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