In this paper we study how perturbing a matrix changes its nonnegative rank. We prove that the nonnegative rank can only increase in a neighborhood of a matrix with no zero columns. Also, 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.
Perturbation of matrices and nonnegative rank with a view toward statistical models
RAPALLO, Fabio
2011-01-01
Abstract
In this paper we study how perturbing a matrix changes its nonnegative rank. We prove that the nonnegative rank can only increase in a neighborhood of a matrix with no zero columns. Also, 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.
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