On a Problem of Weighted Low-Rank Approximation of Matrices

TL;DR

This paper investigates a weighted low-rank matrix approximation problem, proposing an algorithm based on the alternating direction method and comparing it with existing algorithms.

Contribution

It introduces a new weighted low-rank approximation framework inspired by classical constrained problems and provides an algorithm with comparative analysis.

Findings

The proposed algorithm effectively solves the weighted low-rank approximation problem.

Results show competitive performance against state-of-the-art methods.

Theoretical reduction to classical cases validates the approach.

Abstract

We study a weighted low rank approximation that is inspired by a problem of constrained low rank approximation of matrices as initiated by the work of Golub, Hoffman, and Stewart (Linear Algebra and Its Applications, 88-89(1987), 317-327). Our results reduce to that of Golub, Hoffman, and Stewart in the limiting cases. We also propose an algorithm based on the alternating direction method to solve our weighted low rank approximation problem and compare it with the state-of-art general algorithms such as the weighted total alternating least squares and the EM algorithm.