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Modeling relations between individuals is a classical question in socialsciences, ecology, etc. In order to uncover a latent structure in the data, apopular approach consists in clustering individuals according to the observedpatterns of interactions. To do so, Stochastic block models (SBM) and LatentBlock models (LBM) are standard tools for clustering the individuals withrespect to their comportment in a unique network. However, when adopting anintegrative point of view, individuals are not involved in a unique network butare part of several networks, resulting into a potentially complex multipartitenetwork. In this contribution, we propose a stochastic block model able tohandle multipartite networks, thus supplying a clustering of the individualsbased on their connection behavior in more than one network. Our model is anextension of the latent block models (LBM) and stochastic block model (SBM).The parameters -- such as the marginal probabilities of assignment to blocksand the matrix of probabilities of connections between blocks -- are estimatedthrough a variational Expectation-Maximization procedure. The numbers of blocksare chosen with the Integrated Completed Likelihood criterion, a penalizedlikelihood criterion. The pertinence of our methodology is illustrated on twodatasets issued from ecology and ethnobiology.

Block models for multipartite networks.Applications in ecology and ethnobiology