Robust Low-Rank Matrix Completion via a New Sparsity-Inducing Regularizer
This paper presents a novel loss function referred to as hybrid ordinary-Welsch (HOW) and a new sparsity-inducing regularizer associated with HOW. We theoretically show that the regularizer is quasiconvex and that the corresponding Moreau envelope is convex. Moreover, the closed-form solution to its Moreau envelope, namely, the proximity operator, is derived. Compared with nonconvex regularizers like the lp-norm with 0<p<1 that requires iterations to find the corresponding proximity operator, the developed regularizer has a closed-form proximity operator. We apply our regularizer to the robust matrix completion problem, and develop an efficient algorithm based on the alternating direction method of multipliers. The convergence of the suggested method is analyzed and we prove that any generated accumulation point is a stationary point. Finally, experimental results based on synthetic and real-world datasets demonstrate that our algorithm is superior to the state-of-the-art methods in terms of restoration performance.
Code (0)
등록된 구현이 없습니다.
Tasks
Low-Rank Matrix CompletionMatrix CompletionSimilar Papers 제목 키워드 기반
A 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 CompletionLow-Rank Tensor Completion via Novel Sparsity-Inducing Regularizers
To alleviate the bias generated by the l1-norm in the low-rank tensor completion problem, nonconvex surrogates/regularizers have been suggested to replace the tensor nuclear norm, although both can achieve sparsity. Howe…
Low-Rank Inducing Norms with Optimality Interpretations
Optimization problems with rank constraints appear in many diverse fields such as control, machine learning and image analysis. Since the rank constraint is non-convex, these problems are often approximately solved via c…
Matrix 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 CompletionLog-Normal Matrix Completion for Large Scale Link Prediction
The ubiquitous proliferation of online social networks has led to the widescale emergence of relational graphs expressing unique patterns in link formation and descriptive user node features. Matrix Factorization and Com…
DescriptiveLink PredictionMatrix CompletionPrediction