  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
