Effective implementation to reduce execution time of a low-rank matrix approximation problem

Abstract

This paper proposes a new method to compute generalized low-rank matrix approximation (GLRMA). The GLRMA is a general case of the well-known low-rank approximation problem proposed by Eckart–Young in 1936. This new method, so-called the fast-GLRMA method, is based on tensor product and Tikhonov’s regularization to approximate the pseudoinverse and bilateral random projections to estimate, in turn, the low-rank approximation. The fast-GLRMA method significantly reduces the execution time to compute the optimal solution, while preserving the accuracy of the classical method of solving the GLRMA. Computational experiments to measure execution time and speedup confirmed the efficiency of the proposed method.