Nonnegative matrix factorization (NMF) has drawn considerable interest in recent years due to its immense significance in multivariate data analysis. We study NMF and some of its applications, and review some of the major algorithms to date, including a pioneering one, for solving NMF. We analyze an algorithm for solving nonnegative least squares problems called Image Space Reconstruction Algorithm (ISRA) to heuristically justify why the pioneering algorithm for the NMF problem converges slowly. We then propose four algorithms called Alternating Projected Barzilai-Borwein (APBB) Algorithms to solve the NMF problem and numerically compare them with some prominent existing algorithms We show that three of these algorithms have superior performance especially for large scale problems.
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