nonnegative matrix factorization (nmf) is a common method in data mining that have been used in different applications as a dimension reduction, classification or clustering method. methods in alternating least square (als) approach usually used to solve this non-convex minimization problem.  at each step of als algorithms two convex least square problems should be solved, which causes high com...

We study the convergence of the Regularized Alternating Least-Squares algorithm for tensor decompositions. As a main result, we have shown that given the existence of critical points of the Alternating Least-Squares method, the limit points of the converging subsequences of the RALS are the critical points of the least squares cost functional. Some numerical examples indicate a faster convergen...

The canonical polyadic (CP) decomposition of tensors is one the most important tensor decompositions. While well-known alternating least squares (ALS) algorithm often considered workhorse for computing CP decomposition, it known to suffer from slow convergence in many cases and various algorithms have been proposed accelerate it. In this article, we propose a new accelerated ALS that accelerate...

The alternating least squares (ALS) algorithm for CP and Tucker decomposition is dominated in cost by the tensor contractions necessary to set up quadratic optimization subproblems. We introduce a novel family of algorithms that uses perturbative corrections subproblems rather than recomputing contractions. This approximation accurate when factor matrices are changing little across iterations, ...