OVERLAPPING STOCHASTIC BLOCK MODELS WITH APPLICATION TO THE FRENCH POLITICAL BLOGOSPHERE

Pierre Latouche (1) , Etienne Birmelé (1) , Christophe Ambroise (1)

1 SG - Laboratoire Statistique et Génome

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.

Mots clés: Random graph models; blockmodels; overlapping clusters; COMMUNITY STRUCTURE; COMPLEX NETWORKS; BLOCKMODELS; PREDICTION

Mots clés: global and local variational techniques; GRAPHS; MIXTURE

Domaines: Mathématiques [math]; Informatique [cs]; Méthodologie [stat.ME]; Applications [stat.AP]

Pierre Latouche, Etienne Birmelé, Christophe Ambroise. OVERLAPPING STOCHASTIC BLOCK MODELS WITH APPLICATION TO THE FRENCH POLITICAL BLOGOSPHERE. Annals of Applied Statistics, 2011, 5 (1), pp.309 - 336. ⟨10.1214/10-AOAS382⟩. ⟨hal-02652556⟩