This paper is dealing with estimation and model selection in the Latent Block Model (LBM) for categorical data. First, after providing sufficient conditions ensuring the identifiability of this model, it generalises estimation procedures and model selection criteria derived for binary data. Secondly, it develops Bayesian inference through Gibbs sampling. And, with a well calibrated non informative prior distribution, Bayesian estimation is proved to avoid the traps encountered by the LBM with the maximum likelihood methodology. Then model selection criteria are presented. In particular an exact expression of the integrated completed likelihood (ICL) criterion requiring no asymptotic approximation is derived. Finally numerical experiments on both simulated and real data sets highlight the interest of the proposed estimation and model selection procedures.

We propose a method that combines signals from many brain regions observed in functional Magnetic Resonance Imaging (fMRI) to predict the subject's behavior during a scanning session. Such predictions suffer from the huge number of brain regions sampled on the voxel grid of standard fMRI data sets: the curse of dimensionality. Dimensionality reduction is thus needed, but it is often performed using a univariate feature selection procedure, that handles neither the spatial structure of the images, nor the multivariate nature of the signal. By introducing a hierarchical clustering of the brain volume that incorporates connectivity constraints, we reduce the span of the possible spatial configurations to a single tree of nested regions tailored to the signal. We then prune the tree in a supervised setting, hence the name supervised clustering, in order to extract a parcellation (division of the volume) such that parcel-based signal averages best predict the target information. Dimensionality reduction is thus achieved by feature agglomeration, and the constructed features now provide a multi-scale representation of the signal. Comparisons with reference methods on both simulated and real data show that our approach yields higher prediction accuracy than standard voxel-based approaches. Moreover, the method infers an explicit weighting of the regions involved in the regression or classification task.