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

TL;DR

This paper introduces a new robust PCA algorithm that minimizes the trimmed reconstruction error directly on the Stiefel manifold, offering a parameter-free, efficient, and effective approach for outlier-resistant principal component analysis.

Contribution

The paper proposes a novel robust PCA method that avoids deflation, is parameter-free, and computationally efficient by optimizing over the Stiefel manifold.

Findings

Performs better or similar to state-of-the-art methods

More computationally efficient

Effective in background modeling applications

Abstract

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.