# A Nonconvex Projection Method for Robust PCA

arXiv: https://arxiv.org/abs/1805.07962 · HTML: https://mlsanity.com/paper/1805.07962/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 May 2018.

## Built on by (most cited first, 3 of 3)

- [Towards a Better Theoretical Understanding of Independent Subnetwork Training](https://mlsanity.com/paper/2306.16484/) (2023)
- [Inductive Matrix Completion: No Bad Local Minima and a Fast Algorithm](https://mlsanity.com/paper/2201.13052/) (2022)
- [AgFlow: Fast Model Selection of Penalized PCA via Implicit Regularization Effects of Gradient Flow](https://mlsanity.com/paper/2110.03273/) (2021)

## Abstract (arXiv)

Robust principal component analysis (RPCA) is a well-studied problem with the goal of decomposing a matrix into the sum of low-rank and sparse components. In this paper, we propose a nonconvex feasibility reformulation of RPCA problem and apply an alternating projection method to solve it. To the best of our knowledge, we are the first to propose a method that solves RPCA problem without considering any objective function, convex relaxation, or surrogate convex constraints. We demonstrate through extensive numerical experiments on a variety of applications, including shadow removal, background estimation, face detection, and galaxy evolution, that our approach matches and often significantly outperforms current state-of-the-art in various ways.