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Inferring Strange Behavior from Connectivity Pattern in Social Networks

  • Meng Jiang
  • Peng Cui
  • Alex Beutel
  • Christos Faloutsos
  • Shiqiang Yang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8443)

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.

Keywords

Adjacency Matrix Singular Vector Spectral Cluster Connectivity Pattern Social Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Becker, R.A., Volinsky, C., Wilks, A.R.: Fraud detection in telecommunications: History and lessons learned. Technometrics 52(1) (2010)Google Scholar
  2. 2.
    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)CrossRefGoogle Scholar
  3. 3.
    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)Google Scholar
  4. 4.
    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)Google Scholar
  5. 5.
    Fortunato, S.: Community detection in graphs. Physics Reports 486(3), 75–174 (2010)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Chen, J., Saad, Y.: Dense subgraph extraction with application to community detection. IEEE Transactions on Knowledge and Data Engineering 24(7), 1216–1230 (2012)CrossRefGoogle Scholar
  7. 7.
    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)Google Scholar
  8. 8.
    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)CrossRefGoogle Scholar
  9. 9.
    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)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Clauset, A., Newman, M.E., Moore, C.: Finding community structure in very large networks. Physical Review E 70(6), 066111 (2004)Google Scholar
  11. 11.
    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)Google Scholar
  12. 12.
    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)Google Scholar
  13. 13.
    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)Google Scholar
  14. 14.
    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)CrossRefGoogle Scholar
  15. 15.
    Ying, X., Wu, X.: On Randomness Measures for Social Networks. In: SIAM International Conference on Data Mining, vol. 9, pp. 709–720 (2009)Google Scholar
  16. 16.
    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)Google Scholar
  17. 17.
    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)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Meng Jiang
    • 1
  • Peng Cui
    • 1
  • Alex Beutel
    • 2
  • Christos Faloutsos
    • 2
  • Shiqiang Yang
    • 1
  1. 1.Department of Computer Science and TechnologyTsinghua UniversityBeijingChina
  2. 2.Computer Science DepartmentCarnegie Mellon UniversityUSA

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