A Fast Algorithm for a Weighted Low Rank Approximation

TL;DR

This paper introduces a faster algorithm for a specialized weighted low rank matrix approximation, enhancing robustness to outliers and improving background modeling in video analysis.

Contribution

The paper presents a novel, accelerated algorithm for weighted low rank approximation, specifically tailored for robust background estimation in videos.

Findings

The new algorithm significantly reduces computation time.

It effectively handles outliers in background modeling.

Demonstrates improved accuracy in video background estimation.

Abstract

Matrix low rank approximation including the classical PCA and the robust PCA (RPCA) method have been applied to solve the background modeling problem in video analysis. Recently, it has been demonstrated that a special weighted low rank approximation of matrices can be made robust to the outliers similar to the $\ell_1$-norm in RPCA method. In this work, we propose a new algorithm that can speed up the existing algorithm for solving the special weighted low rank approximation and demonstrate its use in background estimation problem.