MULTI-SCALE COMMUNITY DETECTION USING STABILITY AS OPTIMISATION CRITERION IN A GREEDY ALGORITHM

Erwan Le Martelot, Chris Hankin

Abstract

Whether biological, social or technical, many real systems are represented as networks whose structure can be very informative regarding the original system’s organisation. In this respect the field of community detection has received a lot of attention in the past decade. Most of the approaches rely on the notion of modularity to assess the quality of a partition and use this measure as an optimisation criterion. Recently stability was introduced as a new partition quality measure encompassing former partition quality measures such as modularity. The work presented here assesses stability as an optimisation criterion in a greedy approach similar to modularity optimisation techniques and enables multi-scale analysis using Markov time as resolution parameter. The method is validated and compared with other popular approaches against synthetic and various real data networks and the results show that the method enables accurate multi-scale network analysis.

References

  1. Ahn, Y.-Y., Bagrow, J. P., and Lehmann, S. (2010). Link communities reveal multiscale complexity in networks. Nature, 466:761-764.
  2. Arenas, A., Díaz-Guilera, A., and Pérez-Vicente, C. J. (2006). Synchronization reveals topological scales in complex networks. Physical Review Letters.
  3. Arenas, A., Fernandez, A., and Gomez, S. (2008). Analysis of the structure of complex networks at different resolution levels. New Journal of Physics, 10:053039.
  4. Blondel, V. D., Guillaume, J.-L., Lambiotte, R., and Lefebvre, E. (2008). Fast unfolding of communities in large networks. Journal of Statistical Mechanics: Theory and Experiment, 10:1742-5468.
  5. Clauset, A., Newman, M. E. J., and Moore, C. (2004). Finding community structure in very large networks. Physical Review E, 70:066111.
  6. Danon, L., Díaz-Guilera, A., and Arenas, A. (2006). The effect of size heterogeneity on community identification in complex networks. Journal of Statistical Mechanics: Theory and Experiment, 2006(11):P11010.
  7. Delvenne, J.-C., Yaliraki, S. N., and Barahona, M. (2010). Stability of graph communities across time scales. PNAS, 107(29):12755-12760.
  8. Fortunato, S. (2010). Community detection in graphs. Physics Reports, 486(3-5):75-174.
  9. Fortunato, S. and Barthélemy, M. (2007). Resolution limit in community detection. PNAS, 104(1):36-41.
  10. Fred, A. L. N. and Jain, A. K. (2003). Robust data clustering. IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2:128-133.
  11. Girvan, M. and Newman, M. E. J. (2002). Community structure in social and biological networks. PNAS, 99:7821-7826.
  12. Good, B. H., de Montjoye, Y.-A., and Clauset, A. (2010). Performance of modularity maximization in practical contexts. Physical Review E, 81(4):046106.
  13. Guimerà, R., Sales-Pardo, M., and Amaral, L. A. N. (2004). Modularity from fluctuations in random graphs and complex networks. Physical Review E, 70(2):025101.
  14. Khadivi, A., Ajdari Rad, A., and Hasler, M. (2011). Network community-detection enhancement by proper weighting. Physical Review E, 83(4):046104.
  15. Knuth, D. E. (1993). The Stanford GraphBase. A Platform for Combinatorial Computing. Addison-Wesley.
  16. Lambiotte, R. (2010). Multi-scale Modularity in Complex Networks. ArXiv e-prints.
  17. Lambiotte, R., Delvenne, J.-C., and Barahona, M. (2008). Laplacian Dynamics and Multiscale Modular Structure in Networks. ArXiv e-prints.
  18. Lancichinetti, A. and Fortunato, S. (2009). Community detection algorithms: A comparative analysis. Physical Review E, 80(5):056117.
  19. Lusseau, D. and Newman, M. E. J. (2004). Identifying the role that individual animals play in their social network. Proceedings of the Royal Society London B, 271:S477-S481.
  20. Lusseau, D., Schneider, K., Boisseau, O. J., Haase, P., Slooten, E., and Dawson, S. M. (2003). The bottlenose dolphin community of doubtful sound features a large proportion of long-lasting associations. can geographic isolation explain this unique trait? Behavioral Ecology and Sociobiology, 54(4):396-405.
  21. Medus, A., Acuna, G., and Dorso, C. (2005). Detection of community structures in networks via global optimization. Physica A: Statistical Mechanics and its Applications, 358(2-4):593-604.
  22. Newman, M. E. J. (2004). Fast algorithm for detecting community structure in networks. Physical Review E, 69(6):066133.
  23. Newman, M. E. J. (2006). Finding community structure in networks using the eigenvectors of matrices. Physical Review E, 74:036104.
  24. Newman, M. E. J. and Girvan, M. (2004). Finding and evaluating community structure in networks. Phisical Review E, 69:026113.
  25. Ovelgönne, M., Geyer-Schulz, A., and Stein, M. (2010). Randomized greedy modularity optimization for group detection in huge social networks. In Proceedings of the 4th SNA-KDD Workshop 7810 (SNAKDD'10), pages 1-9, Washington, DC, USA.
  26. Palla, G., Derenyi, I., Farkas, I., and Vicsek, T. (2005). Uncovering the overlapping community structure of complex networks in nature and society. Nature, 435(7043):814-818.
  27. Pereira-Leal, J. B., Enright, A. J., and Ouzounis, C. A. (2004). Detection of functional modules from protein interaction networks. Proteins, 54:49-57.
  28. Ravasz, E. and Barabási, A. L. (2003). Hierarchical organization in complex networks. Physical Review E, 67(2):026112.
  29. Reichardt, J. and Bornholdt, S. (2006). Statistical mechanics of community detection. Phys Rev E, 74(1 Pt 2):016110.
  30. Schuetz, P. and Caflisch, A. (2008). Efficient modularity optimization by multistep greedy algorithm and vertex mover refinement. Physical Review E, 77(4):046112.
  31. Simon, H. A. (1962). The architecture of complexity. In Proceedings of the American Philosophical Society, pages 467-482.
  32. Zachary, W. W. (1977). An information flow model for conflict and fission in small groups. Journal of Anthropological Research, 33(4):452-473.
Download


Paper Citation


in Harvard Style

Le Martelot E. and Hankin C. (2011). MULTI-SCALE COMMUNITY DETECTION USING STABILITY AS OPTIMISATION CRITERION IN A GREEDY ALGORITHM . In Proceedings of the International Conference on Knowledge Discovery and Information Retrieval - Volume 1: KDIR, (IC3K 2011) ISBN 978-989-8425-79-9, pages 208-217. DOI: 10.5220/0003655002160225


in Bibtex Style

@conference{kdir11,
author={Erwan Le Martelot and Chris Hankin},
title={MULTI-SCALE COMMUNITY DETECTION USING STABILITY AS OPTIMISATION CRITERION IN A GREEDY ALGORITHM},
booktitle={Proceedings of the International Conference on Knowledge Discovery and Information Retrieval - Volume 1: KDIR, (IC3K 2011)},
year={2011},
pages={208-217},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003655002160225},
isbn={978-989-8425-79-9},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Knowledge Discovery and Information Retrieval - Volume 1: KDIR, (IC3K 2011)
TI - MULTI-SCALE COMMUNITY DETECTION USING STABILITY AS OPTIMISATION CRITERION IN A GREEDY ALGORITHM
SN - 978-989-8425-79-9
AU - Le Martelot E.
AU - Hankin C.
PY - 2011
SP - 208
EP - 217
DO - 10.5220/0003655002160225