Sparse Proximal Support Vector Machine with a Specialized Interior-Point Method
Support vector machine (SVM) is a widely used method for classification. Proximal support vector machine (PSVM) is an extension of SVM and a promising method to lead to a fast and simple algorithm for generating a classifier. Motivated by the fast computational efforts of PSVM and the properties of...
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| Published in: | Journal of the Operations Research Society of China (Internet) Vol. 3; no. 1; pp. 1 - 15 |
|---|---|
| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Heidelberg
Operations Research Society of China
01.03.2015
Springer Nature B.V |
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| ISSN: | 2194-668X, 2194-6698 |
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| Abstract | Support vector machine (SVM) is a widely used method for classification. Proximal support vector machine (PSVM) is an extension of SVM and a promising method to lead to a fast and simple algorithm for generating a classifier. Motivated by the fast computational efforts of PSVM and the properties of sparse solution yielded by
ℓ
1
-norm, in this paper, we first propose a PSVM with a cardinality constraint which is eventually relaxed by
ℓ
1
-norm and leads to a trade-off
ℓ
1
-
ℓ
2
regularized sparse PSVM. Next we convert this
ℓ
1
-
ℓ
2
regularized sparse PSVM into an equivalent form of
ℓ
1
regularized least squares (LS) and solve it by a specialized interior-point method proposed by Kim et al. (J Sel Top Signal Process 12:1932–4553,
2007
). Finally,
ℓ
1
-
ℓ
2
regularized sparse PSVM is illustrated by means of a real-world dataset taken from the University of California, Irvine Machine Learning Repository (UCI Repository). Moreover, we compare the numerical results with the existing models such as generalized eigenvalue proximal SVM (GEPSVM), PSVM, and SVM-Light. The numerical results show that the
ℓ
1
-
ℓ
2
regularized sparse PSVM achieves not only better accuracy rate of classification than those of GEPSVM, PSVM, and SVM-Light, but also a sparser classifier compared with the
ℓ
1
-PSVM. |
|---|---|
| AbstractList | Support vector machine (SVM) is a widely used method for classification. Proximal support vector machine (PSVM) is an extension of SVM and a promising method to lead to a fast and simple algorithm for generating a classifier. Motivated by the fast computational efforts of PSVM and the properties of sparse solution yielded by ℓ1-norm, in this paper, we first propose a PSVM with a cardinality constraint which is eventually relaxed by ℓ1-norm and leads to a trade-off ℓ1-ℓ2 regularized sparse PSVM. Next we convert this ℓ1-ℓ2 regularized sparse PSVM into an equivalent form of ℓ1 regularized least squares (LS) and solve it by a specialized interior-point method proposed by Kim et al. (J Sel Top Signal Process 12:1932–4553, 2007). Finally, ℓ1-ℓ2 regularized sparse PSVM is illustrated by means of a real-world dataset taken from the University of California, Irvine Machine Learning Repository (UCI Repository). Moreover, we compare the numerical results with the existing models such as generalized eigenvalue proximal SVM (GEPSVM), PSVM, and SVM-Light. The numerical results show that the ℓ1-ℓ2 regularized sparse PSVM achieves not only better accuracy rate of classification than those of GEPSVM, PSVM, and SVM-Light, but also a sparser classifier compared with the ℓ1-PSVM. Support vector machine (SVM) is a widely used method for classification. Proximal support vector machine (PSVM) is an extension of SVM and a promising method to lead to a fast and simple algorithm for generating a classifier. Motivated by the fast computational efforts of PSVM and the properties of sparse solution yielded by ℓ 1 -norm, in this paper, we first propose a PSVM with a cardinality constraint which is eventually relaxed by ℓ 1 -norm and leads to a trade-off ℓ 1 - ℓ 2 regularized sparse PSVM. Next we convert this ℓ 1 - ℓ 2 regularized sparse PSVM into an equivalent form of ℓ 1 regularized least squares (LS) and solve it by a specialized interior-point method proposed by Kim et al. (J Sel Top Signal Process 12:1932–4553, 2007 ). Finally, ℓ 1 - ℓ 2 regularized sparse PSVM is illustrated by means of a real-world dataset taken from the University of California, Irvine Machine Learning Repository (UCI Repository). Moreover, we compare the numerical results with the existing models such as generalized eigenvalue proximal SVM (GEPSVM), PSVM, and SVM-Light. The numerical results show that the ℓ 1 - ℓ 2 regularized sparse PSVM achieves not only better accuracy rate of classification than those of GEPSVM, PSVM, and SVM-Light, but also a sparser classifier compared with the ℓ 1 -PSVM. |
| Author | Yan, Wen-Li Bai, Yan-Qin Zhu, Zhao-Ying |
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| Cites_doi | 10.1007/s40305-014-0037-z 10.1109/TIT.2006.871582 10.1142/5089 10.1109/TPAMI.2006.17 10.1080/02331934.2011.611515 10.1007/978-1-4757-2440-0 10.1016/j.procs.2010.04.272 10.1137/S1064827596304010 10.1109/TIT.2005.862083 10.1002/cpa.20124 10.1023/A:1018628609742 10.1145/502512.502527 10.1111/j.2517-6161.1996.tb02080.x |
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| Copyright | Operations Research Society of China, Periodicals Agency of Shanghai University, and Springer-Verlag Berlin Heidelberg 2015 Operations Research Society of China, Periodicals Agency of Shanghai University, and Springer-Verlag Berlin Heidelberg 2015. |
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| SubjectTerms | Algorithms Classification Classifiers Eigenvalues Feature selection Machine learning Management Science Mathematics Mathematics and Statistics Operations Research Optimization Original Paper Repositories Support vector machines |
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| Title | Sparse Proximal Support Vector Machine with a Specialized Interior-Point Method |
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