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.