A global algorithm to estimate the expectations of the components of an observed univariate mixture

This paper deals with the unsupervised classification of univariate observations. Given a set of observations originating from a K-component mixture, we focus on the estimation of the component expectations. We propose an algorithm based on the minimization of the “K-product” (KP) criterion we introduced in a previous work. We show that the global minimum of this criterion can be reached by first solving a linear system then calculating the roots of some polynomial of order K. The KP global minimum provides a first raw estimate of the component expectations, then a nearest-neighbour classification enables to refine this estimation. Our method’s relevance is finally illustrated through simulations of various mixtures. When the mixture components do not strongly overlap, the KP algorithm provides better estimates than the Expectation-Maximization algorithm.