Skip to main content

Efficient Solution of the Correlation Clustering Problem: An Application to Structural Balance

  • Conference paper
On the Move to Meaningful Internet Systems: OTM 2013 Workshops (OTM 2013)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 8186))

Abstract

One challenge for social network researchers is to evaluate balance in a social network. The degree of balance in a social group can be used as a tool to study whether and how this group evolves to a possible balanced state. The solution of clustering problems defined on signed graphs can be used as a criterion to measure the degree of balance in social networks. By considering the original definition of the structural balance, the optimal solution of the Correlation Clustering (CC) Problem arises as one possible measure. In this work, we contribute to the efficient solution of the CC problem by developing sequential and parallel GRASP metaheuristics. Then, by using our GRASP algorithms, we solve the problem of measuring the structural balance of large social networks.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Heider, F.: Attitudes and cognitive organization. Journal of Psychology 21, 107–112 (1946)

    Article  Google Scholar 

  2. Cartwright, D., Harary, F.: Structural balance: A generalization of heiders theory. Psychological Review 63, 277–293 (1956)

    Article  Google Scholar 

  3. Abell, P., Ludwig, M.: Structural balance: a dynamic perspective. Journal of Mathematical Sociology 33, 129–155 (2009)

    Article  MATH  Google Scholar 

  4. Doreian, P., Mrvar, A.: A partitioning approach to structural balance. Social Networks 18, 149–168 (1996)

    Article  Google Scholar 

  5. Doreian, P., Mrvar, A.: Partitioning signed social networks. Social Networks 31, 1–11 (2009)

    Article  Google Scholar 

  6. Inohara, T.: On conditions for a meeting not to reach a deadlock. Applied Mathematics and Computation 90, 1–9 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  7. Yang, B., Cheung, W., Liu, J.: Community mining from signed social networks. IEEE Transactions on Knowledge and Data Engineering 19, 1333–1348 (2007)

    Article  Google Scholar 

  8. Facchetti, G., Iacono, G., Altafini, C.: Computing global structural balance in large-scale signed social networks. Proceedings of the National Academy of Sciences of the United States of America 108, 20953–20958 (2011)

    Article  Google Scholar 

  9. Leskovec, J., Huttenlocher, D., Kleinberg, J.: Signed networks in social media. In: CHI 2010 Proceedings of the SIGCHI Conference on Human Factors in Computing Systems, pp. 1361–1370 (2010)

    Google Scholar 

  10. Srinivasan, A.: Local balancing influences global structure in social networks. Proceedings of the National Academy of Sciences of the United States of America 108, 1751–1752 (2011)

    Article  Google Scholar 

  11. Huffner, F., Betzler, N., Niedermeier, R.: Separator-based data reduction for signed graph balancing. Journal of Combinatorial Optimization 20, 335–360 (2010)

    Article  MathSciNet  Google Scholar 

  12. DasGupta, B., Encisob, G.A., Sontag, E., Zhanga, Y.: Algorithmic and complexity results for decompositions of biological networks into monotone subsystems. BioSystems 90, 161–178 (2007)

    Article  Google Scholar 

  13. Bansal, N., Blum, A., Chawla, S.: Correlation clustering. In: Proceedings of the 43rd Annual IEEE Symposium of Foundations of Computer Science, Vancouver, Canada, pp. 238–250 (2002)

    Google Scholar 

  14. Gülpinar, N., Gutin, G., Mitra, G., Zverovitch, A.: Extracting pure network submatrices in linear programs using signed graphs. Discrete Applied Mathematics 137, 359–372 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  15. Macon, K., Mucha, P., Porter, M.: Community structure in the united nations general assembly. Physica A: Statistical Mechanics and its Applications 391, 343–361 (2012)

    Article  Google Scholar 

  16. Traag, V., Bruggeman, J.: Community detection in networks with positive and negative links. Physical Review E 80, 36115 (2009)

    Article  Google Scholar 

  17. Figueiredo, R., Moura, G.: Mixed integer programming formulations for clustering problems related to structural balance (2012) (Paper submitted)

    Google Scholar 

  18. Pajek, http://pajek.imfm.si/ (accessed June 2013)

  19. Demaine, E.D., Emanuel, D., Fiat, A., Immorlica, N.: Correlation clustering in general weighted graphs. Theoretical Computer Science 361, 172–187 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  20. Elsner, M., Schudy, W.: Bounding and comparing methods for correlation clustering beyond ilp. In: ILP 2009 Proceedings of the Workshop on Integer Linear Programming for Natural Language Processing, pp. 19–27 (2009)

    Google Scholar 

  21. Zhang, Z., Cheng, H., Chen, W., Zhang, S., Fang, Q.: Correlation clustering based on genetic algorithm for documents clustering. In: IEEE Congress on Evolutionary Computation, pp. 3193–3198 (2008)

    Google Scholar 

  22. Kunegis, J., Lommatzsch, A., Bauckhage, C.: The slashdot zoo: mining a social network with negative edges. In: WWW 2009 Proceedings of the 18th International Conference on World Wide Web, pp. 741–750 (2009)

    Google Scholar 

  23. Resende, M., Ribeiro, C.: Search Methodologies, 2nd edn. Springer (2011)

    Google Scholar 

  24. Nascimento, M., Toledo, F., de Carvalho, A.: Investigation of a new grasp-based clustering algorithm applied to biological data. Computers Operations Research 37, 1381–1388 (2010)

    Article  MATH  Google Scholar 

  25. Frinhani, R., Silva, R., Mateus, G., Festa, P., Resende, M.: Grasp with path-relinking for data clustering: A case study for biological data. In: Pardalos, P.M., Rebennack, S. (eds.) SEA 2011. LNCS, vol. 6630, pp. 410–420. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  26. Nascimento, M.C., Pitsoulis, L.: Community detection by modularity maximization using grasp with path relinking. Computers Operations Research (2013) (available online on March 2013)

    Google Scholar 

  27. Figueiredo, R., Frota, Y.: The maximum balanced subgraph of a signed graph: applications and solution approaches (2012) (paper submitted)

    Google Scholar 

  28. Mehrotraa, A., Trick, M.: Cliques and clustering: A combinatorial approach. Operations Research Letters 22, 1–12 (1998)

    Article  MathSciNet  Google Scholar 

  29. Resende, M., Ribeiro, C.: Grasp with path-relinking: Recent advances and applications. In: Ibaraki, T., Nonobe, K., Yagiura, M. (eds.) Metaheuristics: Progress as real problem solvers, pp. 29–63. Springer (2005)

    Google Scholar 

  30. Aiex, R.M., Binato, S., Resende, M.G.C.: Parallel grasp with path-relinking for job shop scheduling. Parallel Computing 29, 393–430 (2004)

    Article  MathSciNet  Google Scholar 

  31. Brusco, M.: An enhanced branch-and-bound algorithm for a partitioning problem. British Journal of Mathematical and Statistical Psychology 56, 83–92 (2003)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Drummond, L., Figueiredo, R., Frota, Y., Levorato, M. (2013). Efficient Solution of the Correlation Clustering Problem: An Application to Structural Balance. In: Demey, Y.T., Panetto, H. (eds) On the Move to Meaningful Internet Systems: OTM 2013 Workshops. OTM 2013. Lecture Notes in Computer Science, vol 8186. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41033-8_85

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-41033-8_85

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-41032-1

  • Online ISBN: 978-3-642-41033-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics