Advertisement

Spectral Clustering: Left-Right-Oscillate Algorithm for Detecting Communities

  • Pavla Dráždilová
  • Jan Martinovič
  • Kateřina Slaninová
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 185)

Abstract

Detection of communities in the complex networks is an actual problem solved in research area. The paper describes a new algorithm for this purpose. Left-Right-Oscillate algorithm (LRO) is based on spectral ordering of graph vertices. This approach allows us to detect a desired community – either by the size of the smallest communities or by the level of modularity. Since the LRO algorithm detects efficiently communities in large network even when these are not sharply partitioned, it turns to be specially suitable for the analysis of social, complex or coauthor networks. In this paper, proposed algorithm is used for finding communities in a large coauthor network - DBLP.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bastian, M., Heymann, S., Jacomy, M.: Gephi: An open source software for exploring and manipulating networks (2009)Google Scholar
  2. 2.
    Bruns, A.: How long is a tweet? mapping dynamic conversation networks on twitter using gawk and gephi. Information Communication Society, 1–29 (December 2011)Google Scholar
  3. 3.
    Cheng, D., Kannan, R., Vempala, S., Wang, G.: On a recursive spectral algorithm for clustering from pairwise similarities. Technical report, MIT (2003)Google Scholar
  4. 4.
    Chung, F.R.K.: Spectral Graph Theory, vol. 92. American Mathematical Society (1997)Google Scholar
  5. 5.
    Clauset, A., Newman, M.E.J., Moore, C.: Finding community structure in very large networks. Physical Review E 70(6), 1–6 (2004)CrossRefGoogle Scholar
  6. 6.
    Dasgupta, A., Hopcroft, J., Kannan, R., Mitra, P.: Spectral Clustering by Recursive Partitioning. In: Azar, Y., Erlebach, T. (eds.) ESA 2006. LNCS, vol. 4168, pp. 256–267. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  7. 7.
    Ding, C., He, X.: Linearized cluster assignment via spectral ordering. In: Twenty First International Conference on Machine Learning, ICML 2004, vol. 21, p. 30 (2004)Google Scholar
  8. 8.
    Dorogovtsev, S.N., Mendes, J.F.F.: Evolution of Networks: From Biological Nets to the Internet and WWW, vol. 57. Oxford University Press (2003)Google Scholar
  9. 9.
    Flake, G.W., Lawrence, S., Giles, C.L., Coetzee, F.M.: Self-organization and identification of web communities. Computer 35(3), 66–70 (2002)CrossRefGoogle Scholar
  10. 10.
    Freeman, L.: Centrality in social networks conceptual clarification. Social Networks 1(3), 215–239 (1979)CrossRefGoogle Scholar
  11. 11.
    Garton, L., Haythornthwaite, C., Wellman, B.: Studying online social networks. Journal of Computer-Mediated Communication 3(1) (1997)Google Scholar
  12. 12.
    Girvan, M., Newman, M.E.J.: Community structure in social and biological networks. Proceedings of the National Academy of Sciences of the United States of America 99(12), 7821–7826 (2002)MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Granovetter, M.S.: The Strength of Weak Ties 78(6), 1360–1380 (1973)Google Scholar
  14. 14.
    Komzsik, L.: Lanczos Method: Evolution and Application. Society for Industrial and Applied Mathematics, Philadelphia (2003)Google Scholar
  15. 15.
    Leetaru, K.H.: Culturomics 2.0: Forecasting large-scale human behavior using global news media tone in time and space. First Monday 16(9), 2 (2011)Google Scholar
  16. 16.
    Montanari, A.: Community detection via spectral methods. Signal Processing (1) (2011)Google Scholar
  17. 17.
    Newman, M.E.J.: The structure and function of complex networks. SIAM Review 45(2), 58 (2003)CrossRefGoogle Scholar
  18. 18.
    Newman, M.E.J.: Detecting community structure in networks. The European Physical Journal B Condensed Matter 38(2), 321–330 (2004)CrossRefGoogle Scholar
  19. 19.
    Newman, M.E.J.: Finding community structure in networks using the eigenvectors of matrices. Physical Review E - Statistical, Nonlinear and Soft Matter Physics 74(3 pt. 2), 36104 (2006)CrossRefGoogle Scholar
  20. 20.
    Newman, M.E.J.: Modularity and community structure in networks. Proceedings of the National Academy of Sciences of the United States of America 103(23), 8577–8582 (2006)CrossRefGoogle Scholar
  21. 21.
    Newman, M.E.J., Barabasi, A.-L., Watts, D.J.: The structure and dynamics of networks, vol. 107. Princeton University Press (2006)Google Scholar
  22. 22.
    Newman, M.E.J., Girvan, M.: Finding and evaluating community structure in networks. Physical Review E - Statistical, Nonlinear and Soft Matter Physics 69(2 pt. 2), 16 (2004)Google Scholar
  23. 23.
    Obadi, G., Drázdilová, P., Martinovic, J., Slaninová, K., Snásel, V.: Using spectral clustering for finding students’ patterns of behavior in social networks. In: DATESO, pp. 118–130 (2010)Google Scholar
  24. 24.
    Pothen, A., Simon, H.D., Liou, K.-P.: Partitioning sparse matrices with eigenvectors of graphs. SIAM J. Matrix Anal. Appl. 11(3), 430–452 (1990)MathSciNetMATHCrossRefGoogle Scholar
  25. 25.
    Schaeffer, S.: Graph clustering. Computer Science Review 1(1), 27–64 (2007)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Slaninová, K., Martinovič, J., Novosád, T., Dráždilová, P., Vojáček, L., Snášel, V.: Web site community analysis based on suffix tree and clustering algorithm. In: Proceedings - 2011 IEEE/WIC/ACM International Joint Conferences on Web Intelligence and Intelligent Agent Technology - Workshops, WI-IAT 2011, pp. 110–113 (2011)Google Scholar
  27. 27.
    Tyler, J., Wilkinson, D., Huberman, B.: E-mail as spectroscopy: Automated discovery of community structure within organizations. The Information Society 21(2), 143–153 (2005)CrossRefGoogle Scholar
  28. 28.
    White, S., Smyth, P.: A spectral clustering approach to finding communities in graphs. In: Proceedings of the Fifth SIAM International Conference on Data Mining, vol. 119, p. 274 (2005)Google Scholar
  29. 29.
    Zarei, M., Samani, K.A.: Eigenvectors of network complement reveal community structure more accurately. Physica A: Statistical Mechanics and its Applications 388(8), 1721–1730 (2009)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Pavla Dráždilová
    • 1
  • Jan Martinovič
    • 1
  • Kateřina Slaninová
    • 1
  1. 1.Faculty of Electrical Engineering and Computer ScienceVŠB - Technical University of OstravaOstravaCzech Republic

Personalised recommendations