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Higher-order Graph Convolutional Network with Flower-Petals Laplacians on Simplicial Complexes (2309.12971v2)

Published 22 Sep 2023 in cs.LG, cond-mat.stat-mech, cs.AI, cs.SI, and physics.soc-ph

Abstract: Despite the recent successes of vanilla Graph Neural Networks (GNNs) on various tasks, their foundation on pairwise networks inherently limits their capacity to discern latent higher-order interactions in complex systems. To bridge this capability gap, we propose a novel approach exploiting the rich mathematical theory of simplicial complexes (SCs) - a robust tool for modeling higher-order interactions. Current SC-based GNNs are burdened by high complexity and rigidity, and quantifying higher-order interaction strengths remains challenging. Innovatively, we present a higher-order Flower-Petals (FP) model, incorporating FP Laplacians into SCs. Further, we introduce a Higher-order Graph Convolutional Network (HiGCN) grounded in FP Laplacians, capable of discerning intrinsic features across varying topological scales. By employing learnable graph filters, a parameter group within each FP Laplacian domain, we can identify diverse patterns where the filters' weights serve as a quantifiable measure of higher-order interaction strengths. The theoretical underpinnings of HiGCN's advanced expressiveness are rigorously demonstrated. Additionally, our empirical investigations reveal that the proposed model accomplishes state-of-the-art performance on a range of graph tasks and provides a scalable and flexible solution to explore higher-order interactions in graphs. Codes and datasets are available at https://github.com/Yiminghh/HiGCN.

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References (68)
  1. Diffusion-convolutional neural networks. Advances in neural information processing systems, 29.
  2. The physics of higher-order interactions in complex systems. Nature Physics, 17(10): 1093–1098.
  3. Networks beyond pairwise interactions: Structure and dynamics. Physics Reports, 874: 1–92.
  4. Simplicial closure and higher-order link prediction. Proceedings of the National Academy of Sciences.
  5. Simplex2vec embeddings for community detection in simplicial complexes. arXiv:1906.09068.
  6. Weisfeiler and lehman go topological: Message passing simplicial networks. In International Conference on Machine Learning (ICML), 1026–1037.
  7. The maximum clique problem. In Handbook of combinatorial optimization, 1–74. Springer.
  8. Protein function prediction via graph kernels. Bioinformatics, 21(suppl_1): i47–i56.
  9. Algorithm 457: Finding All Cliques of an Undirected Graph. Commun. ACM, 16(9): 575–577.
  10. An optimal lower bound on the number of variables for graph identification. Combinatorica, 12(4): 398–140.
  11. Centola, D. 2010. The Spread of Behavior in an Online Social Network Experiment. Science, 329(5996): 1194–1197.
  12. BScNets: Block Simplicial Complex Neural Networks. volume 36, 6333–6341.
  13. Arboricity and subgraph listing algorithms. SIAM J. Comput., 14(1): 210–223.
  14. Adaptive Universal Generalized PageRank Graph Neural Network. In International Conference on Learning Representations.
  15. Natural graph networks. Advances in neural information processing systems, 33: 3636–3646.
  16. Structure-activity relationship of mutagenic aromatic and heteroaromatic nitro compounds. correlation with molecular orbital energies and hydrophobicity. Journal of medicinal chemistry, 34(2): 786–797.
  17. Convolutional neural networks on graphs with fast localized spectral filtering. Advances in neural information processing systems, 29: 3838–3845.
  18. Simplicial Neural Networks. In NeurIPS 2020 Workshop on Topological Data Analysis and Beyond.
  19. Fast graph representation learning with PyTorch Geometric. arXiv:1903.02428.
  20. Sparse low-order interaction network underlies a highly correlated and learnable neural population code. Proceedings of the National Academy of Sciences, 108(23): 9679–9684.
  21. Hypergraph Learning: Methods and Practices. IEEE Transactions on Pattern Analysis and Machine Intelligence, 44(5): 2548–2566.
  22. On graph kernels: Hardness results and efficient alternatives. In Learning Theory and Kernel Machines, 129–143. Springer.
  23. Predict then Propagate: Graph Neural Networks meet Personalized PageRank. In International Conference on Learning Representations.
  24. Higher-order interactions stabilize dynamics in competitive network models. Nature, 548(7666): 210–213.
  25. Hacker, C. 2020. k-simplex2vec: a simplicial extension of node2vec. arXiv:2010.05636.
  26. Simplicial complex representation learning. In Machine Learning on Graphs (MLoG) Workshop at 15th ACM International WSDM Conference.
  27. Hatcher, A. 2002. Algebraic topology. Cambridge University Press.
  28. Bernnet: Learning arbitrary graph spectral filters via bernstein approximation. Advances in Neural Information Processing Systems, 34: 14239–14251.
  29. Open graph benchmark: Datasets for machine learning on graphs. Advances in neural information processing systems, 33: 22118–22133.
  30. Kendall, M. G. 1938. A new measure of rank correlation. Biometrika, 30(1/2): 81–93.
  31. Semi-Supervised Classification with Graph Convolutional Networks. In ICLR.
  32. SGAT: Simplicial Graph Attention Network. In Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence (IJCAI-22), 3192–3200.
  33. Finding global homophily in graph neural networks when meeting heterophily. In International Conference on Machine Learning, 13242–13256. PMLR.
  34. Expertise and dynamics within crowdsourced musical knowledge curation: A case study of the genius platform. In Proceedings of the International AAAI Conference on Web and Social Media, volume 15, 373–384.
  35. Revisiting heterophily for graph neural networks. Advances in neural information processing systems, 35: 1362–1375.
  36. Provably powerful graph networks. Advances in neural information processing systems, 32.
  37. Invariant and Equivariant Graph Networks. In International Conference on Learning Representations.
  38. Milgram, S. 1967. The small world problem. Psychology today, 2(1): 60–67.
  39. Weisfeiler and Leman Go Neural: Higher-Order Graph Neural Networks. Proceedings of the AAAI Conference on Artificial Intelligence, 33(01): 4602–4609.
  40. Propagation kernels: efficient graph kernels from propagated information. Machine Learning, 102: 209–245.
  41. Quantifying randomness in real networks. Nature communications, 6(1): 8627.
  42. Geom-GCN: Geometric Graph Convolutional Networks. In International Conference on Learning Representations.
  43. Principled Simplicial Neural Networks for Trajectory Prediction. In Proceedings of the 38th International Conference on Machine Learning, volume 139, 9020–9029. PMLR.
  44. Multi-scale attributed node embedding. Journal of Complex Networks, 9(2): 1–22.
  45. Random walks on simplicial complexes and the normalized Hodge 1-Laplacian. SIAM Review, 62(2): 353–391.
  46. Pitfalls of Graph Neural Network Evaluation. CoRR, abs/1811.05868.
  47. Weisfeiler-lehman graph kernels. Journal of Machine Learning Research, 12(9).
  48. Efficient graphlet kernels for large graph comparison. In Artificial intelligence and statistics, 488–495. PMLR.
  49. The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains. IEEE Signal Processing Magazine, 30(3): 83–98.
  50. An Overview of Microsoft Academic Service (MAS) and Applications. In Proceedings of the 24th International Conference on World Wide Web. ACM Press.
  51. Statistical evaluation of the predictive toxicology challenge 2000–2001. Bioinformatics, 19(10): 1183–1193.
  52. Social structure of facebook networks. Physica A: Statistical Mechanics and its Applications, 391(16): 4165–4180.
  53. Graph Attention Networks. In International Conference on Learning Representations (ICLR).
  54. How Powerful are Spectral Graph Neural Networks. In International Conference on Machine Learning (ICML).
  55. The reduction of a graph to canonical form and the algebra which appears therein. NTI, Series, 2(9): 12–16.
  56. Simplifying Graph Convolutional Networks. In Chaudhuri, K.; and Salakhutdinov, R., eds., Proceedings of the 36th International Conference on Machine Learning, volume 97 of Proceedings of Machine Learning Research, 6861–6871. PMLR.
  57. How powerful are graph neural networks? In International Conference on Learning Representations (ICLR).
  58. Two sides of the same coin: Heterophily and oversmoothing in graph convolutional neural networks. arXiv:2102.06462.
  59. Deep Graph Kernels. In Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD ’15, 1365–1374. New York, NY, USA: Association for Computing Machinery. ISBN 9781450336642.
  60. Simplicial convolutional neural networks. In ICASSP, 8847–8851.
  61. A generalized simplicial model and its application. arXiv:2309.02851.
  62. Revisiting Semi-Supervised Learning with Graph Embeddings. In Proceedings of The 33rd International Conference on Machine Learning, volume 48 of Proceedings of Machine Learning Research, 40–48. New York, New York, USA: PMLR.
  63. Identifying vital nodes through augmented random walks on higher-order networks. arXiv:2305.06898.
  64. Influential Simplices Mining via Simplicial Convolutional Network. arXiv:2307.05841.
  65. Hyper-Null Models and Their Applications. Entropy, 25(10): 1390.
  66. DRGCN: Dynamic Evolving Initial Residual for Deep Graph Convolutional Networks. arXiv:2302.05083.
  67. An end-to-end deep learning architecture for graph classification. In Proceedings of the AAAI conference on artificial intelligence, volume 32.
  68. Beyond homophily in graph neural networks: Current limitations and effective designs. Advances in Neural Information Processing Systems, 33: 7793–7804.
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