$p$SVM: Soft-margin SVMs with $p$-norm Hinge Loss
<|reference_start|>$p$SVM: Soft-margin SVMs with $p$-norm Hinge Loss: 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.<|reference_end|>
@article{sun2024$p$svm:,
    title={$p$SVM: Soft-margin SVMs with $p$-norm Hinge Loss},
    author={Haoxiang Sun},
    journal={arXiv preprint arXiv:2408.09908},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.09908},
    primaryClass={cs.LG}
}