{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/p-svm-soft-margin-svms-with-p-norm-hinge-loss","title":"$p$SVM: Soft-margin SVMs with $p$-norm Hinge Loss","arxiv_id":"2408.09908","date":"2024-08-19","proceeding":null,"authors":["Haoxiang Sun"],"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.","url_abs":"https://arxiv.org/abs/2408.09908v2","url_pdf":"https://arxiv.org/pdf/2408.09908v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"p-svm-soft-margin-svms-with-p-norm-hinge-loss","repo_url":"https://github.com/coderbak/psvm","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"binary-classification","task_name":"Binary Classification"},{"task_slug":"multi-class-classification","task_name":"Multi-class Classification"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}