Rapid Robust Principal Component Analysis: CUR Accelerated Inexact Low Rank Estimation

TL;DR

This paper introduces IRCUR, a non-convex algorithm that accelerates robust PCA by using CUR decomposition for efficient low-rank approximation, significantly reducing computational costs.

Contribution

The paper presents IRCUR, a novel non-convex method that improves RPCA efficiency by employing CUR decomposition, avoiding full matrix computations.

Findings

IRCUR outperforms existing algorithms in speed on synthetic datasets.

IRCUR maintains high accuracy in low-rank recovery.

Numerical experiments confirm computational advantages on real-world data.

Abstract

Robust principal component analysis (RPCA) is a widely used tool for dimension reduction. In this work, we propose a novel non-convex algorithm, coined Iterated Robust CUR (IRCUR), for solving RPCA problems, which dramatically improves the computational efficiency in comparison with the existing algorithms. IRCUR achieves this acceleration by employing CUR decomposition when updating the low rank component, which allows us to obtain an accurate low rank approximation via only three small submatrices. Consequently, IRCUR is able to process only the small submatrices and avoid expensive computing on the full matrix through the entire algorithm. Numerical experiments establish the computational advantage of IRCUR over the state-of-art algorithms on both synthetic and real-world datasets.