Abstract
Given a multimillion-node social network, how can we summarize connectivity pattern from the data, and how can we find unexpected user behavior? In this paper we study a complete graph from a large who-follows-whom network and spot lockstep behavior that large groups of followers connect to the same groups of followees. Our first contribution is that we study strange patterns on the adjacency matrix and in the spectral subspaces with respect to several flavors of lockstep. We discover that (a) the lockstep behavior on the graph shapes dense “block” in its adjacency matrix and creates “ray” in spectral subspaces, and (b) partially overlapping of the behavior shapes “staircase” in the matrix and creates “pearl” in the subspaces. The second contribution is that we provide a fast algorithm, using the discovery as a guide for practitioners, to detect users who offer the lockstep behavior. We demonstrate that our approach is effective on both synthetic and real data.
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References
Becker, R.A., Volinsky, C., Wilks, A.R.: Fraud detection in telecommunications: History and lessons learned. Technometrics 52(1) (2010)
Chau, D.H., Pandit, S., Faloutsos, C.: Detecting fraudulent personalities in networks of online auctioneers. In: Fürnkranz, J., Scheffer, T., Spiliopoulou, M. (eds.) PKDD 2006. LNCS (LNAI), vol. 4213, pp. 103–114. Springer, Heidelberg (2006)
Beutel, A., Xu, W., Guruswami, V., Palow, C., Faloutsos, C.: CopyCatch: stopping group attacks by spotting lockstep behavior in social networks. In: Proceedings of the 22nd International Conference on World Wide Web, pp. 119–130 (2013)
Leskovec, J., Kevin, J.L., Dasgupta, A., Mahoney, M.W.: Statistical properties of community structure in large social and information networks. In: Proceedings of the 17th International Conference on World Wide Web, pp. 695–704 (2008)
Fortunato, S.: Community detection in graphs. Physics Reports 486(3), 75–174 (2010)
Chen, J., Saad, Y.: Dense subgraph extraction with application to community detection. IEEE Transactions on Knowledge and Data Engineering 24(7), 1216–1230 (2012)
Zha, H., He, X., Ding, C., Simon, H., Gu, M.: Bipartite graph partitioning and data clustering. In: Proceedings of the Tenth International Conference on Information and Knowledge Management, pp. 25–32 (2001)
Günnemann, S., Boden, B., Färber, I., Seidl, T.: Efficient Mining of Combined Subspace and Subgraph Clusters in Graphs with Feature Vectors. In: Pei, J., Tseng, V.S., Cao, L., Motoda, H., Xu, G. (eds.) PAKDD 2013, Part I. LNCS, vol. 7818, pp. 261–275. Springer, Heidelberg (2013)
Chung, F., Lu, L.: The average distances in random graphs with given expected degrees. Proceedings of the National Academy of Sciences 99(25), 15879–15882 (2002)
Clauset, A., Newman, M.E., Moore, C.: Finding community structure in very large networks. Physical Review E 70(6), 066111 (2004)
Wakita, K., Tsurumi, T.: Finding community structure in mega-scale social networks. In: Proceedings of the 16th International Conference on World Wide Web, pp. 1275–1276 (2007)
Ng, A.Y., Jordan, M.I., Weiss, Y.: On spectral clustering: Analysis and an algorithm. In: Advances in Neural Information Processing Systems, vol. 2, pp. 849–856 (2002)
Huang, L., Yan, D., Taft, N., Jordan, M.I.: Spectral clustering with perturbed data. In: Advances in Neural Information Processing Systems, pp. 705–712 (2008)
Prakash, B.A., Sridharan, A., Seshadri, M., Machiraju, S., Faloutsos, C.: EigenSpokes: Surprising patterns and scalable community chipping in large graphs. In: Zaki, M.J., Yu, J.X., Ravindran, B., Pudi, V. (eds.) PAKDD 2010. LNCS, vol. 6119, pp. 435–448. Springer, Heidelberg (2010)
Ying, X., Wu, X.: On Randomness Measures for Social Networks. In: SIAM International Conference on Data Mining, vol. 9, pp. 709–720 (2009)
Wu, L., Ying, X., Wu, X., Zhou, Z.: Line orthogonality in adjacency eigenspace with application to community partition. In: Proceedings of the 22nd International Joint Conference on Artificial Intelligence, pp. 2349–2354 (2011)
Broder, A., Kumar, R., Maghoul, F., Raghavan, P., Rajagopalan, S., Stata, R., Tomkins, A., Wiener, J.: Graph structure in the web. Computer Networks 33(1), 309–320 (2000)
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Jiang, M., Cui, P., Beutel, A., Faloutsos, C., Yang, S. (2014). Inferring Strange Behavior from Connectivity Pattern in Social Networks. In: Tseng, V.S., Ho, T.B., Zhou, ZH., Chen, A.L.P., Kao, HY. (eds) Advances in Knowledge Discovery and Data Mining. PAKDD 2014. Lecture Notes in Computer Science(), vol 8443. Springer, Cham. https://doi.org/10.1007/978-3-319-06608-0_11
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DOI: https://doi.org/10.1007/978-3-319-06608-0_11
Publisher Name: Springer, Cham
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