Modeling and Unsupervised Classification of Multivariate Hidden Markov Chains With Copulas

Abstract

Parametric modeling and estimation of non-Gaussian multidimensional probability density function is a difficult problem whose solution is required by many applications in signal and image processing. A lot of efforts have been devoted to escape the usual Gaussian assumption by developing perturbed Gaussian models such as spherically invariant random vectors (SIRVs). In this work, we introduce an alternative solution based on copulas that enables theoretically to represent any multivariate distribution. Estimation procedures are proposed for some mixtures of copula-based densities and are compared in the hidden Markov chain setting, in order to perform statistical unsupervised classification of signals or images. Useful copulas and SIRV for multivariate signal classification are particularly studied through experiments.