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

Authors:
Bernard Colin;François Dubeau;Hussein Khreibani;Jules Tibeiro
Affiliations:
Département de Mathématiques, Faculté des Sciences, Université de Sherbrooke, Sherbrooke, Canada J1K-2R1;Département de Mathématiques, Faculté des Sciences, Université de Sherbrooke, Sherbrooke, Canada J1K-2R1;Département de Mathématiques, Faculté des Sciences, Université de Sherbrooke, Sherbrooke, Canada J1K-2R1;Université de Moncton à Shippagan, New Brunswick, Canada
Venue:
Journal of Classification
Year:
2013

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Abstract

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.