhall, B., Srinivasan, P.P., Tancik, M., Barron, J.T., Ramamoorthi, R., Ng, R.: Nerf: Representing scenes as neural radiance fields for view synthesis. In: Eur. Conf. Comput. Vis. (2020) Wang et al. [2021] Wang, P., Liu, L., Liu, Y., Theobalt, C., Komura, T., Wang, W.: Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. Adv. Neural Inform. Process. Syst. (2021) Wang et al. [2023] Wang, H., Du, X., Li, J., Yeh, R.A., Shakhnarovich, G.: Score jacobian chaining: Lifting pretrained 2d diffusion models for 3d generation. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 12619–12629 (2023) Kerbl et al. [2023] Kerbl, B., Kopanas, G., Leimkühler, T., Drettakis, G.: 3d gaussian splatting for real-time radiance field rendering. ACM Trans. Graph. 42(4) (2023) Tang et al. [2023] Tang, J., Ren, J., Zhou, H., Liu, Z., Zeng, G.: Dreamgaussian: Generative gaussian splatting for efficient 3d content creation. arXiv preprint arXiv:2309.16653 (2023) Fridovich-Keil et al. [2022] Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. 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[2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. 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[2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. 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[2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. 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[2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. 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Syst. 34, 6087–6101 (2021) Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. 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In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. 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[2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. 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[2023] Kerbl, B., Kopanas, G., Leimkühler, T., Drettakis, G.: 3d gaussian splatting for real-time radiance field rendering. ACM Trans. Graph. 42(4) (2023) Tang et al. [2023] Tang, J., Ren, J., Zhou, H., Liu, Z., Zeng, G.: Dreamgaussian: Generative gaussian splatting for efficient 3d content creation. arXiv preprint arXiv:2309.16653 (2023) Fridovich-Keil et al. [2022] Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. 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[2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Xie, S., Girshick, R., Dollár, P., Tu, Z., He, K.: Aggregated residual transformations for deep neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 1492–1500 (2017) Dosovitskiy et al. [2021] Dosovitskiy, A., Beyer, L., Kolesnikov, A., Weissenborn, D., Zhai, X., Unterthiner, T., Dehghani, M., Minderer, M., Heigold, G., Gelly, S., Uszkoreit, J., Houlsby, N.: An image is worth 16x16 words: Transformers for image recognition at scale. In: Int. Conf. Learn. Represent. (2021) Liu et al. [2021] Liu, Z., Lin, Y., Cao, Y., Hu, H., Wei, Y., Zhang, Z., Lin, S., Guo, B.: Swin transformer: Hierarchical vision transformer using shifted windows. In: Int. Conf. Comput. Vis., pp. 10012–10022 (2021) Caron et al. [2021] Caron, M., Touvron, H., Misra, I., Jégou, H., Mairal, J., Bojanowski, P., Joulin, A.: Emerging properties in self-supervised vision transformers. In: Int. Conf. Comput. Vis., pp. 9650–9660 (2021) Feng et al. [2019] Feng, Y., You, H., Zhang, Z., Ji, R., Gao, Y.: Hypergraph neural networks. In: AAAI Conf. on Artificial Intell., vol. 33, pp. 3558–3565 (2019) Gao et al. [2022] Gao, Y., Feng, Y., Ji, S., Ji, R.: Hgnn+: General hypergraph neural networks. IEEE Trans. Pattern Anal. Mach. Intell. 45(3), 3181–3199 (2022) Liang et al. [2023] Liang, Y., Yang, X., Lin, J., Li, H., Xu, X., Chen, Y.: Luciddreamer: Towards high-fidelity text-to-3d generation via interval score matching. arXiv preprint arXiv:2311.11284 (2023) Radford et al. [2021] Radford, A., Kim, J.W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., Sastry, G., Askell, A., Mishkin, P., Clark, J., et al.: Learning transferable visual models from natural language supervision. In: Int. Conf. on Mach. Learn., pp. 8748–8763 (2021). PMLR Long et al. [2023] Long, X., Guo, Y.-C., Lin, C., Liu, Y., Dou, Z., Liu, L., Ma, Y., Zhang, S.-H., Habermann, M., Theobalt, C., et al.: Wonder3d: Single image to 3d using cross-domain diffusion. arXiv preprint arXiv:2310.15008 (2023) Mildenhall et al. [2020] Mildenhall, B., Srinivasan, P.P., Tancik, M., Barron, J.T., Ramamoorthi, R., Ng, R.: Nerf: Representing scenes as neural radiance fields for view synthesis. In: Eur. Conf. Comput. Vis. (2020) Wang et al. [2021] Wang, P., Liu, L., Liu, Y., Theobalt, C., Komura, T., Wang, W.: Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. Adv. Neural Inform. Process. Syst. (2021) Wang et al. [2023] Wang, H., Du, X., Li, J., Yeh, R.A., Shakhnarovich, G.: Score jacobian chaining: Lifting pretrained 2d diffusion models for 3d generation. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 12619–12629 (2023) Kerbl et al. [2023] Kerbl, B., Kopanas, G., Leimkühler, T., Drettakis, G.: 3d gaussian splatting for real-time radiance field rendering. ACM Trans. Graph. 42(4) (2023) Tang et al. [2023] Tang, J., Ren, J., Zhou, H., Liu, Z., Zeng, G.: Dreamgaussian: Generative gaussian splatting for efficient 3d content creation. arXiv preprint arXiv:2309.16653 (2023) Fridovich-Keil et al. [2022] Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. 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[2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. 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IEEE Trans. Pattern Anal. Mach. Intell. 45(3), 3181–3199 (2022) Liang et al. [2023] Liang, Y., Yang, X., Lin, J., Li, H., Xu, X., Chen, Y.: Luciddreamer: Towards high-fidelity text-to-3d generation via interval score matching. arXiv preprint arXiv:2311.11284 (2023) Radford et al. [2021] Radford, A., Kim, J.W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., Sastry, G., Askell, A., Mishkin, P., Clark, J., et al.: Learning transferable visual models from natural language supervision. In: Int. Conf. on Mach. Learn., pp. 8748–8763 (2021). PMLR Long et al. [2023] Long, X., Guo, Y.-C., Lin, C., Liu, Y., Dou, Z., Liu, L., Ma, Y., Zhang, S.-H., Habermann, M., Theobalt, C., et al.: Wonder3d: Single image to 3d using cross-domain diffusion. arXiv preprint arXiv:2310.15008 (2023) Mildenhall et al. [2020] Mildenhall, B., Srinivasan, P.P., Tancik, M., Barron, J.T., Ramamoorthi, R., Ng, R.: Nerf: Representing scenes as neural radiance fields for view synthesis. In: Eur. Conf. Comput. Vis. 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Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. 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[1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Liang, Y., Yang, X., Lin, J., Li, H., Xu, X., Chen, Y.: Luciddreamer: Towards high-fidelity text-to-3d generation via interval score matching. arXiv preprint arXiv:2311.11284 (2023) Radford et al. [2021] Radford, A., Kim, J.W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., Sastry, G., Askell, A., Mishkin, P., Clark, J., et al.: Learning transferable visual models from natural language supervision. In: Int. Conf. on Mach. Learn., pp. 8748–8763 (2021). PMLR Long et al. [2023] Long, X., Guo, Y.-C., Lin, C., Liu, Y., Dou, Z., Liu, L., Ma, Y., Zhang, S.-H., Habermann, M., Theobalt, C., et al.: Wonder3d: Single image to 3d using cross-domain diffusion. arXiv preprint arXiv:2310.15008 (2023) Mildenhall et al. [2020] Mildenhall, B., Srinivasan, P.P., Tancik, M., Barron, J.T., Ramamoorthi, R., Ng, R.: Nerf: Representing scenes as neural radiance fields for view synthesis. In: Eur. Conf. Comput. Vis. (2020) Wang et al. [2021] Wang, P., Liu, L., Liu, Y., Theobalt, C., Komura, T., Wang, W.: Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. Adv. Neural Inform. Process. Syst. (2021) Wang et al. [2023] Wang, H., Du, X., Li, J., Yeh, R.A., Shakhnarovich, G.: Score jacobian chaining: Lifting pretrained 2d diffusion models for 3d generation. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 12619–12629 (2023) Kerbl et al. [2023] Kerbl, B., Kopanas, G., Leimkühler, T., Drettakis, G.: 3d gaussian splatting for real-time radiance field rendering. ACM Trans. Graph. 42(4) (2023) Tang et al. [2023] Tang, J., Ren, J., Zhou, H., Liu, Z., Zeng, G.: Dreamgaussian: Generative gaussian splatting for efficient 3d content creation. arXiv preprint arXiv:2309.16653 (2023) Fridovich-Keil et al. [2022] Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. 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[2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Long, X., Guo, Y.-C., Lin, C., Liu, Y., Dou, Z., Liu, L., Ma, Y., Zhang, S.-H., Habermann, M., Theobalt, C., et al.: Wonder3d: Single image to 3d using cross-domain diffusion. arXiv preprint arXiv:2310.15008 (2023) Mildenhall et al. [2020] Mildenhall, B., Srinivasan, P.P., Tancik, M., Barron, J.T., Ramamoorthi, R., Ng, R.: Nerf: Representing scenes as neural radiance fields for view synthesis. In: Eur. Conf. Comput. Vis. (2020) Wang et al. [2021] Wang, P., Liu, L., Liu, Y., Theobalt, C., Komura, T., Wang, W.: Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. Adv. Neural Inform. Process. Syst. (2021) Wang et al. 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[2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. 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[2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. 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[1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. 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IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. 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[2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. 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IEEE Trans. Pattern Anal. Mach. Intell. 45(3), 3181–3199 (2022) Liang et al. [2023] Liang, Y., Yang, X., Lin, J., Li, H., Xu, X., Chen, Y.: Luciddreamer: Towards high-fidelity text-to-3d generation via interval score matching. arXiv preprint arXiv:2311.11284 (2023) Radford et al. [2021] Radford, A., Kim, J.W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., Sastry, G., Askell, A., Mishkin, P., Clark, J., et al.: Learning transferable visual models from natural language supervision. In: Int. Conf. on Mach. Learn., pp. 8748–8763 (2021). PMLR Long et al. [2023] Long, X., Guo, Y.-C., Lin, C., Liu, Y., Dou, Z., Liu, L., Ma, Y., Zhang, S.-H., Habermann, M., Theobalt, C., et al.: Wonder3d: Single image to 3d using cross-domain diffusion. arXiv preprint arXiv:2310.15008 (2023) Mildenhall et al. [2020] Mildenhall, B., Srinivasan, P.P., Tancik, M., Barron, J.T., Ramamoorthi, R., Ng, R.: Nerf: Representing scenes as neural radiance fields for view synthesis. In: Eur. Conf. Comput. Vis. 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Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. 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Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Liang, Y., Yang, X., Lin, J., Li, H., Xu, X., Chen, Y.: Luciddreamer: Towards high-fidelity text-to-3d generation via interval score matching. arXiv preprint arXiv:2311.11284 (2023) Radford et al. [2021] Radford, A., Kim, J.W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., Sastry, G., Askell, A., Mishkin, P., Clark, J., et al.: Learning transferable visual models from natural language supervision. In: Int. Conf. on Mach. Learn., pp. 8748–8763 (2021). PMLR Long et al. [2023] Long, X., Guo, Y.-C., Lin, C., Liu, Y., Dou, Z., Liu, L., Ma, Y., Zhang, S.-H., Habermann, M., Theobalt, C., et al.: Wonder3d: Single image to 3d using cross-domain diffusion. arXiv preprint arXiv:2310.15008 (2023) Mildenhall et al. [2020] Mildenhall, B., Srinivasan, P.P., Tancik, M., Barron, J.T., Ramamoorthi, R., Ng, R.: Nerf: Representing scenes as neural radiance fields for view synthesis. In: Eur. Conf. Comput. Vis. (2020) Wang et al. [2021] Wang, P., Liu, L., Liu, Y., Theobalt, C., Komura, T., Wang, W.: Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. Adv. Neural Inform. Process. Syst. (2021) Wang et al. [2023] Wang, H., Du, X., Li, J., Yeh, R.A., Shakhnarovich, G.: Score jacobian chaining: Lifting pretrained 2d diffusion models for 3d generation. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 12619–12629 (2023) Kerbl et al. 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[2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Long, X., Guo, Y.-C., Lin, C., Liu, Y., Dou, Z., Liu, L., Ma, Y., Zhang, S.-H., Habermann, M., Theobalt, C., et al.: Wonder3d: Single image to 3d using cross-domain diffusion. arXiv preprint arXiv:2310.15008 (2023) Mildenhall et al. [2020] Mildenhall, B., Srinivasan, P.P., Tancik, M., Barron, J.T., Ramamoorthi, R., Ng, R.: Nerf: Representing scenes as neural radiance fields for view synthesis. In: Eur. Conf. Comput. Vis. (2020) Wang et al. [2021] Wang, P., Liu, L., Liu, Y., Theobalt, C., Komura, T., Wang, W.: Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. Adv. Neural Inform. Process. Syst. (2021) Wang et al. 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[2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. 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In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. 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In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. 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[2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. 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IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Dosovitskiy, A., Beyer, L., Kolesnikov, A., Weissenborn, D., Zhai, X., Unterthiner, T., Dehghani, M., Minderer, M., Heigold, G., Gelly, S., Uszkoreit, J., Houlsby, N.: An image is worth 16x16 words: Transformers for image recognition at scale. In: Int. Conf. Learn. Represent. (2021) Liu et al. [2021] Liu, Z., Lin, Y., Cao, Y., Hu, H., Wei, Y., Zhang, Z., Lin, S., Guo, B.: Swin transformer: Hierarchical vision transformer using shifted windows. In: Int. Conf. Comput. Vis., pp. 10012–10022 (2021) Caron et al. [2021] Caron, M., Touvron, H., Misra, I., Jégou, H., Mairal, J., Bojanowski, P., Joulin, A.: Emerging properties in self-supervised vision transformers. In: Int. Conf. Comput. Vis., pp. 9650–9660 (2021) Feng et al. [2019] Feng, Y., You, H., Zhang, Z., Ji, R., Gao, Y.: Hypergraph neural networks. In: AAAI Conf. on Artificial Intell., vol. 33, pp. 3558–3565 (2019) Gao et al. 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[2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. 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[2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. 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[2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Caron, M., Touvron, H., Misra, I., Jégou, H., Mairal, J., Bojanowski, P., Joulin, A.: Emerging properties in self-supervised vision transformers. In: Int. Conf. Comput. Vis., pp. 9650–9660 (2021) Feng et al. [2019] Feng, Y., You, H., Zhang, Z., Ji, R., Gao, Y.: Hypergraph neural networks. In: AAAI Conf. on Artificial Intell., vol. 33, pp. 3558–3565 (2019) Gao et al. [2022] Gao, Y., Feng, Y., Ji, S., Ji, R.: Hgnn+: General hypergraph neural networks. IEEE Trans. Pattern Anal. Mach. Intell. 45(3), 3181–3199 (2022) Liang et al. [2023] Liang, Y., Yang, X., Lin, J., Li, H., Xu, X., Chen, Y.: Luciddreamer: Towards high-fidelity text-to-3d generation via interval score matching. arXiv preprint arXiv:2311.11284 (2023) Radford et al. [2021] Radford, A., Kim, J.W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., Sastry, G., Askell, A., Mishkin, P., Clark, J., et al.: Learning transferable visual models from natural language supervision. In: Int. Conf. on Mach. Learn., pp. 8748–8763 (2021). PMLR Long et al. [2023] Long, X., Guo, Y.-C., Lin, C., Liu, Y., Dou, Z., Liu, L., Ma, Y., Zhang, S.-H., Habermann, M., Theobalt, C., et al.: Wonder3d: Single image to 3d using cross-domain diffusion. arXiv preprint arXiv:2310.15008 (2023) Mildenhall et al. [2020] Mildenhall, B., Srinivasan, P.P., Tancik, M., Barron, J.T., Ramamoorthi, R., Ng, R.: Nerf: Representing scenes as neural radiance fields for view synthesis. In: Eur. Conf. Comput. Vis. (2020) Wang et al. [2021] Wang, P., Liu, L., Liu, Y., Theobalt, C., Komura, T., Wang, W.: Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. Adv. Neural Inform. Process. Syst. (2021) Wang et al. 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[2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Feng, Y., You, H., Zhang, Z., Ji, R., Gao, Y.: Hypergraph neural networks. In: AAAI Conf. on Artificial Intell., vol. 33, pp. 3558–3565 (2019) Gao et al. [2022] Gao, Y., Feng, Y., Ji, S., Ji, R.: Hgnn+: General hypergraph neural networks. IEEE Trans. Pattern Anal. Mach. Intell. 45(3), 3181–3199 (2022) Liang et al. [2023] Liang, Y., Yang, X., Lin, J., Li, H., Xu, X., Chen, Y.: Luciddreamer: Towards high-fidelity text-to-3d generation via interval score matching. arXiv preprint arXiv:2311.11284 (2023) Radford et al. [2021] Radford, A., Kim, J.W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., Sastry, G., Askell, A., Mishkin, P., Clark, J., et al.: Learning transferable visual models from natural language supervision. In: Int. Conf. on Mach. Learn., pp. 8748–8763 (2021). 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Syst. 34, 6087–6101 (2021) Radford, A., Kim, J.W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., Sastry, G., Askell, A., Mishkin, P., Clark, J., et al.: Learning transferable visual models from natural language supervision. In: Int. Conf. on Mach. Learn., pp. 8748–8763 (2021). PMLR Long et al. [2023] Long, X., Guo, Y.-C., Lin, C., Liu, Y., Dou, Z., Liu, L., Ma, Y., Zhang, S.-H., Habermann, M., Theobalt, C., et al.: Wonder3d: Single image to 3d using cross-domain diffusion. arXiv preprint arXiv:2310.15008 (2023) Mildenhall et al. [2020] Mildenhall, B., Srinivasan, P.P., Tancik, M., Barron, J.T., Ramamoorthi, R., Ng, R.: Nerf: Representing scenes as neural radiance fields for view synthesis. In: Eur. Conf. Comput. Vis. (2020) Wang et al. [2021] Wang, P., Liu, L., Liu, Y., Theobalt, C., Komura, T., Wang, W.: Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. Adv. Neural Inform. Process. Syst. (2021) Wang et al. 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Syst. 34, 6087–6101 (2021) Wang, P., Liu, L., Liu, Y., Theobalt, C., Komura, T., Wang, W.: Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. Adv. Neural Inform. Process. Syst. (2021) Wang et al. [2023] Wang, H., Du, X., Li, J., Yeh, R.A., Shakhnarovich, G.: Score jacobian chaining: Lifting pretrained 2d diffusion models for 3d generation. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 12619–12629 (2023) Kerbl et al. [2023] Kerbl, B., Kopanas, G., Leimkühler, T., Drettakis, G.: 3d gaussian splatting for real-time radiance field rendering. ACM Trans. Graph. 42(4) (2023) Tang et al. [2023] Tang, J., Ren, J., Zhou, H., Liu, Z., Zeng, G.: Dreamgaussian: Generative gaussian splatting for efficient 3d content creation. arXiv preprint arXiv:2309.16653 (2023) Fridovich-Keil et al. [2022] Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. 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[2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Tang, J., Ren, J., Zhou, H., Liu, Z., Zeng, G.: Dreamgaussian: Generative gaussian splatting for efficient 3d content creation. arXiv preprint arXiv:2309.16653 (2023) Fridovich-Keil et al. [2022] Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. 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Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. 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[2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. 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[2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. 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In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. 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[2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. 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Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. 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Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. 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[2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. 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IEEE Trans. Pattern Anal. Mach. Intell. 45(3), 3181–3199 (2022) Liang et al. [2023] Liang, Y., Yang, X., Lin, J., Li, H., Xu, X., Chen, Y.: Luciddreamer: Towards high-fidelity text-to-3d generation via interval score matching. arXiv preprint arXiv:2311.11284 (2023) Radford et al. [2021] Radford, A., Kim, J.W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., Sastry, G., Askell, A., Mishkin, P., Clark, J., et al.: Learning transferable visual models from natural language supervision. In: Int. Conf. on Mach. Learn., pp. 8748–8763 (2021). PMLR Long et al. [2023] Long, X., Guo, Y.-C., Lin, C., Liu, Y., Dou, Z., Liu, L., Ma, Y., Zhang, S.-H., Habermann, M., Theobalt, C., et al.: Wonder3d: Single image to 3d using cross-domain diffusion. arXiv preprint arXiv:2310.15008 (2023) Mildenhall et al. [2020] Mildenhall, B., Srinivasan, P.P., Tancik, M., Barron, J.T., Ramamoorthi, R., Ng, R.: Nerf: Representing scenes as neural radiance fields for view synthesis. In: Eur. Conf. Comput. Vis. 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Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. 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Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Liang, Y., Yang, X., Lin, J., Li, H., Xu, X., Chen, Y.: Luciddreamer: Towards high-fidelity text-to-3d generation via interval score matching. arXiv preprint arXiv:2311.11284 (2023) Radford et al. [2021] Radford, A., Kim, J.W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., Sastry, G., Askell, A., Mishkin, P., Clark, J., et al.: Learning transferable visual models from natural language supervision. In: Int. Conf. on Mach. Learn., pp. 8748–8763 (2021). PMLR Long et al. [2023] Long, X., Guo, Y.-C., Lin, C., Liu, Y., Dou, Z., Liu, L., Ma, Y., Zhang, S.-H., Habermann, M., Theobalt, C., et al.: Wonder3d: Single image to 3d using cross-domain diffusion. arXiv preprint arXiv:2310.15008 (2023) Mildenhall et al. [2020] Mildenhall, B., Srinivasan, P.P., Tancik, M., Barron, J.T., Ramamoorthi, R., Ng, R.: Nerf: Representing scenes as neural radiance fields for view synthesis. In: Eur. Conf. Comput. Vis. (2020) Wang et al. [2021] Wang, P., Liu, L., Liu, Y., Theobalt, C., Komura, T., Wang, W.: Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. Adv. Neural Inform. Process. Syst. (2021) Wang et al. [2023] Wang, H., Du, X., Li, J., Yeh, R.A., Shakhnarovich, G.: Score jacobian chaining: Lifting pretrained 2d diffusion models for 3d generation. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 12619–12629 (2023) Kerbl et al. [2023] Kerbl, B., Kopanas, G., Leimkühler, T., Drettakis, G.: 3d gaussian splatting for real-time radiance field rendering. ACM Trans. Graph. 42(4) (2023) Tang et al. [2023] Tang, J., Ren, J., Zhou, H., Liu, Z., Zeng, G.: Dreamgaussian: Generative gaussian splatting for efficient 3d content creation. arXiv preprint arXiv:2309.16653 (2023) Fridovich-Keil et al. [2022] Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. 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[2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Long, X., Guo, Y.-C., Lin, C., Liu, Y., Dou, Z., Liu, L., Ma, Y., Zhang, S.-H., Habermann, M., Theobalt, C., et al.: Wonder3d: Single image to 3d using cross-domain diffusion. arXiv preprint arXiv:2310.15008 (2023) Mildenhall et al. [2020] Mildenhall, B., Srinivasan, P.P., Tancik, M., Barron, J.T., Ramamoorthi, R., Ng, R.: Nerf: Representing scenes as neural radiance fields for view synthesis. In: Eur. Conf. Comput. Vis. (2020) Wang et al. [2021] Wang, P., Liu, L., Liu, Y., Theobalt, C., Komura, T., Wang, W.: Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. Adv. Neural Inform. Process. Syst. (2021) Wang et al. 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[2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. 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[2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. 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[1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. 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IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. 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PMLR Long et al. [2023] Long, X., Guo, Y.-C., Lin, C., Liu, Y., Dou, Z., Liu, L., Ma, Y., Zhang, S.-H., Habermann, M., Theobalt, C., et al.: Wonder3d: Single image to 3d using cross-domain diffusion. arXiv preprint arXiv:2310.15008 (2023) Mildenhall et al. [2020] Mildenhall, B., Srinivasan, P.P., Tancik, M., Barron, J.T., Ramamoorthi, R., Ng, R.: Nerf: Representing scenes as neural radiance fields for view synthesis. In: Eur. Conf. Comput. Vis. (2020) Wang et al. [2021] Wang, P., Liu, L., Liu, Y., Theobalt, C., Komura, T., Wang, W.: Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. Adv. Neural Inform. Process. Syst. (2021) Wang et al. [2023] Wang, H., Du, X., Li, J., Yeh, R.A., Shakhnarovich, G.: Score jacobian chaining: Lifting pretrained 2d diffusion models for 3d generation. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 12619–12629 (2023) Kerbl et al. [2023] Kerbl, B., Kopanas, G., Leimkühler, T., Drettakis, G.: 3d gaussian splatting for real-time radiance field rendering. ACM Trans. Graph. 42(4) (2023) Tang et al. [2023] Tang, J., Ren, J., Zhou, H., Liu, Z., Zeng, G.: Dreamgaussian: Generative gaussian splatting for efficient 3d content creation. arXiv preprint arXiv:2309.16653 (2023) Fridovich-Keil et al. [2022] Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. 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[2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Gao, Y., Feng, Y., Ji, S., Ji, R.: Hgnn+: General hypergraph neural networks. IEEE Trans. Pattern Anal. Mach. Intell. 45(3), 3181–3199 (2022) Liang et al. [2023] Liang, Y., Yang, X., Lin, J., Li, H., Xu, X., Chen, Y.: Luciddreamer: Towards high-fidelity text-to-3d generation via interval score matching. arXiv preprint arXiv:2311.11284 (2023) Radford et al. [2021] Radford, A., Kim, J.W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., Sastry, G., Askell, A., Mishkin, P., Clark, J., et al.: Learning transferable visual models from natural language supervision. In: Int. Conf. on Mach. Learn., pp. 8748–8763 (2021). PMLR Long et al. [2023] Long, X., Guo, Y.-C., Lin, C., Liu, Y., Dou, Z., Liu, L., Ma, Y., Zhang, S.-H., Habermann, M., Theobalt, C., et al.: Wonder3d: Single image to 3d using cross-domain diffusion. arXiv preprint arXiv:2310.15008 (2023) Mildenhall et al. [2020] Mildenhall, B., Srinivasan, P.P., Tancik, M., Barron, J.T., Ramamoorthi, R., Ng, R.: Nerf: Representing scenes as neural radiance fields for view synthesis. In: Eur. Conf. Comput. Vis. 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Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Liang, Y., Yang, X., Lin, J., Li, H., Xu, X., Chen, Y.: Luciddreamer: Towards high-fidelity text-to-3d generation via interval score matching. arXiv preprint arXiv:2311.11284 (2023) Radford et al. [2021] Radford, A., Kim, J.W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., Sastry, G., Askell, A., Mishkin, P., Clark, J., et al.: Learning transferable visual models from natural language supervision. In: Int. Conf. on Mach. Learn., pp. 8748–8763 (2021). PMLR Long et al. [2023] Long, X., Guo, Y.-C., Lin, C., Liu, Y., Dou, Z., Liu, L., Ma, Y., Zhang, S.-H., Habermann, M., Theobalt, C., et al.: Wonder3d: Single image to 3d using cross-domain diffusion. arXiv preprint arXiv:2310.15008 (2023) Mildenhall et al. [2020] Mildenhall, B., Srinivasan, P.P., Tancik, M., Barron, J.T., Ramamoorthi, R., Ng, R.: Nerf: Representing scenes as neural radiance fields for view synthesis. In: Eur. Conf. Comput. Vis. (2020) Wang et al. [2021] Wang, P., Liu, L., Liu, Y., Theobalt, C., Komura, T., Wang, W.: Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. Adv. Neural Inform. Process. Syst. (2021) Wang et al. [2023] Wang, H., Du, X., Li, J., Yeh, R.A., Shakhnarovich, G.: Score jacobian chaining: Lifting pretrained 2d diffusion models for 3d generation. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 12619–12629 (2023) Kerbl et al. [2023] Kerbl, B., Kopanas, G., Leimkühler, T., Drettakis, G.: 3d gaussian splatting for real-time radiance field rendering. ACM Trans. Graph. 42(4) (2023) Tang et al. [2023] Tang, J., Ren, J., Zhou, H., Liu, Z., Zeng, G.: Dreamgaussian: Generative gaussian splatting for efficient 3d content creation. arXiv preprint arXiv:2309.16653 (2023) Fridovich-Keil et al. [2022] Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. 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Syst. 34, 6087–6101 (2021) Wang, P., Liu, L., Liu, Y., Theobalt, C., Komura, T., Wang, W.: Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. Adv. Neural Inform. Process. Syst. (2021) Wang et al. [2023] Wang, H., Du, X., Li, J., Yeh, R.A., Shakhnarovich, G.: Score jacobian chaining: Lifting pretrained 2d diffusion models for 3d generation. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 12619–12629 (2023) Kerbl et al. [2023] Kerbl, B., Kopanas, G., Leimkühler, T., Drettakis, G.: 3d gaussian splatting for real-time radiance field rendering. ACM Trans. Graph. 42(4) (2023) Tang et al. [2023] Tang, J., Ren, J., Zhou, H., Liu, Z., Zeng, G.: Dreamgaussian: Generative gaussian splatting for efficient 3d content creation. arXiv preprint arXiv:2309.16653 (2023) Fridovich-Keil et al. [2022] Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. 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[2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Tang, J., Ren, J., Zhou, H., Liu, Z., Zeng, G.: Dreamgaussian: Generative gaussian splatting for efficient 3d content creation. arXiv preprint arXiv:2309.16653 (2023) Fridovich-Keil et al. [2022] Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. 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Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. 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[2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. 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[2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. 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[2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. 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In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. 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[2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. 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[2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. 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[2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. 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[2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. 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In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. 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[2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Feng, Y., You, H., Zhang, Z., Ji, R., Gao, Y.: Hypergraph neural networks. In: AAAI Conf. on Artificial Intell., vol. 33, pp. 3558–3565 (2019) Gao et al. [2022] Gao, Y., Feng, Y., Ji, S., Ji, R.: Hgnn+: General hypergraph neural networks. IEEE Trans. Pattern Anal. Mach. Intell. 45(3), 3181–3199 (2022) Liang et al. [2023] Liang, Y., Yang, X., Lin, J., Li, H., Xu, X., Chen, Y.: Luciddreamer: Towards high-fidelity text-to-3d generation via interval score matching. arXiv preprint arXiv:2311.11284 (2023) Radford et al. [2021] Radford, A., Kim, J.W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., Sastry, G., Askell, A., Mishkin, P., Clark, J., et al.: Learning transferable visual models from natural language supervision. In: Int. Conf. on Mach. Learn., pp. 8748–8763 (2021). 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[2023] Kerbl, B., Kopanas, G., Leimkühler, T., Drettakis, G.: 3d gaussian splatting for real-time radiance field rendering. ACM Trans. Graph. 42(4) (2023) Tang et al. [2023] Tang, J., Ren, J., Zhou, H., Liu, Z., Zeng, G.: Dreamgaussian: Generative gaussian splatting for efficient 3d content creation. arXiv preprint arXiv:2309.16653 (2023) Fridovich-Keil et al. [2022] Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. 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[2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. 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Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. 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[2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. 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IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. 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[1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. 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[2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. 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[2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. 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[2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. 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[2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. 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Syst. 34, 6087–6101 (2021) Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. 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[2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. 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[2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. 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Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. 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Syst. 34, 6087–6101 (2021) Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. 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Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. 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Syst. 34, 6087–6101 (2021) Wang, P., Liu, L., Liu, Y., Theobalt, C., Komura, T., Wang, W.: Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. Adv. Neural Inform. Process. Syst. (2021) Wang et al. [2023] Wang, H., Du, X., Li, J., Yeh, R.A., Shakhnarovich, G.: Score jacobian chaining: Lifting pretrained 2d diffusion models for 3d generation. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 12619–12629 (2023) Kerbl et al. [2023] Kerbl, B., Kopanas, G., Leimkühler, T., Drettakis, G.: 3d gaussian splatting for real-time radiance field rendering. ACM Trans. Graph. 42(4) (2023) Tang et al. [2023] Tang, J., Ren, J., Zhou, H., Liu, Z., Zeng, G.: Dreamgaussian: Generative gaussian splatting for efficient 3d content creation. arXiv preprint arXiv:2309.16653 (2023) Fridovich-Keil et al. [2022] Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. 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[1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Kerbl, B., Kopanas, G., Leimkühler, T., Drettakis, G.: 3d gaussian splatting for real-time radiance field rendering. ACM Trans. Graph. 42(4) (2023) Tang et al. [2023] Tang, J., Ren, J., Zhou, H., Liu, Z., Zeng, G.: Dreamgaussian: Generative gaussian splatting for efficient 3d content creation. arXiv preprint arXiv:2309.16653 (2023) Fridovich-Keil et al. [2022] Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. 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[2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Tang, J., Ren, J., Zhou, H., Liu, Z., Zeng, G.: Dreamgaussian: Generative gaussian splatting for efficient 3d content creation. arXiv preprint arXiv:2309.16653 (2023) Fridovich-Keil et al. [2022] Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. 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[1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. 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[2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. 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Syst. 34, 6087–6101 (2021) Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. 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[2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. 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Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. 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Syst. 34, 6087–6101 (2021) Mildenhall, B., Srinivasan, P.P., Tancik, M., Barron, J.T., Ramamoorthi, R., Ng, R.: Nerf: Representing scenes as neural radiance fields for view synthesis. In: Eur. Conf. Comput. Vis. (2020) Wang et al. [2021] Wang, P., Liu, L., Liu, Y., Theobalt, C., Komura, T., Wang, W.: Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. Adv. Neural Inform. Process. Syst. (2021) Wang et al. [2023] Wang, H., Du, X., Li, J., Yeh, R.A., Shakhnarovich, G.: Score jacobian chaining: Lifting pretrained 2d diffusion models for 3d generation. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 12619–12629 (2023) Kerbl et al. [2023] Kerbl, B., Kopanas, G., Leimkühler, T., Drettakis, G.: 3d gaussian splatting for real-time radiance field rendering. ACM Trans. Graph. 42(4) (2023) Tang et al. 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In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. 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[2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. 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Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Wang, P., Liu, L., Liu, Y., Theobalt, C., Komura, T., Wang, W.: Neus: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. Adv. Neural Inform. Process. Syst. (2021) Wang et al. [2023] Wang, H., Du, X., Li, J., Yeh, R.A., Shakhnarovich, G.: Score jacobian chaining: Lifting pretrained 2d diffusion models for 3d generation. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 12619–12629 (2023) Kerbl et al. [2023] Kerbl, B., Kopanas, G., Leimkühler, T., Drettakis, G.: 3d gaussian splatting for real-time radiance field rendering. ACM Trans. Graph. 42(4) (2023) Tang et al. [2023] Tang, J., Ren, J., Zhou, H., Liu, Z., Zeng, G.: Dreamgaussian: Generative gaussian splatting for efficient 3d content creation. arXiv preprint arXiv:2309.16653 (2023) Fridovich-Keil et al. [2022] Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. 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IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. 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Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. 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[1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. 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[2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. 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[1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. 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[2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. 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[2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. 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IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. 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Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. 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Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. 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Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. 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[2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. 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IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. 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[1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. 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[2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. 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[2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. 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[2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. 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[2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. 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Syst. 34, 6087–6101 (2021) Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. 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[2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. 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[2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. 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[2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. 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[2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. 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[2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. 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[1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. 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IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. 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In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. 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In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. 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[2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. 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IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. 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[2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. 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[2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. 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In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. 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[1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. 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IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. 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IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. 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[2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Fridovich-Keil, S., Yu, A., Tancik, M., Chen, Q., Recht, B., Kanazawa, A.: Plenoxels: Radiance fields without neural networks. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 5501–5510 (2022) Gao et al. [2020] Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. 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[1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. 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[2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. 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In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. 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[2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. 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[2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. 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[2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. 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[2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. 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Syst. 34, 6087–6101 (2021) Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. 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[2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. 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[1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Gao, Y., Zhang, Z., Lin, H., Zhao, X., Du, S., Zou, C.: Hypergraph learning: Methods and practices. IEEE Trans. Pattern Anal. Mach. Intell. 44(5), 2548–2566 (2020) Bai et al. [2021] Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. 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[2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. Pattern Recognition 110, 107637 (2021) Kipf and Welling [2016] Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. 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IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Bai, S., Zhang, F., Torr, P.H.: Hypergraph convolution and hypergraph attention. 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[2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016) Veličković et al. [2018] Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. 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[2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. 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IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. 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[2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. 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[2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. 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[2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. 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[2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. 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[2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. 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[2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. 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[2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. 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IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. 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In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. 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[2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: Int. Conf. Learn. Represent. (2018) Yu et al. [2012] Yu, J., Tao, D., Wang, M.: Adaptive hypergraph learning and its application in image classification. IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. 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IEEE Trans. Image Process. 21(7), 3262–3272 (2012) Ma et al. [2021] Ma, Z., Jiang, Z., Zhang, H.: Hyperspectral image classification using feature fusion hypergraph convolution neural network. IEEE Trans. on Geoscience and Remote Sensing. 60, 1–14 (2021) Di et al. [2021] Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. 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[2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. 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[2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. 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[2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. 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[2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. 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Syst. 34, 6087–6101 (2021) Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. 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[1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. 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[2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Di, D., Shi, F., Yan, F., Xia, L., Mo, Z., Ding, Z., Shan, F., Song, B., Li, S., Wei, Y., et al.: Hypergraph learning for identification of covid-19 with ct imaging. Med. Image Analysis 68, 101910 (2021) Di et al. [2022] Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Di, D., Zou, C., Feng, Y., Zhou, H., Ji, R., Dai, Q., Gao, Y.: Generating hypergraph-based high-order representations of whole-slide histopathological images for survival prediction. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 5800–5815 (2022) Yadati et al. [2020] Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. 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Syst. 34, 6087–6101 (2021) Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. 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[1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. 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[2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. 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[1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. 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[2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Yadati, N., Nitin, V., Nimishakavi, M., Yadav, P., Louis, A., Talukdar, P.: Nhp: Neural hypergraph link prediction. In: Conf. on Info. and Knowl. Manage., pp. 1705–1714 (2020) Li et al. [2013] Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Li, D., Xu, Z., Li, S., Sun, X.: Link prediction in social networks based on hypergraph. In: World Wide Web Conf., pp. 41–42 (2013) Fan et al. [2021] Fan, H., Zhang, F., Wei, Y., Li, Z., Zou, C., Gao, Y., Dai, Q.: Heterogeneous hypergraph variational autoencoder for link prediction. IEEE Trans. Pattern Anal. Mach. Intell. 44(8), 4125–4138 (2021) Liao et al. [2021] Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: Int. Conf. Comput. Vis., pp. 1266–1275 (2021) Gao et al. [2011] Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. 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In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Gao, Y., Tang, J., Hong, R., Yan, S., Dai, Q., Zhang, N., Chua, T.-S.: Camera constraint-free view-based 3-d object retrieval. IEEE Trans. Image Process. 21(4), 2269–2281 (2011) Feng et al. [2023] Feng, Y., Ji, S., Liu, Y.-S., Du, S., Dai, Q., Gao, Y.: Hypergraph-based multi-modal representation for open-set 3d object retrieval. IEEE Trans. Pattern Anal. Mach. Intell. (2023) Purkait et al. [2016] Purkait, P., Chin, T.-J., Sadri, A., Suter, D.: Clustering with hypergraphs: the case for large hyperedges. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. 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IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1697–1711 (2016) Li and Milenkovic [2017] Li, P., Milenkovic, O.: Inhomogeneous hypergraph clustering with applications. Adv. Neural Inform. Process. Syst. 30 (2017) Gao et al. [2012] Gao, Y., Wang, M., Tao, D., Ji, R., Dai, Q.: 3-d object retrieval and recognition with hypergraph analysis. IEEE Trans. Image Process. 21(9), 4290–4303 (2012) Zhang et al. [2020] Zhang, S., Cui, S., Ding, Z.: Hypergraph spectral analysis and processing in 3d point cloud. IEEE Trans. Image Process. 30, 1193–1206 (2020) Nong et al. [2022] Nong, L., Peng, J., Zhang, W., Lin, J., Qiu, H., Wang, J.: Adaptive multi-hypergraph convolutional networks for 3d object classification. IEEE Trans. Multimedia (2022) Jiang et al. [2022] Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. 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Syst. 34, 6087–6101 (2021) Jiang, P., Deng, X., Wang, L., Chen, Z., Zhang, S.: Hypergraph representation for detecting 3d objects from noisy point clouds. IEEE Trans. Knowl. Data Eng. (2022) Song et al. [2020] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020) Krishna and Murty [1999] Krishna, K., Murty, M.N.: Genetic k-means algorithm. IEEE Trans. Cybern. 29(3), 433–439 (1999) Peterson [2009] Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. 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[1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Peterson, L.E.: K-nearest neighbor. Scholarpedia 4(2), 1883 (2009) Rombach et al. [2022] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog., pp. 10684–10695 (2022) Ho and Salimans [2022] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022) Hamerly and Elkan [2003] Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. 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[1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. [1996] Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Hamerly, G., Elkan, C.: Learning the k in k-means. Adv. Neural Inform. Process. Syst. 16 (2003) Ester et al. [1996] Ester, M., Kriegel, H.-P., Sander, J., Xu, X., et al.: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Kdd, vol. 96, pp. 226–231 (1996) Zhuang et al. 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Syst. 34, 6087–6101 (2021) Zhuang, X., Huang, Y., Palaniappan, K., Zhao, Y.: Gaussian mixture density modeling, decomposition, and applications. IEEE Trans. Image Process. 5(9), 1293–1302 (1996) Shen et al. [2021] Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021) Shen, T., Gao, J., Yin, K., Liu, M.-Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3d shape synthesis. Adv. Neural Inform. Process. Syst. 34, 6087–6101 (2021)
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