A non-iterative algorithm to estimate the modes of univariate mixtures with well separated components

Abstract

This paper deals with the estimation of the modes of an univariate mixture when the number of components is known and when the component density are well separated. We propose an algorithm based on the minimization of the "kp" criterion we introduced in a previous work. In this paper we show that the global minimum of this criterion can be reached with a linear least square minimization followed by a roots finding algorithm. This is a major advantage compared to classical iterative algorithms such as K-means or EM which suffer from the potential convergence to some local extrema of the cost function they use. Our algorithm performances are finally illustrated through simulations of a five components mixture.