Generalized Singular Value Thresholding
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Abstract (arXiv)
This work studies the Generalized Singular Value Thresholding (GSVT) operator Proxg^σ(·), beginequation* Proxg^σ(B)=argminlimitsXsumi=1mg(σi(X)) + frac12||X-B||F2, endequation* associated with a nonconvex function g defined on the singular values of X. We prove that GSVT can be obtained by performing the proximal operator of g (denoted as Proxg(·)) on the singular values since Proxg(·) is monotone when g is lower bounded. If the nonconvex g satisfies some conditions (many popular nonconvex surrogate functions, e.g., ℓp-norm, 0<p<1, of ℓ0-norm are special cases), a general solver to find Proxg(b) is proposed for any b≥0. GSVT greatly generalizes the known Singular Value Thresholding (SVT) which is a basic subroutine in many convex low rank minimization methods. We are able to solve the nonconvex low rank minimization problem by using GSVT in place of SVT.
Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). First posted on arXiv 6 Dec 2014.
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Citing papers per year: 2021: 2; 2022: 1; 2023: 3; 2024: 2.
8 papers.
- 2023Low-Rank Tensor Completion via Novel Sparsity-Inducing Regularizerscited by 3
- 2021Tensor Full Feature Measure and Its Nonconvex Relaxation Applications to Tensor Recoverycited by 0
- 2021Provable Low Rank Plus Sparse Matrix Separation Via Nonconvex Regularizerscited by 0
- 2022Low-Rank Tensor Completion Based on Bivariate Equivalent Minimax-Concave Penaltycited by 0
- 2023Robust Low-Rank Matrix Completion via a New Sparsity-Inducing Regularizercited by 0
- 2023A framework to generate sparsity-inducing regularizers for enhanced low-rank matrix completioncited by 0
- 2024Efficient Low-rank Identification via Accelerated Iteratively Reweighted Nuclear Norm Minimizationcited by 0
- 2024Tailed Low-Rank Matrix Factorization for Similarity Matrix Completioncited by 0
- 2024Tailed Low-Rank Matrix Factorization for Similarity Matrix Completion29 Sep 2024
- 2024Efficient Low-rank Identification via Accelerated Iteratively Reweighted Nuclear Norm Minimization22 Jun 2024
- 2023Low-Rank Tensor Completion via Novel Sparsity-Inducing Regularizers10 Oct 2023
- 2023A framework to generate sparsity-inducing regularizers for enhanced low-rank matrix completion8 Oct 2023
- 2023Robust Low-Rank Matrix Completion via a New Sparsity-Inducing Regularizer7 Oct 2023
- 2022Low-Rank Tensor Completion Based on Bivariate Equivalent Minimax-Concave Penalty30 Jan 2022
- 2021Provable Low Rank Plus Sparse Matrix Separation Via Nonconvex Regularizers26 Sep 2021
- 2021Tensor Full Feature Measure and Its Nonconvex Relaxation Applications to Tensor Recovery25 Sep 2021