Model selection for Gaussian latent block clustering with the integrated classification likelihood

Block clustering aims to reveal homogeneous block structures in a data table. Among the different approaches of block clustering, we consider here a model-based method: the Gaussian latent block model for continuous data which is an extension of the Gaussian mixture model for one-way clustering. For a given data table, several candidate models are usually examined, which differ for example in the number of clusters. Model selection then becomes a critical issue. To this end, we develop a criterion based on an approximation of the integrated classification likelihood for the Gaussian latent block model, and propose a Bayesian information criterion-like variant following the same pattern. We also propose a non-asymptotic exact criterion, thus circumventing the controversial definition of the asymptotic regime arising from the dual nature of the rows and columns in co-clustering. The experimental results show steady performances of these criteria for medium to large data tables.