Alternating block linearized Bregman iterations for regularized nonnegative matrix factorization

Abstract

In this paper, we propose an alternating block variant of the linearized Bregman iterations for a class of regularized nonnegative matrix factorization (NMF) problems. The proposed method exploits the block structure of NMF, utilizes the smooth adaptable property of the loss function based on the Bregman distance, and at the same time follows the iterative regularization idea of the linearized Bregman iterations method. Theoretically, we show that the proposed method is a descent method by adjusting the involved parameters. Finally, we end with several illustrative numerical experiments.