Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
167 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
42 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

The Map Equation Goes Neural: Mapping Network Flows with Graph Neural Networks (2310.01144v4)

Published 2 Oct 2023 in cs.LG

Abstract: Community detection is an essential tool for unsupervised data exploration and revealing the organisational structure of networked systems. With a long history in network science, community detection typically relies on objective functions, optimised with custom-tailored search algorithms, but often without leveraging recent advances in deep learning. Recently, first works have started incorporating such objectives into loss functions for deep graph clustering and pooling. We consider the map equation, a popular information-theoretic objective function for unsupervised community detection, and express it in differentiable tensor form for optimisation through gradient descent. Our formulation turns the map equation compatible with any neural network architecture, enables end-to-end learning, incorporates node features, and chooses the optimal number of clusters automatically, all without requiring explicit regularisation. Applied to unsupervised graph clustering tasks, we achieve competitive performance against state-of-the-art deep graph clustering baselines in synthetic and real-world datasets.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (66)
  1. Deep graph clustering via mutual information maximization and mixture model. arXiv preprint arXiv:2205.05168, 2022.
  2. Link communities reveal multiscale complexity in networks. Nature, 466(7307):761–764, 2010.
  3. Exploring the limits of community detection strategies in complex networks. Sci. Rep., 3:2216, 2013.
  4. Unsupervised constrained community detection via self-expressive graph neural network. In Uncertainty in Artificial Intelligence, pp.  1078–1088. PMLR, 2021.
  5. Mapping nonlocal relationships between metadata and network structure with metadata-dependent encoding of random walks. Science Advances, 8(43):eabn7558, 2022. doi: 10.1126/sciadv.abn7558. URL https://www.science.org/doi/abs/10.1126/sciadv.abn7558.
  6. The expressive power of pooling in graph neural networks. arXiv preprint arXiv:2304.01575, 2023.
  7. Spectral clustering with graph neural networks for graph pooling. In International conference on machine learning, pp. 874–883. PMLR, 2020.
  8. Christopher Blöcker. Through the Coding-Lens – Community Detection and Beyond. PhD thesis, Umeå University, 2022.
  9. Structural deep clustering network. In Proceedings of the web conference 2020, pp.  1400–1410, 2020.
  10. Sean M Carroll. Spacetime and geometry. Cambridge University Press, 2019.
  11. Cluster-gcn: An efficient algorithm for training deep and large graph convolutional networks. In Proceedings of the 25th ACM SIGKDD international conference on knowledge discovery & data mining, pp.  257–266, 2019.
  12. Benchmarking graph neural networks. arXiv preprint arXiv:2003.00982, 2020.
  13. Mapping higher-order network flows in memory and multilayer networks with infomap. Algorithms, 10(4), 2017. ISSN 1999-4893. doi: 10.3390/a10040112. URL https://www.mdpi.com/1999-4893/10/4/112.
  14. Variable markov dynamics as a multi-focal lens to map multi-scale complex networks, 2022.
  15. Map equation with metadata: Varying the role of attributes in community detection. Phys. Rev. E, 100:022301, Aug 2019. doi: 10.1103/PhysRevE.100.022301. URL https://link.aps.org/doi/10.1103/PhysRevE.100.022301.
  16. T. S. Evans and R. Lambiotte. Line graphs, link partitions, and overlapping communities. Phys. Rev. E, 80:016105, Jul 2009. doi: 10.1103/PhysRevE.80.016105. URL https://link.aps.org/doi/10.1103/PhysRevE.80.016105.
  17. Soft clustering. Wiley Interdisciplinary Reviews: Computational Statistics, 12(1):e1480, 2020.
  18. Fast graph representation learning with pytorch geometric. arXiv preprint arXiv:1903.02428, 2019.
  19. Santo Fortunato. Community detection in graphs. Physics Reports, 486(3):75–174, 2010. ISSN 0370-1573. doi: https://doi.org/10.1016/j.physrep.2009.11.002. URL https://www.sciencedirect.com/science/article/pii/S0370157309002841.
  20. 20 years of network community detection. Nature Physics, 18(8):848–850, 2022.
  21. Neural message passing for quantum chemistry. In Doina Precup and Yee Whye Teh (eds.), Proceedings of the 34th International Conference on Machine Learning, volume 70 of Proceedings of Machine Learning Research, pp.  1263–1272. PMLR, 06–11 Aug 2017. URL https://proceedings.mlr.press/v70/gilmer17a.html.
  22. Finding the right scale of a network: efficient identification of causal emergence through spectral clustering. arXiv preprint arXiv:1908.07565, 2019.
  23. Node2vec: Scalable feature learning for networks. In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD ’16, pp.  855–864, New York, NY, USA, 2016. Association for Computing Machinery. ISBN 9781450342322. doi: 10.1145/2939672.2939754. URL https://doi.org/10.1145/2939672.2939754.
  24. Mapping biased higher-order walks reveals overlapping communities, 2023.
  25. Open graph benchmark: Datasets for machine learning on graphs. Advances in neural information processing systems, 33:22118–22133, 2020.
  26. David A. Huffman. A method for the construction of minimum-redundancy codes. Proceedings of the IRE, 40(9):1098–1101, 1952. doi: 10.1109/JRPROC.1952.273898.
  27. Semi-supervised classification with graph convolutional networks. In International Conference on Learning Representations, 2017. URL https://openreview.net/forum?id=SJU4ayYgl.
  28. Self-normalizing neural networks. Advances in neural information processing systems, 30, 2017.
  29. Network community detection via neural embeddings. arXiv preprint arXiv:2306.13400, 2023.
  30. R. Lambiotte and M. Rosvall. Ranking and clustering of nodes in networks with smart teleportation. Phys. Rev. E, 85:056107, May 2012. doi: 10.1103/PhysRevE.85.056107. URL https://link.aps.org/doi/10.1103/PhysRevE.85.056107.
  31. Community detection algorithms: A comparative analysis. Phys. Rev. E, 80:056117, 2009.
  32. Benchmark graphs for testing community detection algorithms. Phys. Rev. E, 78:046110, Oct 2008. doi: 10.1103/PhysRevE.78.046110. URL https://link.aps.org/doi/10.1103/PhysRevE.78.046110.
  33. Sign and basis invariant networks for spectral graph representation learning. arXiv preprint arXiv:2202.13013, 2022.
  34. Rethinking graph auto-encoder models for attributed graph clustering. IEEE Transactions on Knowledge and Data Engineering, 2022.
  35. Modularity optimization as a training criterion for graph neural networks. In Sean Cornelius, Kate Coronges, Bruno Gonçalves, Roberta Sinatra, and Alessandro Vespignani (eds.), Complex Networks IX, pp. 123–135, Cham, 2018. Springer International Publishing. ISBN 978-3-319-73198-8.
  36. M. E. J. Newman. Modularity and community structure in networks. Proceedings of the National Academy of Sciences, 103(23):8577–8582, 2006. doi: 10.1073/pnas.0601602103. URL https://www.pnas.org/doi/abs/10.1073/pnas.0601602103.
  37. PyTorch: An Imperative Style, High-Performance Deep Learning Library. In H. Wallach, H. Larochelle, A. Beygelzimer, F. d’Alché Buc, E. Fox, and R. Garnett (eds.), Advances in Neural Information Processing Systems 32, pp.  8024–8035. Curran Associates, Inc., 2019. URL http://papers.neurips.cc/paper/9015-pytorch-an-imperative-style-high-performance-deep-learning-library.pdf.
  38. Tiago P Peixoto. Efficient monte carlo and greedy heuristic for the inference of stochastic block models. Physical Review E, 89(1):012804, 2014.
  39. Implicit models, latent compression, intrinsic biases, and cheap lunches in community detection. arXiv preprint arXiv:2210.09186, 2022.
  40. Deepwalk: Online learning of social representations. In Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD ’14, pp.  701–710, New York, NY, USA, 2014. Association for Computing Machinery. ISBN 9781450329569. doi: 10.1145/2623330.2623732. URL https://doi.org/10.1145/2623330.2623732.
  41. Higher-order patterns reveal causal temporal scales in time series network data. In The First Learning on Graphs Conference, 2022.
  42. Jorma Rissanen. Modeling by shortest data description. Automatica, 14(5):465–471, 1978.
  43. M. Rosvall and C. T. Bergstrom. Multilevel Compression of Random Walks on Networks Reveals Hierarchical Organization in Large Integrated Systems. PLoS One, 6:e18209, 2011.
  44. Maps of random walks on complex networks reveal community structure. Proceedings of the National Academy of Sciences, 105(4):1118–1123, 2008. ISSN 0027-8424. doi: 10.1073/pnas.0706851105. URL https://www.pnas.org/content/105/4/1118.
  45. Memory in network flows and its effects on spreading dynamics and community detection. Nature Communications, 5(1):4630, Aug 2014. ISSN 2041-1723. doi: 10.1038/ncomms5630. URL https://doi.org/10.1038/ncomms5630.
  46. The graph neural network model. IEEE Transactions on Neural Networks, 20(1):61–80, 2009. doi: 10.1109/TNN.2008.2005605.
  47. Satu Elisa Schaeffer. Graph clustering. Computer science review, 1(1):27–64, 2007.
  48. Collective classification in network data. AI magazine, 29(3):93–93, 2008.
  49. C. E. Shannon. A mathematical theory of communication. Bell Syst. Tech. J., 27:379–423, 1948.
  50. Overlapping community detection with graph neural networks. arXiv preprint arXiv:1909.12201, 2019.
  51. Pitfalls of graph neural network evaluation. arXiv preprint arXiv:1811.05868, 2018.
  52. Normalized cuts and image segmentation. IEEE Transactions on pattern analysis and machine intelligence, 22(8):888–905, 2000.
  53. Mapping flows on weighted and directed networks with incomplete observations. Journal of Complex Networks, 9(6):cnab044, 12 2021. ISSN 2051-1329. doi: 10.1093/comnet/cnab044. URL https://doi.org/10.1093/comnet/cnab044.
  54. Community detection in networks using graph embeddings. Physical Review E, 103(2):022316, 2021.
  55. Graph clustering with graph neural networks. Journal of Machine Learning Research, 24(127):1–21, 2023. URL http://jmlr.org/papers/v24/20-998.html.
  56. Deep graph infomax. arXiv preprint arXiv:1809.10341, 2018.
  57. Multi-scale laplacian community detection in heterogeneous networks, 2023.
  58. Mgae: Marginalized graph autoencoder for graph clustering. In Proceedings of the 2017 ACM on Conference on Information and Knowledge Management, pp.  889–898, 2017.
  59. Attributed graph clustering: A deep attentional embedding approach. arXiv preprint arXiv:1906.06532, 2019.
  60. A comprehensive survey on community detection with deep learning. IEEE Trans. Neural Netw. Learn. Syst, 2022.
  61. How powerful are graph neural networks? In International Conference on Learning Representations, 2019. URL https://openreview.net/forum?id=ryGs6iA5Km.
  62. Hierarchical graph representation learning with differentiable pooling. Advances in neural information processing systems, 31, 2018.
  63. Soft clustering on graphs. Advances in neural information processing systems, 18, 2005.
  64. A survey of deep graph clustering: Taxonomy, challenge, and application. arXiv preprint arXiv:2211.12875, 2022.
  65. Attributed graph clustering via adaptive graph convolution. arXiv preprint arXiv:1906.01210, 2019.
  66. Clustering scientific publications based on citation relations: A systematic comparison of different methods. PLOS ONE, 11(4):1–23, 04 2016. doi: 10.1371/journal.pone.0154404. URL https://doi.org/10.1371/journal.pone.0154404.
Citations (1)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now