Perturbation of matrices and non-negative rank with a view toward statistical models

Abstract

In this paper we study how perturbing a matrix changes its non-negative rank. We prove that the non-negative rank is upper-semicontinuos and we describe some special families of perturbations. We show how our results relate to Statistics in terms of the study of Maximum Likelihood Estimation for mixture models.Comment: 13 pages, 3 figures. A theorem has been rewritten, and some improvements in the presentations have been implemente