A Novel M-Estimator for Robust PCA

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.