# Best Pair Formulation & Accelerated Scheme for Non-convex Principal Component Pursuit

## TL;DR

This paper formulates robust principal component analysis as a best pair problem and introduces an accelerated proximal gradient method with proven convergence and superior performance in experiments.

## Contribution

It is the first to formulate RPCA as a best pair problem and develops an accelerated scheme with theoretical convergence guarantees.

## Key findings

- The proposed algorithm outperforms baseline methods in experiments.
- Global convergence and local linear rate are established for the scheme.
- Numerical results demonstrate superior efficiency on real and synthetic data.

## Abstract

The best pair problem aims to find a pair of points that minimize the distance between two disjoint sets. In this paper, we formulate the classical robust principal component analysis (RPCA) as the best pair; which was not considered before. We design an accelerated proximal gradient scheme to solve it, for which we show global convergence, as well as the local linear rate. Our extensive numerical experiments on both real and synthetic data suggest that the algorithm outperforms relevant baseline algorithms in the literature.