Principal Component Analysis with Contaminated Data: The High Dimensional Case

We consider the dimensionality-reduction problem (finding a subspace of observed data) for contaminated data in the high dimensional, where the number of observations is of the same magnitude as the number variables of each observation, and the data set contains some (arbitrarily) observations. We propose a High-dimensional Robust Principal Analysis (HR-PCA) algorithm that is tractable, robust to contaminated, and easily kernelizable. The resulting subspace has a bounded deviation the desired one, achieves maximal robustness -- a breakdown point of 50% all existing algorithms have a breakdown point of zero, and unlike PCA algorithms, achieves optimality in the limit case where the of corrupted points goes to zero.