A Majorization Penalty Method for SVM with Sparse Constraint

Lu Sitong; Li Qinana

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arXiv · 2105.07121

A Majorization Penalty Method for SVM with Sparse Constraint

Lu Sitong·Li Qinana

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Abstract

Support vector machine is an important and fundamental technique in machine learning. Soft-margin SVM models have stronger generalization performance compared with the hard-margin SVM. Most existing works use the hinge-loss function which can be regarded as an upper bound of the 0-1 loss function. However, it can not explicitly limit the number of misclassified samples. In this paper, we use the idea of soft-margin SVM and propose a new SVM model with a sparse constraint. Our model can strictly limit the number of misclassified samples, expressing the soft-margin constraint as a sparse constraint. By constructing a majorization function, a majorization penalty method can be used to solve the sparse-constrained optimization problem. We apply Conjugate-Gradient (CG) method to solve the resulting subproblem. Extensive numerical results demonstrate the impressive performance of the proposed majorization penalty method.

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Lu Sitong, Li Qinana. 2021-05-15. A Majorization Penalty Method for SVM with Sparse Constraint. https://arxiv.org/abs/2105.07121

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