Discrete-Aware Matrix Completion via Proximal Gradient

We present a novel algorithm for the completion of low-rank matrices whose entries are limited to a finite discrete alphabet such as recommender systems. The proposed method is based on the proximal gradient (PG) framework borrowed from optimization theory, which is applied here to solve a regularized formulation of the completion problem that includes a term enforcing the discrete-alphabet membership of the matrix entries as well as a low-rank regularizer. Simulation results demonstrate the superior performance of the proposed method in comparison with recently proposed state-of-the-art alternatives. Also, possible applications of the proposed method are listed in the conclusion.