Index search method for solving nonnegative matrix factorization

Nonnegative matrix factorization (NMF) has been widely used for dimensionality reduction in recent years, while playing an important role in many fields such as image processing and data analysis. NMF is a classic non-convex optimization problem, and the alternating nonnegative least squares (ANLS) framework is a popular method for solving the problem. In general, ANLS divides the NMF problem into two convex optimization problems, called nonnegative least squares (NNLS) problems. In this paper, we first introduce an active set method for NNLS, called indexed search method (ISM). Meanwhile, our goal is to propose a robust algorithm that combines ANLS and ISM for solving NMF. Finally, numerical experiments are provided to support the theoretical results.