Abstract
This paper presents a novel spectral algorithm with additive clustering, designed to identify overlapping communities in networks. The algorithm is based on geometric properties of the spectrum of the expected adjacency matrix in a random graph model that we call stochastic blockmodel with overlap (SBMO). An adaptive version of the algorithm, that does not require the knowledge of the number of hidden communities, is proved to be consistent under the SBMO when the degrees in the graph are (slightly more than) logarithmic. The algorithm is shown to perform well on simulated data and on real-world graphs with known overlapping communities.
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References
Airoldi, E., Blei, D., Fienberg, S., Xing, E.: Mixed membership stochastic blockmodels. J. Mach. Learn. Res. 9, 1981–2014 (2008)
Anandkumar, A., Ge, R., Hsu, D., Kakade, S.: A tensor spectral approach to learning mixed membership community models. JMLR 15(1), 2239–2312 (2014)
Arthur, D., Vassilvitskii, S.: k-means++: the advantage of careful seeding. In: Proceedings of the 18th ACM-SIAM Symposium on Discrete Algorithms (2007)
Ball, B., Karrer, B., Newman, M.E.: An efficient and principled way for detecting communities in networks. Phys. Rev. E 84, 036103 (2011)
Chatterjee, S.: Matrix estimation by universal singular value thresholding. Ann. Stat. 43(1), 177–214 (2015)
Holland, P.W., Leinhardt, S.: Stochastic blockmodels: first steps. Soc. Netw. 5(2), 109–137 (1983)
Karrer, B., Newman, M.E.: Stochastic blockmodels and community structure in networks. Phys. Rev. E 83, 016107 (2011)
Latouche, P., Birmelé, E., Ambroise, C.: Overlapping stochastic block models with applications to the French political blogoshpere. Ann. Appl. Stat. 5(1), 309–336 (2011)
Mc Auley, J., Leskovec, J.: Learning to discover social circles in ego networks. In: NIPS, vol. 25, pp. 548–556 (2012)
Newman, M.E.: Spectral methods for network community detection and graph partitioning. Phys. Rev. E 88, 042822 (2013)
Palla, G., Derényi, I., Farkas, I., Vicsek, T.: Uncovering the overlapping community structure of complex networks in nature and society. Nature 435, 814–818 (2005)
Rohe, K., Chatterjee, S., Yu, B.: Spectral clustering and the high-dimensional stochastic blockmodel. Ann. Stat. 39(4), 1978–1915 (2011)
Shepard, R.N., Arabie, P.: Additive clustering: representation of similarities as combinations of discrete overlapping properties. Psychol. Rev. 86(2), 87 (1979)
Von Luxburg, U.: A tutorial on spectral clustering. Stat. Comput. 17, 395–416 (2007)
Xie, J., Kelley, S., Szymanski, B.: Overlapping community detection in networks: state of the art and comparative study. ACM Comput. Surv. 45, 43 (2013)
Yang, J., Leskovec, J.: Community-affiliation graph model for overlapping community detection. In: IEEE International Conference on Data Mining (2012)
Zelnik-Manor, L., Perona, P.: Self-tuning spectral clustering. In: Advances in Neural Information Processing Systems (2004)
Zhang, S., Wang, R.-S., Zhang, X.-S.: Identification of overlapping community structure in complex networks using fuzzy c-means clustering. Phyisca A 374, 483–490 (2007)
Zhang, Y., Levina, E., Zhu, J.: Detecting overlapping communities in networks with spectral methods (2014). arXiv:1412.3432v1
Zhao, Y., Levina, E., Zhu, J.: Consistency of community detection in networks under degree-corrected stochastic block models. Ann. Stat. 40(4), 2266–2292 (2012)
Acknowledgment
The authors acknowledge the support of the French Agence Nationale de la Recherche (ANR) under reference ANR-11-JS02-005-01 (GAP).
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Kaufmann, E., Bonald, T., Lelarge, M. (2016). A Spectral Algorithm with Additive Clustering for the Recovery of Overlapping Communities in Networks. In: Ortner, R., Simon, H., Zilles, S. (eds) Algorithmic Learning Theory. ALT 2016. Lecture Notes in Computer Science(), vol 9925. Springer, Cham. https://doi.org/10.1007/978-3-319-46379-7_24
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DOI: https://doi.org/10.1007/978-3-319-46379-7_24
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