L0 norm based dictionary learning by proximal methods with global convergence

Chenglong Bao Department of Mathematics, National University of Singapore, Singapore, 119076 Hui Ji Department of Mathematics, National University of Singapore, Singapore, 119076 Yuhui Quan Department of Mathematics, National University of Singapore, Singapore, 119076 Zuowei Shen Department of Mathematics, National University of Singapore, Singapore, 119076

Machine Learning mathscidoc:2206.41009

CVPR, 2014.7
Sparse coding and dictionary learning have seen their applications in many vision tasks, which usually is formulated as a non-convex optimization problem. Many iterative methods have been proposed to tackle such an optimization problem. However, it remains an open problem to have a method that is not only practically fast but also is globally convergent. In this paper, we proposed a fast proximal method for solving \ell_0 norm based dictionary learning problems, and we proved that the whole sequence generated by the proposed method converges to a stationary point with sub-linear convergence rate. The benefit of having a fast and convergent dictionary learning method is demonstrated in the applications of image recovery and face recognition.
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@inproceedings{chenglong2014l0,
  title={L0 norm based dictionary learning by proximal methods with global convergence},
  author={Chenglong Bao, Hui Ji, Yuhui Quan, and Zuowei Shen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220616154550407420381},
  booktitle={CVPR},
  year={2014},
}
Chenglong Bao, Hui Ji, Yuhui Quan, and Zuowei Shen. L0 norm based dictionary learning by proximal methods with global convergence. 2014. In CVPR. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220616154550407420381.
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