An Alternating Minimization Method for Robust Principal Component Analysis

We focus on solving robust principal component analysis (RPCA) arising from various applications such as information theory, statistics, engineering, and etc. We adopt a model to minimize the sum of observation error and sparsity measurement subject to the rank constraint. To solve this problem, we propose a two-step alternating minimization method. In one step, a symmetric low rank product minimization, which essentially is partial singular value decomposition, can be efficiently solved to moderate accuracy. Meanwhile the second step has closed-form solution. The new proposed approach is almost parameter-free, and its global convergence to a strict local minimizer can be derived under almost no assumption. We compare the proposed approach with some existing solvers and the numerical experiments demonstrate the outstanding performance of our new approach in solving a bunch of synthetic and real RPCA test problems. Especially, we discover the great potential of the proposed approach in solving problem with large size to moderate accuracy.