Novel Alternating Least Squares Algorithm for Nonnegative Matrix and Tensor Factorizations

Abstract

Alternative least squares (ALS) algorithm is considered as a work-horse algorithm for general tensor factorizations. For nonnegative tensor factorizations (NTF), we usually use a nonlinear projection (rectifier) to remove negative entries during the iteration process. However, this kind of ALS algorithm often fails and cannot converge to the desired solution. In this paper, we proposed a novel algorithm for NTF by recursively solving nonnegative quadratic programming problems. The validity and high performance of the proposed algorithm has been confirmed for difficult benchmarks, and also in an application of object classification.