Robust PCA: Optimization of the Robust Reconstruction Error Over the Stiefel Manifold
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.
KeywordsPrincipal Component Analysis Reconstruction Error Breakdown Point Robust Principal Component Analysis Ground Truth Information
M.H. has been partially supported by the ERC Starting Grant NOLEPRO and M.H. and S.S. have been partially supported by the DFG Priority Program 1324, “Extraction of quantifiable information from complex systems”.
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