Kaie Kubjas: Uniqueness of nonnegative matrix factorizations

Abstract

Nonnegative matrix factorizations are often encountered in data mining applications where they are used to explain datasets by a small number of parts. For many of these applications it is desirable that there exists a unique nonnegative matrix factorization up to trivial modifications given by scalings and permutations. This means that model parameters are uniquely identifiable from the data. Different sufficient conditions for the uniqueness of nonnegative matrix factorizations have been well studied, however, a little is known about necessary conditions. We will give so far the strongest necessary condition for the uniqueness of a nonnegative factorization. The talk is based on the joint work with Robert Krone.