A Learning Framework of Nonparallel Hyperplanes Classifier
A novel learning framework of nonparallel hyperplanes support vector machines (NPSVMs) is proposed for binary classification and multiclass classification. This framework not only includes twin SVM (TWSVM) and its many deformation versions but also extends them into multiclass classification problem...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2015/497617 |
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| _version_ | 1850179341047037952 |
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| author | Zhi-Xia Yang Yuan-Hai Shao Yao-Lin Jiang |
| author_facet | Zhi-Xia Yang Yuan-Hai Shao Yao-Lin Jiang |
| author_sort | Zhi-Xia Yang |
| collection | DOAJ |
| description | A novel learning framework of nonparallel hyperplanes support vector machines (NPSVMs) is proposed for binary classification and multiclass classification. This framework not only includes twin SVM (TWSVM) and its many deformation versions but also extends them into multiclass classification problem when different parameters or loss functions are chosen. Concretely, we discuss the linear and nonlinear cases of the framework, in which we select the hinge loss function as example. Moreover, we also give the primal problems of several extension versions of TWSVM’s deformation versions. It is worth mentioning that, in the decision function, the Euclidean distance is replaced by the absolute value |wTx+b|, which keeps the consistency between the decision function and the optimization problem and reduces the computational cost particularly when the kernel function is introduced. The numerical experiments on several artificial and benchmark datasets indicate that our framework is not only fast but also shows good generalization. |
| format | Article |
| id | doaj-art-9e55e4b8b16c47ec92c21ba75a07c54d |
| institution | OA Journals |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-9e55e4b8b16c47ec92c21ba75a07c54d2025-08-20T02:18:32ZengWileyThe Scientific World Journal2356-61401537-744X2015-01-01201510.1155/2015/497617497617A Learning Framework of Nonparallel Hyperplanes ClassifierZhi-Xia Yang0Yuan-Hai Shao1Yao-Lin Jiang2College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, ChinaZhijiang College, Zhejiang University of Technology, Hangzhou 310024, ChinaCollege of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, ChinaA novel learning framework of nonparallel hyperplanes support vector machines (NPSVMs) is proposed for binary classification and multiclass classification. This framework not only includes twin SVM (TWSVM) and its many deformation versions but also extends them into multiclass classification problem when different parameters or loss functions are chosen. Concretely, we discuss the linear and nonlinear cases of the framework, in which we select the hinge loss function as example. Moreover, we also give the primal problems of several extension versions of TWSVM’s deformation versions. It is worth mentioning that, in the decision function, the Euclidean distance is replaced by the absolute value |wTx+b|, which keeps the consistency between the decision function and the optimization problem and reduces the computational cost particularly when the kernel function is introduced. The numerical experiments on several artificial and benchmark datasets indicate that our framework is not only fast but also shows good generalization.http://dx.doi.org/10.1155/2015/497617 |
| spellingShingle | Zhi-Xia Yang Yuan-Hai Shao Yao-Lin Jiang A Learning Framework of Nonparallel Hyperplanes Classifier The Scientific World Journal |
| title | A Learning Framework of Nonparallel Hyperplanes Classifier |
| title_full | A Learning Framework of Nonparallel Hyperplanes Classifier |
| title_fullStr | A Learning Framework of Nonparallel Hyperplanes Classifier |
| title_full_unstemmed | A Learning Framework of Nonparallel Hyperplanes Classifier |
| title_short | A Learning Framework of Nonparallel Hyperplanes Classifier |
| title_sort | learning framework of nonparallel hyperplanes classifier |
| url | http://dx.doi.org/10.1155/2015/497617 |
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