An efficient nonmonotone projected Barzilai–Borwein method for nonnegative matrix factorization with extrapolation

In this paper, we present an efficient method for nonnegative matrix factorization (NMF) based on the alternating nonnegative least-squares framework. To solve the nonnegativity constrained least-squares problems efficiently, we propose an extrapolated quadratic regularization projected Barzilai–Borwein (EQRPBB) method utilizing the extrapolation technique and a modified nonmonotone line search. The efficiency of the proposed method is demonstrated through experiments on synthetic and image datasets. We observe that our method significantly outperform existing ones in terms of computational speed.