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Alignment and Comparison of Directed Networks via Transition Couplings of Random Walks (2106.07106v3)

Published 13 Jun 2021 in cs.LG and stat.ML

Abstract: We describe and study a transport based procedure called NetOTC (network optimal transition coupling) for the comparison and alignment of two networks. The networks of interest may be directed or undirected, weighted or unweighted, and may have distinct vertex sets of different sizes. Given two networks and a cost function relating their vertices, NetOTC finds a transition coupling of their associated random walks having minimum expected cost. The minimizing cost quantifies the difference between the networks, while the optimal transport plan itself provides alignments of both the vertices and the edges of the two networks. Coupling of the full random walks, rather than their marginal distributions, ensures that NetOTC captures local and global information about the networks, and preserves edges. NetOTC has no free parameters, and does not rely on randomization. We investigate a number of theoretical properties of NetOTC and present experiments establishing its empirical performance.

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References (92)
  1. Abbe, E. (2018) Community detection and stochastic block models: Recent developments. Journal of Machine Learning Research, 18, 1–86. URL http://jmlr.org/papers/v18/16-480.html.
  2. 2015 IEEE 56th Annual Symposium on Foundations of Computer Science, 670–688.
  3. Babai, L. (2015) Graph isomorphism in quasipolynomial time. ArXiv, abs/1512.03547.
  4. In NeurIPS.
  5. In European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases.
  6. Neural Computation, 15, 1373–1396.
  7. Cambridge University Press. URL https://books.google.com/books?id=koHCDwAAQBAJ.
  8. ArXiv, abs/2302.08621. URL https://api.semanticscholar.org/CorpusID:257020095.
  9. In International Conference on Machine Learning, 1542–1553. PMLR.
  10. In Proceedings of the 39th International Conference on Machine Learning, Proceedings of Machine Learning Research, 3371–3416. PMLR.
  11. ArXiv, abs/2302.00713.
  12. In Computer Vision – ECCV 2010 (eds. K. Daniilidis, P. Maragos and N. Paragios), 492–505. Berlin, Heidelberg: Springer Berlin Heidelberg.
  13. IEEE Transactions on Pattern Analysis and Machine Intelligence, 26, 1367–1372.
  14. In Advances in Neural Information Processing Systems, vol. 19.
  15. ArXiv, abs/1711.06783.
  16. Abstracts of the 2020 SIGMETRICS/Performance Joint International Conference on Measurement and Modeling of Computer Systems.
  17. De La Rue, T. (2005) An introduction to joinings in ergodic theory. arXiv preprint math/0507429.
  18. de la Rue, T. (2009) Joinings in ergodic theory. In Encyclopedia of Complexity and Systems Science. Springer, New York, NY.
  19. Journal of Medicinal Chemistry, 34, 786–797.
  20. Probability Theory and Related Fields, 179, 29–115.
  21. In Advances in Neural Information Processing Systems.
  22. Ellis, M. H. (1976) The d¯¯𝑑\overline{d}over¯ start_ARG italic_d end_ARG-distance between two Markov processes cannot always be attained by a Markov joining. Israel Journal of Mathematics, 24, 269–273.
  23. Ellis, M. H. (1978) Distances between two-state Markov processes attainable by Markov joinings. Transactions of the American Mathematical Society, 241, 129–153.
  24. Ellis, M. H. (1980) On Kamae’s conjecture concerning the d-distance between two-state Markov processes. The Annals of Probability, 372–376.
  25. Ellis, M. H. et al. (1980) Conditions for attaining d¯¯𝑑\bar{d}over¯ start_ARG italic_d end_ARG by a Markovian joining. The Annals of Probability, 8, 431–440.
  26. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 13, 689–705.
  27. Cham: Springer International Publishing.
  28. In 2009 IEEE 12th International Conference on Computer Vision, 1295–1302.
  29. Journal of Evolutionary Economics, 20, 479–514.
  30. IEEE Transactions on Network Science and Engineering, 7, 1182–1197.
  31. Theory of Computing Systems, 1, 1–49.
  32. W. H. Freeman & Co.
  33. American Mathematical Society.
  34. IEEE Transactions on Pattern Analysis and Machine Intelligence, 18, 377 – 388.
  35. The Annals of Probability, 315–328.
  36. Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining.
  37. Hamilton, W. L. (2020) Graph representation learning. Synthesis Lectures on Artificial Intelligence and Machine Learning, 14, 1–159.
  38. Social Networks, 5, 109–137.
  39. Howard, R. A. (1960) Dynamic Programming and Markov Processes. John Wiley.
  40. Journal of Marriage and Family, 76, 967–982.
  41. In Advances in Neural Information Processing Systems, vol. 30.
  42. Journal of computational biology : a journal of computational molecular cell biology, 16 8, 989–99.
  43. Proceedings of the National Academy of Sciences of the United States of America, 100, 11394 – 11399.
  44. http://graphkernels.cs.tu-dortmund.de.
  45. Klau, G. W. (2009) A new graph-based method for pairwise global network alignment. BMC Bioinformatics, 10, S59 – S59.
  46. ArXiv, abs/1307.1690.
  47. In International Workshop on Cost-Sensitive Learning, 31–44. PMLR.
  48. Journal of The Royal Society Interface, 7, 1341 – 1354.
  49. Bioinformatics, 27 10, 1390–6.
  50. Lassalle, R. (2013) Causal transport plans and their monge–kantorovich problems. Stochastic Analysis and Applications, 36, 452 – 484.
  51. Applied Network Science, 4, 1–50.
  52. In IEEE International Conference on Computer Vision, vol. 2, 1482–1489 Vol. 2.
  53. In Advances in Neural Information Processing Systems, vol. 22.
  54. American Mathematical Soc.
  55. Cambridge University Press.
  56. European Journal of Operational Research, 176, 657–690.
  57. J. Mach. Learn. Res., 15, 3513–3540.
  58. Computational and Structural Biotechnology Journal, 18, 2647–2656.
  59. arXiv preprint arXiv:2003.06048.
  60. J. Symb. Comput., 60, 94–112.
  61. Mémoli, F. (2011) Gromov–Wasserstein distances and the metric approach to object matching. Foundations of Computational Mathematics, 11, 417–487.
  62. BMC Bioinformatics, 18.
  63. In Proceedings of the 7th ACM SIGCOMM conference on Internet measurement, 29–42.
  64. arXiv preprint arXiv:2107.11858.
  65. Journal of Machine Learning Research, 23, 1–52.
  66. Ornstein, D. S. (1973) An application of ergodic theory to probability theory. The Annals of Probability, 1, 43–58.
  67. Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery and data mining.
  68. Now Publishers, Inc.
  69. In International Conference on Machine Learning, 2664–2672. PMLR.
  70. Plummer, M. D. (2007) Graph factors and factorization: 1985–2003: a survey. Discrete Mathematics, 307, 791–821.
  71. In Joint International Workshops on Statistical Techniques in Pattern Recognition and Structural and Syntactic Pattern Recognition, 287–297. Springer.
  72. In Energy Minimization Methods in Computer Vision and Pattern Recognition, 171–186. Berlin, Heidelberg: Springer Berlin Heidelberg.
  73. Proceedings of the National Academy of Sciences, 105, 12763–12768.
  74. In Proceedings of the 2016 international conference on autonomous agents & multiagent systems, 468–476. International Foundation for Autonomous Agents and Multiagent Systems.
  75. Journal of Chemical Information and Computer Sciences, 43, 1906–1915.
  76. In International Conference on Machine Learning, 6275–6284.
  77. In International Conference on Knowledge Discovery and Data Mining, 965–973.
  78. Torr, P. H. S. (2003) Solving Markov Random Fields using Semi Definite Programming. AI & Society.
  79. IEEE Transactions on Pattern Analysis and Machine Intelligence, 26, 1526–1530.
  80. Algorithms, 13, 212.
  81. Springer-Verlag Berlin Heidelberg.
  82. Journal of Machine Learning Research, 11, 1201–1242.
  83. In Advances in Neural Information Processing Systems, 3052–3062.
  84. In International Conference on Machine Learning, 6932–6941.
  85. In Proceedings of the 2016 ACM on International Conference on Multimedia Retrieval, 167–174. New York, NY, USA: Association for Computing Machinery. URL https://doi.org/10.1145/2911996.2912035.
  86. In SIGMOD Conference.
  87. In COSN ’13.
  88. In Advances in Neural Information Processing Systems, vol. 31. Curran Associates, Inc.
  89. Neuroimage, 53, 1197–1207.
  90. IEEE Transactions on Pattern Analysis and Machine Intelligence, 31, 2227–2242.
  91. Zhang, S. (2000) Existence and application of optimal Markovian coupling with respect to non-negative lower semi-continuous functions. Acta Mathematica Sinica, 16, 261–270.
  92. IEEE Transactions on Pattern Analysis and Machine Intelligence, 38, 1774–1789.
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