Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.09908 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914917463883776 |
|---|---|
| author | Sun, Haoxiang |
| author_facet | Sun, Haoxiang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_09908 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $p$SVM: Soft-margin SVMs with $p$-norm Hinge Loss Sun, Haoxiang Machine Learning 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. |
| title | $p$SVM: Soft-margin SVMs with $p$-norm Hinge Loss |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2408.09908 |