We finally (me and Pierre Latouche) released our preprint on graph clustering with stochastic block model when the number of cluster is unknown. In our proposal this is solved thank to a model selection approach based on the integrated complete data log likelihood. Algorithmic issues to perform clustering and model selection at the same time are also discussed. It his availbale at arXiv or here and the abstract follow:

The stochastic block model (SBM) is a mixture model used for the clustering of nodes in networks. It has now been employed for more than a decade to analyze very different types of networks in many scientific fields such as Biology and social sciences. Because of conditional dependency, there is no analytical expression for the posterior distribution over the latent variables, given the data and model parameters. Therefore, approximation strategies, based on variational techniques or sampling, have been proposed for clustering. Moreover, two SBM model selection criteria exist for the estimation of the number K of clusters in networks but, again, both of them rely on some approximations. In this paper, we show how an analytical expression can be derived for the integrated complete data log likelihood. We then propose an inference algorithm to maximize this exact quantity. This strategy enables the clustering of nodes as well as the estimation of the number clusters to be performed at the same time and no model selection criterion has to be computed for various values of K. The algorithm we propose has a better computational cost than existing inference techniques for SBM and can be employed to analyze large networks with ten thousand nodes. Using toy and true data sets, we compare our work with other approaches.

blogbd

Adjacency matrix of a blogs network, the rows/columns are sorted by cluster number
with clusters found by the greedy ICL algorithm. The cluster boundaries are depicted with white
lines.

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