Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-10T14:42:37.410Z Has data issue: false hasContentIssue false
  • English
  • Français

Bootstrap clustering for graph partitioning∗

Published online by Cambridge University Press:  01 March 2012

Philippe Gambette  and
Alain Guénoche
Philippe Gambette
Affiliation:
IML – CNRS, 163 Av. de Luminy, 13009 Marseille, France. guenoche@iml.univ-mrs.fr
Alain Guénoche
Affiliation:
IML – CNRS, 163 Av. de Luminy, 13009 Marseille, France. guenoche@iml.univ-mrs.fr
Get access

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.

Keywords

Graph partitioningclusteringmodularityconsensus of partitionsbootstrap
Type
Research Article
Information
RAIRO - Operations Research , Volume 45 , Issue 4 , October 2011 , pp. 339 - 352
Copyright
© EDP Sciences, ROADEF, SMAI, 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

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. Google ScholarPubMed
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) 3–16. Google Scholar
Barthélemy, J.P. and Leclerc, B., The median procedure for partitions. DIMACS series in Discrete Mathematics and Theoretical Computer Science 19 (1995) 3–34. Google Scholar
V. Blondel, J.-L. Guillaume, R. Lambiotte and E. Lefebvre, Fast unfolding of communities in large networks. J. Stat. Mech. Theor. Exp. (2008) P10008.
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) 121–132. Google Scholar
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) 542–549. Google Scholar
A.C. Davison and D.V. Hinkley, Bootstrap methods and their application. Cambridge University Press (1997).
Dice, L.R., Measures of the amount of ecologic association between species. Ecology 26 (1945) 297–302. Google Scholar
Duch, J. and Arenas, A., Community detection in complex networks using extremal optimization. Phys. Rev. E 72 (2005) 027104. Google ScholarPubMed
J. Felsenstein, Inferring Phylogenies. Sunderland (MA), Sinauer Associates Inc. (2003).
Fortunato, S., Community detection in graphs. Phys. Rep. 486 (2010) 75–174. Google Scholar
Guénoche, A., Comparison of algorithms in graph partitioning. RAIRO 42 (2008) 469–484. Google Scholar
Guénoche, A., Consensus of partitions : a constructive approach. Adv. Data Anal. Classif. 5 (2011) 215–229. Google Scholar
Hubert, L. and Arabie, P., Comparing partitions, J. Classif. 2 (1985) 193–218. Google Scholar
Jain, A.K. and Moreau, J.V., Bootstrap technique in cluster analysis. Pattern Recogn. 20 (1987) 547–568. Google Scholar
Newman, M.E.J., Modularity and community structure in networks. PNAS 103 (2006) 8577–8582. Google ScholarPubMed
Newman, M.E.J. and Girvan, M., Finding and evaluating community structure in networks. Phys. Rev. E 69 (2004) 026133. Google ScholarPubMed
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.
Régnier, S., Sur quelques aspects mathématiques des problèmes de classification automatique. I.C.C. Bulletin 4 (1965) 175–191. Reprint, Math. Sci. Hum. 82 (1983) 13–29. Google Scholar
Zahn, C.T., Approximating symmetric relations by equivalence relations. SIAM J. Appl. Math. 12 (1964) 840–847. Google Scholar