Iterative algorithm for the Q-weighted nonnegative matrix factorization

Abstract

Nonnegative matrix factorization, which decomposes a target matrix into the product of two matrices with nonnegative elements, has been widely used in various fields of science, engineering and technology. In this paper, we consider the more general Q-weighted nonnegative matrix factorization (QWNMF) problem. By using the additive representation of the Q-weighted norm, the QWNMF problem is transformed into an unconstraint optimization problem, and then a new iterative algorithm is designed to solve it. The numerical analysis of this algorithm is also given. Numerical examples show that the new method is feasible and effective.