A block column iteration for nonnegative matrix factorization

Alternating nonnegative least squares (ANLS) framework is a popular method for nonnegative matrix fac-torization. This approach, at each step, substitutes the non-convex NMF problem with two nonnegativities constrained least-squares subproblems, so the method for solving these subproblems is critical. This paper adopts a version of block-column iterative methods with nonnegativity constraints (BCI-NC) for solving the subproblems and presents an efficient algorithm in NMF decomposition based on the ANLS framework. The advantages of this method include simplicity and ease of implementation. Also, BCI-NC determines the step lengths without time-consuming line searches, unlike the existing ones. Numerical experiments on real-world image and text datasets show that the proposed algorithm is efficient. We observe that BCI-NC provides the best performance in balancing between accuracy and computation time.

Automated summary

This paper introduces an efficient algorithm for NMF decomposition based on the ANLS framework, using the BCI-NC method to solve nonnegativity constrained least-squares subproblems. Experimental results show that the algorithm performs efficiently on image and text datasets.