Proximal gradient method for huberized support vector machine

Yangyang Xu; Ioannis Akrotirianakis; Amit Chakraborty

doi:10.1007/s10044-015-0485-z

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arXiv · 1511.09159

Proximal gradient method for huberized support vector machine

Yangyang Xu·Ioannis Akrotirianakis·Amit Chakraborty

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Abstract

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 $\ell_1$-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 methods over some state-of-the-art methods for both binary- and multi-class SVMs.

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BibTeX RIS

Yangyang Xu, Ioannis Akrotirianakis, Amit Chakraborty. 2015-11-30. Proximal gradient method for huberized support vector machine. https://doi.org/10.1007/s10044-015-0485-z

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