# Robust PCA: Optimization of the Robust Reconstruction Error over the Stiefel Manifold

arXiv: https://arxiv.org/abs/1506.00323 · HTML: https://mlsanity.com/paper/1506.00323/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jun 2015.

## Built on by (most cited first, 2 of 2)

- [Non-Linear Spectral Dimensionality Reduction Under Uncertainty](https://mlsanity.com/paper/2202.04678/) (2022)
- [Riemannian Bilevel Optimization](https://mlsanity.com/paper/2405.15816/) (2024)

## Abstract (arXiv)

It is well known that Principal Component Analysis (PCA) is strongly affected by outliers and a lot of effort has been put into robustification of PCA. In this paper we present a new algorithm for robust PCA minimizing the trimmed reconstruction error. By directly minimizing over the Stiefel manifold, we avoid deflation as often used by projection pursuit methods. In distinction to other methods for robust PCA, our method has no free parameter and is computationally very efficient. We illustrate the performance on various datasets including an application to background modeling and subtraction. Our method performs better or similar to current state-of-the-art methods while being faster.