$p$SVM: Soft-margin SVMs with $p$-norm Hinge Loss

• URL: http://arxiv.org/abs/2408.09908v2
• Date: Tue, 20 Aug 2024 12:00:00 GMT
• Title: $p$SVM: Soft-margin SVMs with $p$-norm Hinge Loss
• Authors: Haoxiang Sun,
• Abstract summary: Support Vector Machines (SVMs) based on hinge loss have been extensively discussed and applied to various binary classification tasks. In this paper, we explore the properties, performance, and training algorithms of $p$SVMs.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Support Vector Machines (SVMs) based on hinge loss have been extensively discussed and applied to various binary classification tasks. These SVMs achieve a balance between margin maximization and the minimization of slack due to outliers. Although many efforts have been dedicated to enhancing the performance of SVMs with hinge loss, studies on $p$SVMs, soft-margin SVMs with $p$-norm hinge loss, remain relatively scarce. In this paper, we explore the properties, performance, and training algorithms of $p$SVMs. We first derive the generalization bound of $p$SVMs, then formulate the dual optimization problem, comparing it with the traditional approach. Furthermore, we discuss a generalized version of the Sequential Minimal Optimization (SMO) algorithm, $p$SMO, to train our $p$SVM model. Comparative experiments on various datasets, including binary and multi-class classification tasks, demonstrate the effectiveness and advantages of our $p$SVM model and the $p$SMO method. Code is available at https://github.com/CoderBak/pSVM.

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