Binary matrix completion with nonconvex regularizers

Abstract

Many practical problems involve the recovery of a binary matrix from partial information, which makes the binary matrix completion (BMC) technique received increasing attention in machine learning. In particular, we consider a special case of BMC problem, 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, the 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, for solving 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 in the order of $1/T$, where $T$ is the number of iterations. Extensive experiments conducted on both synthetic and real-world data sets demonstrate the superiority of the proposed approach over other competing methods.

References in corpus (11)

• The Augmented Lagrange Multiplier Method for Exact Recovery of Corrupted Low-Rank Matrices
• A Simpler Approach to Matrix Completion
• Estimation of high-dimensional low-rank matrices
• A General Iterative Shrinkage and Thresholding Algorithm for Non-convex Regularized Optimization Problems
• Positive-Unlabeled Learning with Non-Negative Risk Estimator
• A Max-Norm Constrained Minimization Approach to 1-Bit Matrix Completion
• PU Learning for Matrix Completion
• Link Prediction via Matrix Completion
• Matrix Completion via Max-Norm Constrained Optimization
• Binary Matrix Completion Using Unobserved Entries
• Social Trust Prediction via Max-norm Constrained 1-bit Matrix Completion