The effect of finite sample size on on-line K-means

Abstract

The asymptotic convergence of on-line algorithms when the number of training samples becomes infinite is well understood from a theoretical point of view (Adaptive Algorithms and Stochastic Approximations, Springer, Berlin, 1990, Advances in Neural Processing Systems 7, MIT Press, Boston, 1995, Theory and Practice of Recursive Identification, MIT Press, Boston, 1983). However, much less is known about the real convergence of these algorithms when the data sample size is finite. In this paper, we address the study of the real convergence of the popular K-means algorithm (Proceedings of the Fifth Berkeley Symposium on Mathematics, Statistics and Probablity, Vol. 1, 1967, 281) when it deals with finite data resources.