A Mean-Field Variational Bayesian Approach to Detecting Overlapping Communities with Inner Roles Using Poisson Link Generation

  • Gianni CostaEmail author
  • Riccardo Ortale
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9897)


A novel model-based machine-learning approach is presented for the unsupervised and exploratory analysis of node affiliations to overlapping communities with roles in networks. At the heart of our approach is a new Bayesian probabilistic generative model of directed networks, that treats roles as abstract behavioral classes explaining node linking behavior. A generalized weighted instance of directed affiliation modeling rules the strength of node participation in communities with whichever role through Gamma priors. Moreover, link establishment between nodes is governed by a Poisson distribution. The latter is parameterized so that, the stronger the affiliations of two nodes to common communities with respective roles, the more likely it is the formation of a connection. A coordinate-ascent algorithm is designed to implement mean-field variational inference for affiliation analysis and link prediction. A comparative experimentation on real-world networks demonstrates the superiority of our approach in community compactness, link prediction and scalability.


  1. 1.
    Bishop, C.M.: Pattern Recognition and Machine Learning. Springer, New York (2006)zbMATHGoogle Scholar
  2. 2.
    Blei, D., Kucukelbir, A., McAuliffe, J.: Variational inference: a review forstatisticians. arXiv:1601.00670 (2016)
  3. 3.
    Chatterjee, N., Sinha, S.: Understanding the mind of a worm: hierarchical network structure underlying nervous system function in C. elegans. In: Banerjee, R., Chakrabarti, B.K. (eds) Progress in Brain Research, pp. 145–153. Elsevier (2008)Google Scholar
  4. 4.
    Costa, G., Ortale, R.: A bayesian hierarchical approach for exploratory analysis of communities and roles in social networks. In: Proceedings of the IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining, pp. 194–201 (2012)Google Scholar
  5. 5.
    Costa, G., Ortale, R.: Probabilistic analysis of communities and inner roles in networks: Bayesian generative models and approximate inference. Soc. Netw. Anal. Min. 3(4), 1015–1038 (2013)CrossRefGoogle Scholar
  6. 6.
    Costa, G., Ortale, R.: A unified generative bayesian model for communitydiscovery and role assignment based upon latent interaction factors. In: IEEE/ACMASONAM, pp. 93–100 (2014)Google Scholar
  7. 7.
    Costa, G., Ortale, R.: Model-based collaborative personalized recommendation on signed social rating networks. ACM Trans. Int. Technol. 16(3), 20:1–20:21 (2016)CrossRefGoogle Scholar
  8. 8.
    Creamer, G., Rowe, R., Hershkop, S., Stolfo, S.J.: Segmentation and automated social hierarchy detection through email network analysis. In: Zhang, H., Spiliopoulou, M., Mobasher, B., Giles, C.L., McCallum, A., Nasraoui, O., Srivastava, J., Yen, J. (eds.) SNAKDD/WebKDD -2007. LNCS (LNAI), vol. 5439, pp. 40–58. Springer, Heidelberg (2009). doi: 10.1007/978-3-642-00528-2_3 CrossRefGoogle Scholar
  9. 9.
    Gopalan, P., Hofman, J., Blei, D.: Scalable recommendation with hierarchical Poisson factorization. In: UAI, pp. 326–335 (2015)Google Scholar
  10. 10.
    Henderson, K., Eliassi-Rad, T., Papadimitriou, S., Faloutsos, C.: HCDF: a hybrid community discovery framework. In: Proceedings of SIAM International Conference on Data Mining, pp. 754–765 (2010)Google Scholar
  11. 11.
    Henderson, K., Eliassi Rad, T.: Applying latent dirichlet allocation to group discovery in large graphs. In: Proceedings of ACM Symposium on Applied Computing, pp. 1456–1461 (2009)Google Scholar
  12. 12.
    Lattanzi, S., Sivakumar, D.: Affiliation networks. In: ACM STOC, pp. 427–434 (2009)Google Scholar
  13. 13.
    McAuley, J., Leskovec, J.: Learning to discover social circles in ego networks. In: NIPS, pp. 548–556 (2012)Google Scholar
  14. 14.
    Pathak, N., Delong, C., Banerjee, A., Erickson, K.: Social topic models for community extraction. In: Proceedings of KDD Workshop on Social Network Mining and Analysis (2008)Google Scholar
  15. 15.
    Sohn, Y., Choi, M.-K., Ahn, Y.-Y., Lee, J., Jeong, J.: Topological cluster analysis reveals the systemic organization of the caenorhabditis elegans connectome. PLoS Comput. Biol. 7(5), e1001139 (2011)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Watts, D.J., Strogatz, S.H.: Collective dynamics of small-world networks. Nature 393(6684), 440–442 (1998)CrossRefGoogle Scholar
  17. 17.
    White, J.G., Southgate, E., Thompson, J.N., Brenner, S.: The structure of the nervous system of the nematode caenorhabditis elegans. Philos. Trans. Royal Soc. B Biol. Sci. 314(1165), 1–340 (1986)CrossRefGoogle Scholar
  18. 18.
    Yang, J., Leskovec, J.: Structure, overlaps of ground-truth communities in networks. ACM Trans. Intell. Syst. Technol. 5(2), 26:1–26:35 (2014)CrossRefGoogle Scholar
  19. 19.
    Yang, J., McAuley, J., Leskovec, J.: Detecting cohesive and 2-mode communities in directed and undirected networks. In: WSDM, pp. 323–332 (2014)Google Scholar
  20. 20.
    Zhang, H., Qiu, B., Giles, C.L., Foley, H.C., Yen, J.: An LDA-based community structure discovery approach for large-scale social networks. In: IEEE ISI, pp. 200–207 (2007)Google Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.ICAR-CNRRendeItaly

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