Binary Matrix Completion With Nonconvex Regularizers

Many practical problems involve the recovery of a binary matrix from partial information, so the binary matrix completion (BMC) technique has increasingly been of interest in machine learning. In particular, we consider a special case of the BMC problems, in which only a subset of positive elements can be observed. In recent years, convex regularization-based methods are the mainstream approaches for this task. However, applications of nonconvex surrogates in standard matrix completion have demonstrated better empirical performance. Accordingly, we propose a novel BMC model with nonconvex regularizers and provide the recovery guarantee for the model. Furthermore, to solve the resultant nonconvex optimization problem, we improve the popular proximal algorithm with acceleration strategies. It can be guaranteed that the convergence rate of the algorithm is on the order of 1/T, where T is the number of iterations. The extensive experiments conducted on both synthetic and real-world data sets demonstrate the superiority of the proposed approach over other competing methods.