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March 2011 Overlapping stochastic block models with application to the French political blogosphere
Pierre Latouche, Etienne Birmelé, Christophe Ambroise
Ann. Appl. Stat. 5(1): 309-336 (March 2011). DOI: 10.1214/10-AOAS382


Complex systems in nature and in society are often represented as networks, describing the rich set of interactions between objects of interest. Many deterministic and probabilistic clustering methods have been developed to analyze such structures. Given a network, almost all of them partition the vertices into disjoint clusters, according to their connection profile. However, recent studies have shown that these techniques were too restrictive and that most of the existing networks contained overlapping clusters. To tackle this issue, we present in this paper the Overlapping Stochastic Block Model. Our approach allows the vertices to belong to multiple clusters, and, to some extent, generalizes the well-known Stochastic Block Model [Nowicki and Snijders (2001)]. We show that the model is generically identifiable within classes of equivalence and we propose an approximate inference procedure, based on global and local variational techniques. Using toy data sets as well as the French Political Blogosphere network and the transcriptional network of Saccharomyces cerevisiae, we compare our work with other approaches.


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Pierre Latouche. Etienne Birmelé. Christophe Ambroise. "Overlapping stochastic block models with application to the French political blogosphere." Ann. Appl. Stat. 5 (1) 309 - 336, March 2011.


Published: March 2011
First available in Project Euclid: 21 March 2011

zbMATH: 1220.62083
MathSciNet: MR2810399
Digital Object Identifier: 10.1214/10-AOAS382

Keywords: blockmodels , global and local variational techniques , overlapping clusters , Random graph models

Rights: Copyright © 2011 Institute of Mathematical Statistics

Vol.5 • No. 1 • March 2011
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