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Bootstrap clustering for graph partitioning

  • Philippe Gambette (a1) and Alain Guénoche (a1)
Abstract

Given a simple undirected weighted or unweighted graph, we try to cluster the vertex set into communities and also to quantify the robustness of these clusters. For that task, we propose a new method, called bootstrap clustering which consists in (i) defining a new clustering algorithm for graphs, (ii) building a set of graphs similar to the initial one, (iii) applying the clustering method to each of them, making a profile (set) of partitions, (iv) computing a consensus partition for this profile, which is the final graph partitioning. This allows to evaluate the robustness of a cluster as the average percentage of partitions in the profile joining its element pairs ; this notion can be extended to partitions. Doing so, the initial and consensus partitions can be compared. A simulation protocol, based on random graphs structured in communities is designed to evaluate the efficiency of the Bootstrap Clustering approach.

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[1] Aloise, D., Cafieri, S., Caporossi, G., Hansen, P., Liberti, L. and Perron, S., Column generation algorithms for exact modularity maximization in networks. Phys. Rev. E 82 (2010) 046112.
[2] Angelelli, J.B., Baudot, A., Brun, C. and Guénoche, A., Two local dissimilarity measures for weighted graph with application to biological networks. Adv. Data Anal. Classif. 2 (2008) 316.
[3] Barthélemy, J.P. and Leclerc, B., The median procedure for partitions. DIMACS series in Discrete Mathematics and Theoretical Computer Science 19 (1995) 334.
[4] V. Blondel, J.-L. Guillaume, R. Lambiotte and E. Lefebvre, Fast unfolding of communities in large networks. J. Stat. Mech. Theor. Exp. (2008) P10008.
[5] Brandes, U., Delling, D., Gaertler, M., Görke, R., Hoefer, M., Nikoloski, Z. and Wagner, D., On modularity – NP-completeness and beyond. Proceedings of WG 2007. Lett. Notes Comput. Sci. 4769 (2007) 121132.
[6] Dale, S.V. and Stoeckert, C.J. Jr., Computational modeling of the Plasmodium falciparum interactome reveals protein function on a genome-wide scale. Gen. Res. 16 (2006) 542549.
[7] A.C. Davison and D.V. Hinkley, Bootstrap methods and their application. Cambridge University Press (1997).
[8] Dice, L.R., Measures of the amount of ecologic association between species. Ecology 26 (1945) 297302.
[9] Duch, J. and Arenas, A., Community detection in complex networks using extremal optimization. Phys. Rev. E 72 (2005) 027104.
[10] J. Felsenstein, Inferring Phylogenies. Sunderland (MA), Sinauer Associates Inc. (2003).
[11] Fortunato, S., Community detection in graphs. Phys. Rep. 486 (2010) 75174.
[12] Guénoche, A., Comparison of algorithms in graph partitioning. RAIRO 42 (2008) 469484.
[13] Guénoche, A., Consensus of partitions : a constructive approach. Adv. Data Anal. Classif. 5 (2011) 215229.
[14] Hubert, L. and Arabie, P., Comparing partitions, J. Classif. 2 (1985) 193218.
[15] Jain, A.K. and Moreau, J.V., Bootstrap technique in cluster analysis. Pattern Recogn. 20 (1987) 547568.
[16] Newman, M.E.J., Modularity and community structure in networks. PNAS 103 (2006) 85778582.
[17] Newman, M.E.J. and Girvan, M., Finding and evaluating community structure in networks. Phys. Rev. E 69 (2004) 026133.
[18] A. Noack and R. Rotta, Multi-level algorithms for modularity clustering, Proceedings of SEA’2009, edited by J. Vahrenhold. Lett. Notes Comput. Sci. 5526 (2009) 257–268.
[19] Régnier, S., Sur quelques aspects mathématiques des problèmes de classification automatique. I.C.C. Bulletin 4 (1965) 175191. Reprint, Math. Sci. Hum. 82 (1983) 13–29.
[20] Zahn, C.T., Approximating symmetric relations by equivalence relations. SIAM J. Appl. Math. 12 (1964) 840847.
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RAIRO - Operations Research
  • ISSN: 0399-0559
  • EISSN: 1290-3868
  • URL: /core/journals/rairo-operations-research
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