Robust support vector machine classifier with truncated loss function by gradient algorithm
The support vector machine (SVM) is an increasingly important tool in machine learning. Despite its popularity, the SVM classifier can be adversely affected under the presence of noise in the training dataset. The SVM can be fit in the regularization framework of Loss ＋ Penalty. The loss function pl...
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| Vydané v: | Computers & industrial engineering Ročník 172; s. 108630 |
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| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Elsevier Ltd
01.10.2022
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| ISSN: | 0360-8352, 1879-0550 |
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| Abstract | The support vector machine (SVM) is an increasingly important tool in machine learning. Despite its popularity, the SVM classifier can be adversely affected under the presence of noise in the training dataset. The SVM can be fit in the regularization framework of Loss ＋ Penalty. The loss function plays an essential role which is used to keep the fidelity of the resulting model to the data. Most SVMs use convex losses, however, they often suffer from the negative impact of points far away from their own classes. This paper proposes a new nonconvex differentiable loss, namely huberied truncated pinball loss, which can be able to reduce the effects of noise in the training sample. The SVM classifier with the huberied truncated pinball loss (HTPSVM) is proposed. The HTPSVM combines the elastic net penalty and the nonconvex huberied truncated pinball loss. It inherits the benefits of both ℓ1 and ℓ2 norm regularizers. The HTPSVM involves nonconvex minimization, the accelerated proximal gradient (APG) algorithm was used to solve the corresponding optimization. To evaluate the performance of classifiers, classification accuracy and area under ROC curve (AUC) were employed as the accuracy indicators. The numerical results show that our new classifier is effective. Friedman and Nemenyi post hoc tests of the experimental results indicate that the proposed HTPSVM is shown to be more robust to noise than HSVM, PSVM and HHSVM.
•We propose a novel robust and smooth loss function.•Accelerated proximal gradient algorithm is applied to solve the proposed method.•Classification accuracy and AUC are employed to evaluate the performance of classifiers.•Statistical evaluation of the experimental results shows the effectiveness of the proposed method. |
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| AbstractList | The support vector machine (SVM) is an increasingly important tool in machine learning. Despite its popularity, the SVM classifier can be adversely affected under the presence of noise in the training dataset. The SVM can be fit in the regularization framework of Loss ＋ Penalty. The loss function plays an essential role which is used to keep the fidelity of the resulting model to the data. Most SVMs use convex losses, however, they often suffer from the negative impact of points far away from their own classes. This paper proposes a new nonconvex differentiable loss, namely huberied truncated pinball loss, which can be able to reduce the effects of noise in the training sample. The SVM classifier with the huberied truncated pinball loss (HTPSVM) is proposed. The HTPSVM combines the elastic net penalty and the nonconvex huberied truncated pinball loss. It inherits the benefits of both ℓ1 and ℓ2 norm regularizers. The HTPSVM involves nonconvex minimization, the accelerated proximal gradient (APG) algorithm was used to solve the corresponding optimization. To evaluate the performance of classifiers, classification accuracy and area under ROC curve (AUC) were employed as the accuracy indicators. The numerical results show that our new classifier is effective. Friedman and Nemenyi post hoc tests of the experimental results indicate that the proposed HTPSVM is shown to be more robust to noise than HSVM, PSVM and HHSVM.
•We propose a novel robust and smooth loss function.•Accelerated proximal gradient algorithm is applied to solve the proposed method.•Classification accuracy and AUC are employed to evaluate the performance of classifiers.•Statistical evaluation of the experimental results shows the effectiveness of the proposed method. |
| ArticleNumber | 108630 |
| Author | Xiao, Yingyuan Song, Yunyan Zhu, Wenxin |
| Author_xml | – sequence: 1 givenname: Wenxin surname: Zhu fullname: Zhu, Wenxin email: zhuwenxin@tjau.edu.cn organization: Tianjin Key Laboratory of Intelligence Computing and Novel Software Technology, Tianjin University of Technology, 300384, Tianjin, China – sequence: 2 givenname: Yunyan orcidid: 0000-0003-2329-6038 surname: Song fullname: Song, Yunyan email: songyunyanlg@email.tjut.edu.cn organization: College of Science, Tianjin University of Technology, 300384, Tianjin, China – sequence: 3 givenname: Yingyuan surname: Xiao fullname: Xiao, Yingyuan email: yyxiao@tjut.edu.cn organization: Tianjin Key Laboratory of Intelligence Computing and Novel Software Technology, Tianjin University of Technology, 300384, Tianjin, China |
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| Cites_doi | 10.1111/j.1467-9868.2005.00503.x 10.1214/aoms/1177731944 10.1145/1961189.1961199 10.1016/j.amc.2020.125186 10.1109/TPAMI.2013.178 10.1007/s10044-015-0485-z 10.1093/biostatistics/kxg046 10.1023/A:1008288411710 10.1162/08997660360581958 10.1093/bioinformatics/btm579 10.1162/NECO_a_00837 10.1109/72.788646 10.1166/asl.2014.5640 10.1137/080716542 10.1198/016214507000000617 10.1002/cjs.10105 10.1007/s00500-014-1448-9 10.1080/01621459.1937.10503522 10.1007/s11063-013-9336-3 10.1016/j.engappai.2020.103635 |
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| Keywords | Friedman test Nemenyi post hoc test Support vector machine Accelerated proximal gradient algorithm Huberized truncated pinball loss AUC |
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