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Support vector machine classifier via L0/1 soft-margin loss

Support vector machine classifier via L0/1 soft-margin loss
Support vector machine classifier via L0/1 soft-margin loss
Support vector machine (SVM) has attracted great attentions for the last two decades due to its extensive applications, and thus numerous optimization models have been proposed. To distinguish all of them, in this paper, we introduce a new model equipped with an L 0/1 soft-margin loss (dubbed as L 0/1-SVM) which well captures the nature of the binary classification. Many of the existing convex/non-convex soft-margin losses can be viewed as a surrogate of the L 0/1 soft-margin loss. Despite the discrete nature of L 0/1, we manage to establish the existence of global minimizer of the new model as well as revealing the relationship among its minimizers and KKT/P-stationary points. These theoretical properties allow us to take advantage of the alternating direction method of multipliers. In addition, the L 0/1-support vector operator is introduced as a filter to prevent outliers from being support vectors during the training process. Hence, the method is expected to be relatively robust. Finally, numerical experiments demonstrate that our proposed method generates better performance in terms of much shorter computational time with much fewer number of support vectors when against with some other leading methods in areas of SVM. When the data size gets bigger, its advantage becomes more evident.
Wang, Huajun
abb5a240-9c74-45da-938a-92f24d8c28fe
Shao, Yuanhai
36274cde-31ce-46f9-9ed5-0c6691093699
Zhou, Shenglong
d183edc9-a9f6-4b07-a140-a82213dbd8c3
Zhang, Ce
4e15b496-cca9-4133-8ff5-f27ddd16684c
Xiu, Naihua
8b5770f7-ae35-4dbe-884a-02fb4ea27bee
Wang, Huajun
abb5a240-9c74-45da-938a-92f24d8c28fe
Shao, Yuanhai
36274cde-31ce-46f9-9ed5-0c6691093699
Zhou, Shenglong
d183edc9-a9f6-4b07-a140-a82213dbd8c3
Zhang, Ce
4e15b496-cca9-4133-8ff5-f27ddd16684c
Xiu, Naihua
8b5770f7-ae35-4dbe-884a-02fb4ea27bee

Wang, Huajun, Shao, Yuanhai, Zhou, Shenglong, Zhang, Ce and Xiu, Naihua (2019) Support vector machine classifier via L0/1 soft-margin loss. arXiv, (1912.07418). (In Press)

Record type: Article

Abstract

Support vector machine (SVM) has attracted great attentions for the last two decades due to its extensive applications, and thus numerous optimization models have been proposed. To distinguish all of them, in this paper, we introduce a new model equipped with an L 0/1 soft-margin loss (dubbed as L 0/1-SVM) which well captures the nature of the binary classification. Many of the existing convex/non-convex soft-margin losses can be viewed as a surrogate of the L 0/1 soft-margin loss. Despite the discrete nature of L 0/1, we manage to establish the existence of global minimizer of the new model as well as revealing the relationship among its minimizers and KKT/P-stationary points. These theoretical properties allow us to take advantage of the alternating direction method of multipliers. In addition, the L 0/1-support vector operator is introduced as a filter to prevent outliers from being support vectors during the training process. Hence, the method is expected to be relatively robust. Finally, numerical experiments demonstrate that our proposed method generates better performance in terms of much shorter computational time with much fewer number of support vectors when against with some other leading methods in areas of SVM. When the data size gets bigger, its advantage becomes more evident.

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L01-SVM - Author's Original
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More information

Accepted/In Press date: 16 December 2019

Identifiers

Local EPrints ID: 437630
URI: http://eprints.soton.ac.uk/id/eprint/437630
PURE UUID: f51a784f-1279-4c00-8c9f-d744536def05
ORCID for Shenglong Zhou: ORCID iD orcid.org/0000-0003-2843-1614

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Date deposited: 07 Feb 2020 17:30
Last modified: 16 Mar 2024 06:10

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Contributors

Author: Huajun Wang
Author: Yuanhai Shao
Author: Shenglong Zhou ORCID iD
Author: Ce Zhang
Author: Naihua Xiu

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