Efficient Nonnegative Matrix Factorization via Modified Monotone Barzilai-Borwein Method with Adaptive Step Sizes Strategy (Journal of Computational Mathematics, 2023)
In this paper, we develop an active set identification technique. By means of the activeset technique, we present an active set adaptive monotone projected Barzilai-Borweinmethod (ASAMPBB) for solving nonnegative matrix factorization (NMF) based on thealternating nonnegative least squares framework, in which the Barzilai-Borwein (BB) stepsizes can be adaptively picked to get meaningful convergence rate improvements. To getoptimal step size, we take into account of the curvature information. In addition, the largerstep size technique is exploited to accelerate convergence of the proposed method. Theglobal convergence of the proposed method is analysed under mild assumption. Finally,the results of the numerical experiments on both synthetic and real-world datasets showthat the proposed method is effective.
Keywords: Adaptive step sizes; Alternating nonnegative least squares; Monotone projected Barzilai-Borwein method; Active set strategy; Larger step size.