Accelerated Alternating Projections for Robust Principal Component Analysis

We study robust PCA for the fully observed setting, which is about separating a low rank matrix and a sparse matrix from their sum . In this paper, a new algorithm, termed accelerated alternating projections, is introduced for robust PCA which accelerates existing alternating projections proposed in [Netrapalli, Praneeth, et al., 2014]. Let and be the current estimates of the low rank matrix and the sparse matrix, respectively. The algorithm achieves significant acceleration by first projecting onto a low dimensional subspace before obtaining the new estimate of via truncated SVD. Exact recovery guarantee has been established which shows linear convergence of the proposed algorithm. Empirical performance evaluations establish the advantage of our algorithm over other state-of-the-art algorithms for robust PCA.
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