Accelerating Nonnegative Matrix Factorization Algorithms using Extrapolation

Abstract

In this paper, we propose a general framework to accelerate significantly the algorithms for nonnegative matrix factorization (NMF). This framework is inspired from the extrapolation scheme used to accelerate gradient methods in convex optimization and from the method of parallel tangents. However, the use of extrapolation in the context of the two-block exact coordinate descent algorithms tackling the non-convex NMF problems is novel. We illustrate the performance of this approach on two state-of-the-art NMF algorithms, namely, accelerated hierarchical alternating least squares (A-HALS) and alternating nonnegative least squares (ANLS), using synthetic, image and document data sets.Comment: 19 pages, 6 figures, 6 tables. v2: few typos corrected, additional comparison with the extrapolated projected gradient method of Xu and Yin (SIAM J. on Imaging Sciences, 2013