A global algorithm for clustering univariate observations

Abstract

This paper deals with the clustering of univariate observations: given a set of observations coming from $K$ possible clusters, one has to estimate the cluster means. 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 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 cluster means, and a final clustering step enables to recover the cluster means. Our method's relevance and superiority to the Expectation-Maximization algorithm is illustrated through simulations of various Gaussian mixtures. \keywords{unsupervised clustering \and non-iterative algorithm \and optimization criterion \and univariate observations