Stochastic Algorithms for Clustering

Abstract

It is well known that, generally, the solution provided by a partitioning algorithm depends upon its initial position. In this paper, we consider two algorithms which incorporate random perturbations to reduce the initial-position dependence. Both appear to be variations of a general Classification EM algorithm (CEM), conceived to optimizing Classification Maximum Likelihood (CML) criteria in the mixture context. In Section 2, we present the CEM algorithm and we give its main characteristics. In Section 3, we present a Stochastic version (SEM) of the CEM algorithm and a simulated annealing algorithm for clustering (CAEM) conceived in the same framework. Both algorithms can be performed to optimize most of clustering criteria, but here we focus on the variance criterion. In Section 4, we summarize the conclusions of numerical experiments performed to analyze the practical behaviour of both algorithms to optimizing the variance criterion.