Proximal gradient method for huberized support vector machine

Yangyang Xu

Numerical Linear Algebra mathscidoc:1912.43153

2016.6
The support vector machine (SVM) has been used in a wide variety of classification problems. The original SVM uses the hinge loss function, which is non-differentiable and makes the problem difficult to solve in particular for regularized SVMs, such as with 1 -regularization. This paper considers the Huberized SVM (HSVM), which uses a differentiable approximation of the hinge loss function. We first explore the use of the proximal gradient (PG) method to solving binary-class HSVM (B-HSVM) and then generalize it to multi-class HSVM (M-HSVM). Under strong convexity assumptions, we show that our algorithm converges linearly. In addition, we give a finite convergence result about the support of the solution, based on which we further accelerate the algorithm by a two-stage method. We present extensive numerical experiments on both synthetic and real datasets which demonstrate the superiority of our
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@inproceedings{yangyang2016proximal,
  title={Proximal gradient method for huberized support vector machine},
  author={Yangyang Xu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112608239282713},
  year={2016},
}
Yangyang Xu. Proximal gradient method for huberized support vector machine. 2016. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112608239282713.
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