A Note on Clustering Difference by Maximizing Variation of Information

  • Nam P. NguyenEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9197)


In this paper, we investigate the problem of maximizing the difference between two partitions (or clusterings) of a complex network. Particularly, given the input network represented as an undirected graph and its initial partition X, we are interested in finding a partition Y such that the difference between X and Y, evaluated by the Variation of Information measure, is maximized. This problem is important in understanding fundamental properties of not only the network’s structural organization (via its clusters) but also the internal and mutual interactions among those structures in response to adversarial perturbation. We propose an approximation algorithm to define the new partition Y with a guarantee ratio of \(1 - \alpha - \beta \) (where \(\alpha \) and \(\beta \) are constants derived from the network’s initial partition), and present further optimization to improve the quality of the suggested approach.


Mutual Information Normalize Mutual Information Critical Node Marginal Gain Initial Partition 
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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  1. 1.
    Berkhin, P.: Survey Of Clustering Data Mining Techniques. Technical report, Accrue Software, San Jose, CA (2002)Google Scholar
  2. 2.
    Fortunato, S.: Community detection in graphs. Physics Reports 486(3–5), 75–174 (2010)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Atwood, J., Ribeiro, B., Towsley, D.: Efficient network generation under general preferential attachment. Computational Social Networks 2(1), 7 (2015)CrossRefGoogle Scholar
  4. 4.
    Atabati, O., Farzad, B.: A strategic model for network formation. Computational Social Networks 2(1), 1 (2015)CrossRefzbMATHGoogle Scholar
  5. 5.
    Alim, M.A., Nguyen, N.P., Dinh, T.N., Thai, M.T.: Structural vulnerability analysis of overlapping communities in complex networks. In: 2014 IEEE/WIC/ACM International Joint Conferences on Web Intelligence (WI) and Intelligent Agent Technologies (IAT), vol. 1, pp. 5–12, August 2014Google Scholar
  6. 6.
    Dinh, T.N., Xuan, Y., Thai, M.T., Pardalos, P.M., Znati, T.: On new approaches of assessing network vulnerability: hardness and approximation. IEEE/ACM Trans. Netw. 20(2), 609–619 (2012)CrossRefGoogle Scholar
  7. 7.
    Ventresca, M., Aleman, D.: Efficiently identifying critical nodes in large complex networks. Computational Social Networks 2(1), 6 (2015)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Peters, K., Buzna, L., Helbing, D.: Modelling of cascading effects and efficient response to disaster spreading in complex networks. IJCIS 4(1/2), 46–62 (2008)CrossRefGoogle Scholar
  9. 9.
    Kim, H., Beznosov, K., Yoneki, E.: A study on the influential neighbors to maximize information diffusion in online social networks. Computational Social Networks 2(1), 3 (2015)CrossRefGoogle Scholar
  10. 10.
    Fidler, D.: Power and loyalty defined by proximity to influential relations. Computational Social Networks 2(1), 2 (2015)CrossRefGoogle Scholar
  11. 11.
    Vinh, N.X., Epps, J., Bailey, J.: Information theoretic measures for clusterings comparison: Variants, properties, normalization and correction for chance. J. Mach. Learn. Res. 11, 2837–2854 (2010)MathSciNetGoogle Scholar
  12. 12.
    Meil, M.: Comparing clusteringsan information based distance. Journal of Multivariate Analysis 98(5), 873–895 (2007)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Aggarwal, C.C., Reddy, K.C.: Data Clustering: Algorithms and Applications. CRC Press (2013)Google Scholar
  14. 14.
    Caruana, R., Elhawary, M., Nguyen, N., Smith, C.: Meta clustering. In: 2013 IEEE 13th International Conference on Data Mining, pp. 107–118 (2006)Google Scholar
  15. 15.
    Dasgupta, S., Ng, V.: Mining clustering dimensions. In: Frnkranz, J., Joachims, T. (eds.), ICML, pp. 263–270. Omnipress (2010)Google Scholar
  16. 16.
    Jain, P., Meka, R., Dhillon, I.S.: Simultaneous unsupervised learning of disparate clusterings. Stat. Anal. Data Min. 1(3), 195–210 (2008)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Hong, X., Bailey, D.J.: Generation of alternative clusterings using the cami approach. In: SIAM SDM (2010)Google Scholar
  18. 18.
    Bae, E., Bailey, J., Dong, G.: A clustering comparison measure using density profiles and its application to the discovery of alternate clusterings. Data Min. Knowl. Discov. 21(3), 427–471 (2010)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Qi, Z., Davidson, I.: A principled and flexible framework for finding alternative clusterings. In: Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2009, pp. 717–726. ACM, New York (2009)Google Scholar
  20. 20.
    Cui, Y., Fern, X.Z., Dy, J.G.: Non-redundant multi-view clustering via orthogonalization. In: Proceedings of the 2007 Seventh IEEE International Conference on Data Mining, ICDM 2007, pp. 133–142. IEEE Computer Society, Washington, DC, (2007)Google Scholar
  21. 21.
    Gondek, D., Hofmann, T.: Non-redundant clustering with conditional ensembles. In: Proceedings of the Eleventh ACM SIGKDD International Conference on Knowledge Discovery in Data Mining, KDD 2005, pp. 70–77. ACM, New York (2005)Google Scholar
  22. 22.
    Dang, X.-H., Bailey, J.: A hierarchical information theoretic technique for the discovery of non linear alternative clusterings. In: Proceedings of the 16th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2010, pp. 573–582. ACM, New York (2010)Google Scholar
  23. 23.
    Vinh, N.X., Epps, J.: Mincentropy: a novel information theoretic approach for the generation of alternative clusterings. In: Proceedings of the 2010 IEEE International Conference on Data Mining, ICDM 2010, pp. 521–530. IEEE Computer Society, Washington, DC (2010)Google Scholar
  24. 24.
    Cover, T.M., Thomas, J.A.: Elements of Information Theory. Wiley-Interscience (1991)Google Scholar
  25. 25.
    Nguyen, N.P., Alim, M.A., Shen, Y., Thai, M.T.: Assessing network vulnerability in a community structure point of view. In: Proceedings of the 2013 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining, ASONAM 2013, pp. 231–235. ACM, New York (2013)Google Scholar
  26. 26.
    Vazirani, V.V.: Approximation Algorithms. Springer (2003)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Computer and Information SciencesTowson UniversityTowsonUSA

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