Non-parametric latent modeling and network clustering

Abstract: The paper exposes a non-parametric approach to latent and co-latent modeling of bivariate data, based upon alternating minimization of the Kullback-Leibler divergence (EM algorithm) for complete log-linear models. For categorical data, the iterative algorithm generates a soft clustering of both rows and columns of the contingency table. Well-known results are systematically revisited, and some variants are presumably original. In particular, the consideration of square contingency tables induces a clustering algorithm for weighted networks, differing from spectral clustering or modularity maximization techniques. Also, we present a co-clustering algorithm applicable to HMM models of general kind, distinct from the Baum-Welch algorithm. Three case studies illustrate the theory.