A proximal ANLS algorithm for nonnegative tensor factorization with a periodic enhanced line search

TL;DR: A Proximal ANLS (PANLS) algorithm to enforce convergence and to speed up the PANLS method, it is proposed to combine it with a periodic enhanced line search strategy and the resulting algorithm, PANLS/PELS, converges to a critical point of the nonnegative tensor factorization problem under mild conditions.

Abstract: The Alternating Nonnegative Least Squares (ANLS) method is commonly used for solving nonnegative tensor factorization problems. In this paper, we focus on algorithmic improvement of this method. We present a Proximal ANLS (PANLS) algorithm to enforce convergence. To speed up the PANLS method, we propose to combine it with a periodic enhanced line search strategy. The resulting algorithm, PANLS/PELS, converges to a critical point of the nonnegative tensor factorization problem under mild conditions. We also provide some numerical results comparing the ANLS and PANLS/PELS methods.