Robust PCA: Optimization of the Robust Reconstruction Error over the Stiefel Manifold
This addresses the issue of outlier sensitivity in PCA for data analysis applications, such as background modeling, but appears incremental as it builds on existing robust PCA methods.
The paper tackles the problem of making Principal Component Analysis (PCA) robust to outliers by minimizing the trimmed reconstruction error, resulting in a method that performs better or similar to state-of-the-art approaches while being faster.
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.