Generalized Singular Value Thresholding

Canyi Lu, Changbo Zhu, Chunyan Xu, Shuicheng Yan, Zhouchen Lin

AAAI 2015 pp. 1805-1811

doi:10.1609/AAAI.V29I1.9464 /aaai/2015/lu2015aaai-generalized/

Abstract

This work studies the Generalized Singular Value Thresholding (GSVT) operator 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 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.

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Text

Lu et al. "Generalized Singular Value Thresholding." AAAI Conference on Artificial Intelligence, 2015. doi:10.1609/AAAI.V29I1.9464

Markdown

[Lu et al. "Generalized Singular Value Thresholding." AAAI Conference on Artificial Intelligence, 2015.](https://mlanthology.org/aaai/2015/lu2015aaai-generalized/) doi:10.1609/AAAI.V29I1.9464

BibTeX

@inproceedings{lu2015aaai-generalized,
  title     = {{Generalized Singular Value Thresholding}},
  author    = {Lu, Canyi and Zhu, Changbo and Xu, Chunyan and Yan, Shuicheng and Lin, Zhouchen},
  booktitle = {AAAI Conference on Artificial Intelligence},
  year      = {2015},
  pages     = {1805-1811},
  doi       = {10.1609/AAAI.V29I1.9464},
  url       = {https://mlanthology.org/aaai/2015/lu2015aaai-generalized/}
}