About nonnegative matrix factorization: On the posrank approximation

Abstract

This work addresses the concept of nonnegative matrix factorization (NMF). Some relevant issues for its formulation as as a non-linear optimization problem will be discussed. The primary goal of NMF is that of obtaining good quality approximations, namely for video/image visualization. The importance of the rank of the factor matrices and the use of global optimization techniques is investigated. Some computational experience is reported indicating that, in general, the relation between the quality of the obtained local minima and the factor matrices dimensions has a strong impact on the quality of the solutions associated with the decomposition. © 2011 Springer-Verlag.