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 L and a sparse matrix S from their sum D = L + S. In this paper, a new algorithm, dubbed accelerated alternating projections, is introduced for robust PCA which signi fi cantly improves the computational e ffi ciency of the existing alternating projections proposed in (Netrapalli et al., 2014) when updating the low rank factor. The acceleration is achieved by fi rst projecting a matrix onto some low dimensional subspace before obtaining a new estimate of the low rank matrix 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-theart algorithms for robust PCA.