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Evaluating the Community Structures from Network Images Using Neural Networks

  • Md. Khaledur Rahman
  • Ariful AzadEmail author
Conference paper
Part of the Studies in Computational Intelligence book series (SCI, volume 881)

Abstract

Communities or clusters in a network unveil important structures of a physical or social system. Suppose a Google image search for “complex network” returns thousands of network images. Can we infer the community structures in the original networks just from these images? Traditional community detection algorithms will fail in this case because they do not work with images. We developed an approach where convolutional neural networks (CNNs) are trained to reveal community information from images of complex networks. We trained three CNNs with images of simulated networks having ground truth communities. The training process uses state-of-the-art community detection, graph drawing, and deep learning training algorithms. The trained networks are then used to predict the number of communities and the modularity score (a measure of community structure of networks) for real-world networks. We formulated these two tasks as a classification and a regression problem and used appropriate loss functions for them. The CNN models can attain test accuracy of 81% and 33.3% for simulated and real networks, respectively. This result is statistically significant as can be seen by Spearman’s rank correlation of 0.77 with a p-value of \(6.2\times 10^{-13}\) for real-world networks.

Keywords

Community detection Convolutional neural networks Graph layout 

Notes

Acknowledgements

Funding for this work was provided by the Indiana University Grand Challenge Precision Health Initiative.

References

  1. 1.
    Blondel, V.D., Guillaume, J.-L., Lambiotte, R., Lefebvre, E.: Fast unfolding of communities in large networks. J. Stat. Mech: Theory Exp. 2008(10), P10008 (2008)CrossRefGoogle Scholar
  2. 2.
    Casas-Roma, J., Herrera-Joancomartí, J., Torra, V.: Anonymizing graphs: measuring quality for clustering. Knowl. Inf. Syst. 44(3), 507–528 (2015)CrossRefGoogle Scholar
  3. 3.
    Foggia, P., Percannella, G., Sansone, C., Vento, M.: Benchmarking graph-based clustering algorithms. Image Vis. Comput. 27(7), 979–988 (2009)CrossRefGoogle Scholar
  4. 4.
    Fruchterman, T.M., Reingold, E.M.: Graph drawing by force-directed placement. Softw. Pract. Exp. 21(11), 1129–1164 (1991)CrossRefGoogle Scholar
  5. 5.
    Girvan, M., Newman, M.: Community structure in social and biological networks. Proc. Nat. Acad. Sci. 99(12), 7821–7826 (2002)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Hauke, J., Kossowski, T.: Comparison of values of Pearson’s and Spearman’s correlation coefficients on the same sets of data. Quaest. Geogr. 30(2), 87–93 (2011)CrossRefGoogle Scholar
  7. 7.
    He, K., Zhang, X., Ren, S., Sun, J.: Deep residual learning for image recognition. In: Proceedings of the IEEE CVPR, pp. 770–778 (2016)Google Scholar
  8. 8.
    Hinton, G., Deng, L., Yu, D., Dahl, G., Mohamed, A.-R., Jaitly, N., Senior, A., Vanhoucke, V., Nguyen, P., Kingsbury, B., et al.: Deep neural networks for acoustic modeling in speech recognition. IEEE Sig. Process. Mag. 29, 82–97 (2012)CrossRefGoogle Scholar
  9. 9.
    Huang, G., Liu, Z., Van Der Maaten, L., Weinberger, K.Q.: Densely connected convolutional networks. In: Proceedings of the IEEE Conference on CVPR, pp. 4700–4708 (2017)Google Scholar
  10. 10.
    Ioffe, S., Szegedy, C.: Batch normalization: accelerating deep network training by reducing internal covariate shift. arXiv preprint arXiv:1502.03167 (2015)
  11. 11.
    Jain, A.K., Mao, J., Mohiuddin, K.M.: Artificial neural networks: a tutorial. Computer 29(3), 31–44 (1996)CrossRefGoogle Scholar
  12. 12.
    Kingma, D.P., Ba, J.: Adam: a method for stochastic optimization. arXiv preprint arXiv:1412.6980 (2014)
  13. 13.
    Krizhevsky, A., Sutskever, I., Hinton, G.E.: Imagenet classification with deep convolutional neural networks. In: Advances in Neural Information Processing Systems, pp. 1097–1105 (2012)Google Scholar
  14. 14.
    Lancichinetti, A., Fortunato, S., Radicchi, F.: Benchmark graphs for testing community detection algorithms. Phys. Rev. E 78(4), 046110 (2008)CrossRefGoogle Scholar
  15. 15.
    Min, S., Lee, B., Yoon, S.: Deep learning in bioinformatics. Brief. Bioinform. 18(5), 851–869 (2017)Google Scholar
  16. 16.
    Newman, M.E.: Fast algorithm for detecting community structure in networks. Phys. Rev. E 69(6), 066133 (2004)CrossRefGoogle Scholar
  17. 17.
    Newman, M.E., Girvan, M.: Finding and evaluating community structure in networks. Phys. Rev. E 69(2), 026113 (2004)CrossRefGoogle Scholar
  18. 18.
    Noack, A.: Energy models for graph clustering. J. Graph Algorithms Appl. 11(2), 453–480 (2007)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Robbins, H., Monro, S.: A stochastic approximation method. Ann. Math. Stat. 22(6), 400–407 (1951)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Srivastava, N., Hinton, G., Krizhevsky, A., Sutskever, I., Salakhutdinov, R.: Dropout: a simple way to prevent neural networks from overfitting. J. Mach. Learn. Res. 15(1), 1929–1958 (2014)MathSciNetzbMATHGoogle Scholar
  21. 21.
    Tian, F., Gao, B., Cui, Q., Chen, E., Liu, T.-Y.: Learning deep representations for graph clustering. In: AAAI Conference on Artificial Intelligence (2014)Google Scholar
  22. 22.
    Wakita, K., Tsurumi, T.: Finding community structure in mega-scale social networks. In: 16th Proceedings of WWW, pp. 1275–1276. ACM (2007)Google Scholar
  23. 23.
    Yosinski, J., Clune, J., Bengio, Y., Lipson, H.: How transferable are features in deep neural networks? In: Advances in Neural Information Processing Systems, pp. 3320–3328 (2014)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Computer ScienceIndiana University BloomingtonBloomingtonUSA
  2. 2.Department of Intelligent Systems EngineeringIndiana University BloomingtonBloomingtonUSA

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