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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2307.07343 |
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| _version_ | 1866929682545377280 |
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| author | Luo, Linkai Yang, Qiaoling Peng, Hong Wang, Yiding Chen, Ziyang |
| author_facet | Luo, Linkai Yang, Qiaoling Peng, Hong Wang, Yiding Chen, Ziyang |
| contents | The selection of Gaussian kernel parameters plays an important role in the applications of support vector classification (SVC). A commonly used method is the k-fold cross validation with grid search (CV), which is extremely time-consuming because it needs to train a large number of SVC models. In this paper, a new approach is proposed to train SVC and optimize the selection of Gaussian kernel parameters. We first formulate the training and the parameter selection of SVC as a minimax optimization problem named as MaxMin-L2-SVC-NCH, in which the minimization problem is an optimization problem of finding the closest points between two normal convex hulls (L2-SVC-NCH) while the maximization problem is an optimization problem of finding the optimal Gaussian kernel parameters. A lower time complexity can be expected in MaxMin-L2-SVC-NCH because CV is not needed. We then propose a projected gradient algorithm (PGA) for the training of L2-SVC-NCH. It is revealed that the famous sequential minimal optimization (SMO) algorithm is a special case of the PGA. Thus, the PGA can provide more flexibility than the SMO. Furthermore, the solution of the maximization problem is done by a gradient ascent algorithm with dynamic learning rate. The comparative experiments between MaxMin-L2-SVC-NCH and the previous best approaches on public datasets show that MaxMin-L2-SVC-NCH greatly reduces the number of models to be trained while maintaining competitive test accuracy. These findings indicate that MaxMin-L2-SVC-NCH is a better choice for SVC tasks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_07343 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | MaxMin-L2-SVC-NCH: A Novel Approach for Support Vector Classifier Training and Parameter Selection Luo, Linkai Yang, Qiaoling Peng, Hong Wang, Yiding Chen, Ziyang Machine Learning The selection of Gaussian kernel parameters plays an important role in the applications of support vector classification (SVC). A commonly used method is the k-fold cross validation with grid search (CV), which is extremely time-consuming because it needs to train a large number of SVC models. In this paper, a new approach is proposed to train SVC and optimize the selection of Gaussian kernel parameters. We first formulate the training and the parameter selection of SVC as a minimax optimization problem named as MaxMin-L2-SVC-NCH, in which the minimization problem is an optimization problem of finding the closest points between two normal convex hulls (L2-SVC-NCH) while the maximization problem is an optimization problem of finding the optimal Gaussian kernel parameters. A lower time complexity can be expected in MaxMin-L2-SVC-NCH because CV is not needed. We then propose a projected gradient algorithm (PGA) for the training of L2-SVC-NCH. It is revealed that the famous sequential minimal optimization (SMO) algorithm is a special case of the PGA. Thus, the PGA can provide more flexibility than the SMO. Furthermore, the solution of the maximization problem is done by a gradient ascent algorithm with dynamic learning rate. The comparative experiments between MaxMin-L2-SVC-NCH and the previous best approaches on public datasets show that MaxMin-L2-SVC-NCH greatly reduces the number of models to be trained while maintaining competitive test accuracy. These findings indicate that MaxMin-L2-SVC-NCH is a better choice for SVC tasks. |
| title | MaxMin-L2-SVC-NCH: A Novel Approach for Support Vector Classifier Training and Parameter Selection |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2307.07343 |