Optimal Quantization of the Support of a Continuous Multivariate Distribution based on Mutual Information

Based on the notion of mutual information between the components of a random vector, we construct, for data reduction reasons, an optimal quantization of the support of its probability measure. More precisely, we propose a simultaneous discretization of the whole set of the components of the random vector which takes into account, as much as possible, the stochastic dependence between them. Examples are presented. Copyright Springer Science+Business Media New York 2013