Robust Support Vector Machine With Asymmetric Truncated Generalized Pinball Loss
The support vector machine (SVM) with pinball loss (Pin-SVM) can handle noise sensitivity and instability to re-sampling but loses sparsity. To solve this limitation, SVM with a generalized pinball loss that incorporates an insensitive zone (GP-SVM) was proposed. The GP-SVM can handle sparsity by op...
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| Published in: | IEEE access Vol. 12; pp. 155696 - 155717 |
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| Format: | Journal Article |
| Language: | English |
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2024
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| ISSN: | 2169-3536, 2169-3536 |
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| Abstract | The support vector machine (SVM) with pinball loss (Pin-SVM) can handle noise sensitivity and instability to re-sampling but loses sparsity. To solve this limitation, SVM with a generalized pinball loss that incorporates an insensitive zone (GP-SVM) was proposed. The GP-SVM can handle sparsity by optimizing the asymmetric spread of the insensitive zone. Despite these improvements, the unboundedness of the loss functions can result in a lack of robustness to outliers. In this paper, we introduce a novel robust support vector classification based on an <inline-formula> <tex-math notation="LaTeX">(\alpha _{1}, \alpha _{2}) </tex-math></inline-formula>-asymmetric bounded loss function, an asymmetric truncated generalized pinball loss (called <inline-formula> <tex-math notation="LaTeX">L_{tgp}^{\alpha _{1}, \alpha _{2}} </tex-math></inline-formula>). A characteristic of SVM with <inline-formula> <tex-math notation="LaTeX">L_{tgp}^{\alpha _{1}, \alpha _{2}} </tex-math></inline-formula> (ATGP-SVM) is its ability to balance generalization and sparsity while minimizing the impact of outliers. However, <inline-formula> <tex-math notation="LaTeX">L_{tgp}^{\alpha _{1}, \alpha _{2}} </tex-math></inline-formula> is a non-convex function, ATGP-SVM is difficult to solve. Therefore, we formulated the ATGP-SVM utilizing DC (difference of convex functions) programming and subsequently resolved it through the DC algorithm (DCA). The experimental results obtained from diverse benchmark datasets underscore the effectiveness of our proposed formulation when compared to other state-of-the-art classification models. |
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| AbstractList | The support vector machine (SVM) with pinball loss (Pin-SVM) can handle noise sensitivity and instability to re-sampling but loses sparsity. To solve this limitation, SVM with a generalized pinball loss that incorporates an insensitive zone (GP-SVM) was proposed. The GP-SVM can handle sparsity by optimizing the asymmetric spread of the insensitive zone. Despite these improvements, the unboundedness of the loss functions can result in a lack of robustness to outliers. In this paper, we introduce a novel robust support vector classification based on an <inline-formula> <tex-math notation="LaTeX">(\alpha _{1}, \alpha _{2}) </tex-math></inline-formula>-asymmetric bounded loss function, an asymmetric truncated generalized pinball loss (called <inline-formula> <tex-math notation="LaTeX">L_{tgp}^{\alpha _{1}, \alpha _{2}} </tex-math></inline-formula>). A characteristic of SVM with <inline-formula> <tex-math notation="LaTeX">L_{tgp}^{\alpha _{1}, \alpha _{2}} </tex-math></inline-formula> (ATGP-SVM) is its ability to balance generalization and sparsity while minimizing the impact of outliers. However, <inline-formula> <tex-math notation="LaTeX">L_{tgp}^{\alpha _{1}, \alpha _{2}} </tex-math></inline-formula> is a non-convex function, ATGP-SVM is difficult to solve. Therefore, we formulated the ATGP-SVM utilizing DC (difference of convex functions) programming and subsequently resolved it through the DC algorithm (DCA). The experimental results obtained from diverse benchmark datasets underscore the effectiveness of our proposed formulation when compared to other state-of-the-art classification models. The support vector machine (SVM) with pinball loss (Pin-SVM) can handle noise sensitivity and instability to re-sampling but loses sparsity. To solve this limitation, SVM with a generalized pinball loss that incorporates an insensitive zone (GP-SVM) was proposed. The GP-SVM can handle sparsity by optimizing the asymmetric spread of the insensitive zone. Despite these improvements, the unboundedness of the loss functions can result in a lack of robustness to outliers. In this paper, we introduce a novel robust support vector classification based on an [Formula Omitted]-asymmetric bounded loss function, an asymmetric truncated generalized pinball loss (called [Formula Omitted]). A characteristic of SVM with [Formula Omitted] (ATGP-SVM) is its ability to balance generalization and sparsity while minimizing the impact of outliers. However, [Formula Omitted] is a non-convex function, ATGP-SVM is difficult to solve. Therefore, we formulated the ATGP-SVM utilizing DC (difference of convex functions) programming and subsequently resolved it through the DC algorithm (DCA). The experimental results obtained from diverse benchmark datasets underscore the effectiveness of our proposed formulation when compared to other state-of-the-art classification models. The support vector machine (SVM) with pinball loss (Pin-SVM) can handle noise sensitivity and instability to re-sampling but loses sparsity. To solve this limitation, SVM with a generalized pinball loss that incorporates an insensitive zone (GP-SVM) was proposed. The GP-SVM can handle sparsity by optimizing the asymmetric spread of the insensitive zone. Despite these improvements, the unboundedness of the loss functions can result in a lack of robustness to outliers. In this paper, we introduce a novel robust support vector classification based on an <tex-math notation="LaTeX">$(\alpha _{1}, \alpha _{2})$ </tex-math>-asymmetric bounded loss function, an asymmetric truncated generalized pinball loss (called <tex-math notation="LaTeX">$L_{tgp}^{\alpha _{1}, \alpha _{2}}$ </tex-math>). A characteristic of SVM with <tex-math notation="LaTeX">$L_{tgp}^{\alpha _{1}, \alpha _{2}}$ </tex-math> (ATGP-SVM) is its ability to balance generalization and sparsity while minimizing the impact of outliers. However, <tex-math notation="LaTeX">$L_{tgp}^{\alpha _{1}, \alpha _{2}}$ </tex-math> is a non-convex function, ATGP-SVM is difficult to solve. Therefore, we formulated the ATGP-SVM utilizing DC (difference of convex functions) programming and subsequently resolved it through the DC algorithm (DCA). The experimental results obtained from diverse benchmark datasets underscore the effectiveness of our proposed formulation when compared to other state-of-the-art classification models. |
| Author | Wangkeeree, Rabian Suppalap, Siwakon |
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| SubjectTerms | Algorithms Asymmetry Classification Convex functions difference of convex functions programming Fasteners generalized pinball loss Noise Noise sensitivity Optimization methods pinball loss Programming Robustness Sensitivity Sparsity Support vector machine Support vector machines Training Vectors |
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| Title | Robust Support Vector Machine With Asymmetric Truncated Generalized Pinball Loss |
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