Quadratic regularization projected Barzilai–Borwein method for nonnegative matrix factorization

Abstract

In this paper, based on the alternating nonnegative least squares framework, we present a new efficient method for nonnegative matrix factorization that uses a quadratic regularization projected Barzilai---Borwein (QRPBB) method to solve the subproblems. At each iteration, the QRPBB method first generates a point by solving a strongly convex quadratic minimization problem, which has a simple closed-form solution that is inexpensive to calculate, and then applies a projected Barzilai---Borwein method to update the solution of NMF. Global convergence result is established under mild conditions. Numerical comparisons of methods on both synthetic and real-world datasets show that the proposed method is efficient.