A Novel M-Estimator for Robust PCA

Details A Novel M-Estimator for Robust PCA A Novel M-Estimator for Robust PCA

2011-12-20

arxiv.org/abs/1112.4863v1

Statistics

Machine Learning

Scientific paper

We formulate a convex minimization to robustly recover a subspace from a contaminated data set, partially sampled around it, and propose a fast iterative algorithm to achieve the corresponding minimum. We establish exact recovery by this minimizer, quantify the effect of noise and regularization, explain how to take advantage of a known intrinsic dimension and establish linear convergence of the iterative algorithm. Our minimizer is an M-estimator. We demonstrate its significance by adapting it to formulate a convex minimization equivalent to the non-convex total least squares (which is solved by PCA). We compare our method with many other algorithms for robust PCA on synthetic and real data sets and demonstrate state-of-the-art speed and accuracy.

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