Abstract
We propose an overlapping community model based on the Affiliation Graph Model (AGM), that exhibits the pluralistic homophily property that the probability of a link between nodes increases with increasing number of shared communities. We take inspiration from the Mixed Membership Stochastic Blockmodel (MMSB), in proposing an edgewise community affiliation. This allows decoupling of community affiliations between nodes, opening the way to scalable inference. We show that our model corresponds to an AGM with soft community affiliations and develop a scalable algorithm based on a Stochastic Gradient Riemannian Langevin Dynamics (SGRLD) sampler. Empirical results show that the model can scale to network sizes that are beyond the capabilities of MCMC samplers of the standard AGM. We achieve comparable performance in terms of accuracy and run-time efficiency to scalable MMSB samplers.
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References
Abadi, M., et al.: TensorFlow: Large-scale machine learning on heterogeneous systems (2015). https://www.tensorflow.org/
Airoldi, E.M., Blei, D.M., Fienberg, S.E., Xing, E.P.: Mixed membership stochastic blockmodels. J. Mach. Learn. Res. 9(Sep), 1981–2014 (2008)
Butland, G., et al.: Interaction network containing conserved and essential protein complexes in escherichia coli. Nature 433(7025), 531 (2005)
Corman, S.R., Kuhn, T., McPhee, R.D., Dooley, K.J.: Studying complex discursive systems. Centering resonance analysis of communication. Hum. Commun. Res. 28(2), 157–206 (2002)
El-Helw, I., Hofman, R., Bal, H.E.: Towards fast overlapping community detection. In: 2016 16th IEEE/ACM International Symposium on Cluster, Cloud and Grid Computing (CCGrid), pp. 175–178. IEEE (2016)
Evans, T.S.: Clique graphs and overlapping communities. J. Stat. Mech: Theory Exp. 2010(12), P12037 (2010)
Fruchterman, T.M., Reingold, E.M.: Graph drawing by force-directed placement. Software Pract. Exper. 21(11), 1129–1164 (1991)
Girolami, M., Calderhead, B.: Riemann manifold Langevin and Hamiltonian Monte Carlo methods. J. Roy. Stat. Soc. B (Stat. Methodol.) 73(2), 123–214 (2011)
Gopalan, P.K., Gerrish, S., Freedman, M., Blei, D.M., Mimno, D.M.: Scalable inference of overlapping communities. In: Advances in Neural Information Processing Systems, pp. 2249–2257 (2012)
Gschwind, T., Irnich, S., Furini, F., et al.: Social network analysis and community detection by decomposing a graph into relaxed cliques. Technical report (2015)
Lancichinetti, A., Fortunato, S., Kertesz, J.: Detecting the overlapping and hierarchical community structure in complex networks. New J. Phys. 11(3), 033015 (2009)
Leskovec, J., Kleinberg, J., Faloutsos, C.: Graph evolution: densification and shrinking diameters. ACM Trans. Knowl. Discovery Data (TKDD) 1(1), 2 (2007)
Li, W., Ahn, S., Welling, M.: Scalable MCMC for mixed membership stochastic blockmodels. In: Artificial Intelligence and Statistics, pp. 723–731 (2016)
Miller, K., Jordan, M.I., Griffiths, T.L.: Nonparametric latent feature models for link prediction. In: Advances in neural information processing systems, pp. 1276–1284 (2009)
Mørup, M., Schmidt, M.N., Hansen, L.K.: Infinite multiple membership relational modeling for complex networks. In: 2011 IEEE International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6. IEEE (2011)
Nelson, D.L., McEvoy, C.L., Schreiber, T.A.: The University of South Florida free association, rhyme, and word fragment norms. Behav. Res. Methods Instrum. Comput. 36(3), 402–407 (2004)
Newman, M.E.: The structure and function of complex networks. SIAM Rev. 45(2), 167–256 (2003)
Patterson, S., Teh, Y.W.: Stochastic gradient Riemannian Langevin dynamics on the probability simplex. In: Advances in Neural Information Processing Systems, pp. 3102–3110 (2013)
Roberts, G.O., Rosenthal, J.S.: Optimal scaling of discrete approximations to Langevin diffusions. J. Roy. Stat. Soc. B (Stat. Methodol.) 60(1), 255–268 (1998)
Traud, A.L., Frost, C., Mucha, P.J., Porter, M.A.: Visualization of communities in networks. Chaos Interdisc. J. Nonlinear Sci. 19(4), 041104 (2009)
Welling, M., Teh, Y.W.: Bayesian learning via stochastic gradient Langevin dynamics. In: Proceedings of the 28th International Conference on Machine Learning (ICML-11), pp. 681–688 (2011)
Yang, J., Leskovec, J.: Community-affiliation graph model for overlapping network community detection. In: 2012 IEEE 12th International Conference on Data Mining (ICDM), pp. 1170–1175. IEEE (2012)
Yang, J., Leskovec, J.: Overlapping community detection at scale: a nonnegative matrix factorization approach. In: Proceedings of the Sixth ACM International Conference on Web Search and Data Mining, pp. 587–596. ACM (2013)
Yang, J., Leskovec, J.: Defining and evaluating network communities based on ground-truth. Knowl. Inf. Syst. 42(1), 181–213 (2013). https://doi.org/10.1007/s10115-013-0693-z
Zhou, M.: Infinite edge partition models for overlapping community detection and link prediction. In: Artificial Intelligence and Statistics (AISTATS), pp. 1135–1143 (2015)
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This project has been funded by Science Foundation Ireland under Grant No. SFI/12/RC/2289.
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Laitonjam, N., Huáng, W., Hurley, N.J. (2020). A Soft Affiliation Graph Model for Scalable Overlapping Community Detection. In: Brefeld, U., Fromont, E., Hotho, A., Knobbe, A., Maathuis, M., Robardet, C. (eds) Machine Learning and Knowledge Discovery in Databases. ECML PKDD 2019. Lecture Notes in Computer Science(), vol 11906. Springer, Cham. https://doi.org/10.1007/978-3-030-46150-8_30
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