Binary matrix completion with nonconvex regularizers
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.
Code (0)
등록된 구현이 없습니다.
Tasks
Matrix CompletionSimilar Papers 제목 키워드 기반
Factor Group-Sparse Regularization for Efficient Low-Rank Matrix Recovery
This paper develops a new class of nonconvex regularizers for low-rank matrix recovery. Many regularizers are motivated as convex relaxations of the matrix rank function. Our new factor group-sparse regularizers are moti…
Low-Rank Matrix CompletionMatrix CompletionA framework to generate sparsity-inducing regularizers for enhanced low-rank matrix completion
Applying half-quadratic optimization to loss functions can yield the corresponding regularizers, while these regularizers are usually not sparsity-inducing regularizers (SIRs). To solve this problem, we devise a framewor…
Low-Rank Matrix CompletionMatrix CompletionProvable Low Rank Plus Sparse Matrix Separation Via Nonconvex Regularizers
This paper considers a large class of problems where we seek to recover a low rank matrix and/or sparse vector from some set of measurements. While methods based on convex relaxations suffer from a (possibly large) estim…
Matrix CompletionLarge-Scale Low-Rank Matrix Learning with Nonconvex Regularizers
Low-rank modeling has many important applications in computer vision and machine learning. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrat…
Matrix CompletionFast Low-Rank Matrix Learning with Nonconvex Regularization
Low-rank modeling has a lot of important applications in machine learning, computer vision and social network analysis. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-ran…
Matrix Completion