Principal Component Analysis with Contaminated Data: The High Dimensional Case

We consider the dimensionality-reduction problem (finding a subspace approximation of observed data) for contaminated data in the high dimensional regime, where the number of observations is of the same magnitude as the number of variables of each observation, and the data set contains some (arbitrarily) corrupted observations. We propose a High-dimensional Robust Principal Component Analysis (HR-PCA) algorithm that is tractable, robust to contaminated points, and easily kernelizable. The resulting subspace has a bounded deviation from the desired one, achieves maximal robustness

• Type: Journal
• Year: 2010
• Where: COLT
• Authors: Huan Xu, Constantine Caramanis, Shie Mannor
• Keywords: Algorithms, Breakdown Point, COLT 2010, Machine Learning, Ordinary Pca Algorithms