The "K-Product" Criterion for Gaussian Mixture Estimation

This paper deals with the estimation of complex Gaussian mixtures. The purpose is to estimate the mixture components means (mixture modes) from a set of observations. We propose an algorithm based on a new criterion called "K-product". This algorithm first consists in finding a minimum of this criterion to get a first estimation of the mixture modes. Then each observation is assigned to one of these modes and the resulting clusters means give the final set of estimated modes. A theoretical analysis of the "K-product" minima is performed in a simplified case and the algorithm performances are illustrated through simulations. Theory and simulations show that this algorithm is a relevant candidate for the Gaussian mixture estimation