Fast-robust PCA

Abstract

Principal Component Analysis (PCA) is a powerful and widely used tool in Computer Vision and is applied, e.g., for dimensionality reduction. But as a drawback, it is not robust to outliers. Hence, if the input data is corrupted, an arbitrarily wrong representation is obtained. To overcome this problem, various methods have been proposed to robustly estimate the PCA coefficients, but these methods are computationally too expensive for practical applications. Thus, in this paper we propose a novel fast and robust PCA (FR-PCA), which drastically reduces the computational effort. Moreover, more accurate representations are obtained. In particular, we propose a two-stage outlier detection procedure, where in the first stage outliers are detected by analyzing a large number of smaller subspaces. In the second stage, remaining outliers are detected by a robust least-square fitting. To show these benefits, in the experiments we evaluate the FR-PCA method for the task of robust image reconstruction on the publicly available ALOI database. The results clearly show that our approach outperforms existing methods in terms of accuracy and speed when processing corrupted data. © 2009 Springer Berlin Heidelberg.