A Fast Proximal Alternating Method for Robust Matrix Factorization of Matrix Recovery with Outliers

This paper concerns a class of robust factorization models of low-rank matrix recovery, which have been widely applied in various fields such as machine learning and imaging sciences. An ℓ1-loss robust factorized model incorporating the ℓ2,0-norm regularization term is proposed to address the presence of outliers. Since the resulting problem is nonconvex, nonsmooth, and discontinuous, an approximation problem that shares the same set of stationary points as the original formulation is constructed. Subsequently, a proximal alternating minimization method is proposed to solve the approximation problem. The global convergence of its iterate sequence is also established. Numerical experiments on matrix completion with outliers and image restoration tasks demonstrate that the proposed algorithm achieves low relative errors in shorter computational time, especially for large-scale datasets.