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Although detecting communities in networks has attracted considerable recent attention, estimating the number of communities is still an open problem. In this paper, we propose a model, which replicates the generative process of the mixed-membership stochastic block model (MMSB) within the generic allocation framework of Bayesian allocation model (BAM) and BAM-MMSB. In contrast to traditional blockmodels, BAM-MMSB considers the observations as Poisson counts generated by a base Poisson process and marks according to the generative process of MMSB. Moreover, the optimal number of communities for BAM-MMSB is estimated by computing the variational approximations of the marginal likelihood for each model order. Experiments on synthetic and real data sets show that the proposed approach promises a generalized model selection solution that can choose not only the model size but also the most appropriate decomposition.

A Bayesian Allocation Model Based Approach to Mixed Membership Stochastic Blockmodels