Bayesian methods for graph clustering

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

1 SG - Laboratoire Statistique et Génome

It is now widely accepted that knowledge can be acquired from networks by clustering their vertices according to connection profiles. Many methods have been proposed and in this paper we concentrate on the Stochastic Block Model (SBM). The clustering of vertices and the estimation of SBM model parameters have been subject to previous work and numerous inference strategies such as variational Expectation Maximization (EM) and classification EM have been proposed. However, SBM still suffers from a lack of criteria to estimate the number of components in the mixture. To our knowledge, only one model based criterion, ICL, has been derived for SBM in the literature. It relies on an asymptotic approximation of the Integrated Complete-data Likelihood and recent studies have shown that it tends to be too conservative in the case of small networks. To tackle this issue, we propose a new criterion that we call ILvb, based on a non asymptotic approximation of the marginal likelihood. We describe how the criterion can be computed through a variational Bayes EM algorithm.

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Pierre Latouche, Etienne E. Birmelé, Christophe Ambroise. Bayesian methods for graph clustering. Andreas Fink, Berthold Lausen, Wilfried Seidel and Alfred Ultsch. Advances in Data Analysis, Data Handling and Business Intelligence, Springer, pp.229-239, 2009, Studies in Classification, Data Analysis, and Knowledge Organization, 978-3-642-01043-9. ⟨10.1007/978-3-642-01044-6⟩. ⟨hal-00629294⟩