A Multiclass Nonparallel Parametric-Margin Support Vector Machine
The twin parametric-margin support vector machine (TPMSVM) is an excellent kernel-based nonparallel classifier. However, TPMSVM was originally designed for binary classification, which is unsuitable for real-world multiclass applications. Therefore, this paper extends TPMSVM for multiclass classific...
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| Format: | Article |
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MDPI AG
2021-12-01
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| Series: | Information |
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| Online Access: | https://www.mdpi.com/2078-2489/12/12/515 |
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| author | Shu-Wang Du Ming-Chuan Zhang Pei Chen Hui-Feng Sun Wei-Jie Chen Yuan-Hai Shao |
| author_facet | Shu-Wang Du Ming-Chuan Zhang Pei Chen Hui-Feng Sun Wei-Jie Chen Yuan-Hai Shao |
| author_sort | Shu-Wang Du |
| collection | DOAJ |
| description | The twin parametric-margin support vector machine (TPMSVM) is an excellent kernel-based nonparallel classifier. However, TPMSVM was originally designed for binary classification, which is unsuitable for real-world multiclass applications. Therefore, this paper extends TPMSVM for multiclass classification and proposes a novel <i>K</i> multiclass nonparallel parametric-margin support vector machine (MNP-KSVC). Specifically, our MNP-KSVC enjoys the following characteristics. (1) Under the “one-versus-one-versus-rest” multiclass framework, MNP-KSVC encodes the complicated multiclass learning task into a series of subproblems with the ternary output <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>{</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>,</mo><mo>+</mo><mn>1</mn><mo>}</mo></mrow></semantics></math></inline-formula>. In contrast to the “one-versus-one” or “one-versus-rest” strategy, each subproblem not only focuses on separating the two selected class instances but also considers the side information of the remaining class instances. (2) MNP-KSVC aims to find a pair of nonparallel parametric-margin hyperplanes for each subproblem. As a result, these hyperplanes are closer to their corresponding class and at least one distance away from the other class. At the same time, they attempt to bound the remaining class instances into an insensitive region. (3) MNP-KSVC utilizes a hybrid classification and regression loss joined with the regularization to formulate its optimization model. Then, the optimal solutions are derived from the corresponding dual problems. Finally, we conduct numerical experiments to compare the proposed method with four state-of-the-art multiclass models: Multi-SVM, MBSVM, MTPMSVM, and Twin-KSVC. Experimental results demonstrate the feasibility and effectiveness of MNP-KSVC in terms of multiclass accuracy and learning time. |
| first_indexed | 2024-03-10T03:53:49Z |
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| issn | 2078-2489 |
| language | English |
| last_indexed | 2024-03-10T03:53:49Z |
| publishDate | 2021-12-01 |
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| spelling | doaj.art-91bb9f7270fa47229f6a253f1200a2542023-11-23T08:51:36ZengMDPI AGInformation2078-24892021-12-01121251510.3390/info12120515A Multiclass Nonparallel Parametric-Margin Support Vector MachineShu-Wang Du0Ming-Chuan Zhang1Pei Chen2Hui-Feng Sun3Wei-Jie Chen4Yuan-Hai Shao5Zhijiang College, Zhejiang University of Technology, Shaoxing 312030, ChinaCollege of Computer Science and Technology, Zhejiang University of Technology, Hangzhou 310024, ChinaCollege of Computer Science and Technology, Zhejiang University of Technology, Hangzhou 310024, ChinaCollege of Computer Science and Technology, Zhejiang University of Technology, Hangzhou 310024, ChinaZhijiang College, Zhejiang University of Technology, Shaoxing 312030, ChinaManagement School, Hainan University, Haikou 570228, ChinaThe twin parametric-margin support vector machine (TPMSVM) is an excellent kernel-based nonparallel classifier. However, TPMSVM was originally designed for binary classification, which is unsuitable for real-world multiclass applications. Therefore, this paper extends TPMSVM for multiclass classification and proposes a novel <i>K</i> multiclass nonparallel parametric-margin support vector machine (MNP-KSVC). Specifically, our MNP-KSVC enjoys the following characteristics. (1) Under the “one-versus-one-versus-rest” multiclass framework, MNP-KSVC encodes the complicated multiclass learning task into a series of subproblems with the ternary output <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>{</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>,</mo><mo>+</mo><mn>1</mn><mo>}</mo></mrow></semantics></math></inline-formula>. In contrast to the “one-versus-one” or “one-versus-rest” strategy, each subproblem not only focuses on separating the two selected class instances but also considers the side information of the remaining class instances. (2) MNP-KSVC aims to find a pair of nonparallel parametric-margin hyperplanes for each subproblem. As a result, these hyperplanes are closer to their corresponding class and at least one distance away from the other class. At the same time, they attempt to bound the remaining class instances into an insensitive region. (3) MNP-KSVC utilizes a hybrid classification and regression loss joined with the regularization to formulate its optimization model. Then, the optimal solutions are derived from the corresponding dual problems. Finally, we conduct numerical experiments to compare the proposed method with four state-of-the-art multiclass models: Multi-SVM, MBSVM, MTPMSVM, and Twin-KSVC. Experimental results demonstrate the feasibility and effectiveness of MNP-KSVC in terms of multiclass accuracy and learning time.https://www.mdpi.com/2078-2489/12/12/515multiclass classificationtwin support vector machinenonparallel hyperplanehybrid classification and regressionMNP-KSVC |
| spellingShingle | Shu-Wang Du Ming-Chuan Zhang Pei Chen Hui-Feng Sun Wei-Jie Chen Yuan-Hai Shao A Multiclass Nonparallel Parametric-Margin Support Vector Machine Information multiclass classification twin support vector machine nonparallel hyperplane hybrid classification and regression MNP-KSVC |
| title | A Multiclass Nonparallel Parametric-Margin Support Vector Machine |
| title_full | A Multiclass Nonparallel Parametric-Margin Support Vector Machine |
| title_fullStr | A Multiclass Nonparallel Parametric-Margin Support Vector Machine |
| title_full_unstemmed | A Multiclass Nonparallel Parametric-Margin Support Vector Machine |
| title_short | A Multiclass Nonparallel Parametric-Margin Support Vector Machine |
| title_sort | multiclass nonparallel parametric margin support vector machine |
| topic | multiclass classification twin support vector machine nonparallel hyperplane hybrid classification and regression MNP-KSVC |
| url | https://www.mdpi.com/2078-2489/12/12/515 |
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