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Robust truncated L\(_2\)-norm twin support vector machine

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Abstract

This paper proposes a new robust truncated L\(_2\)-norm twin support vector machine (T\(^2\)SVM), where the truncated L\(_2\)-norm is used to measure the empirical risk to make the classifiers more robust when encountering lots of outliers. Meanwhile, chance constraints are also employed to specify false positive and false negative error rates. T\(^2\)SVM considers a pair of chance constrained nonconvex nonsmooth problems. To solve these difficult problems, we propose an efficient iterative method for T\(^2\)SVM based on difference of convex functions (DC) programs and DC Algorithms (DCA). Experiments on benchmark data sets and artificial data sets demonstrate the significant virtues of T\(^2\)SVM in terms of robustness and generalization performance.

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  1. SeDuMi: http://sedumi.mcmaster.ca/

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Acknowledgements

This research is partially supported by National Natural Science Foundation of China (Grant No.11871128), Natural Science Foundation of Chongqing (Grants No. cstc2019jcyj-msxmX0282), Scientific and Technological Research Program of Chongqing Municipal Education Commission (Grant No. KJQN201900531), and Program of Chongqing Innovation Research Group Project in University (CXQT20014) and the Innovation Project for Scientific Research of Postgraduate of Chongqing (CYS20247).

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Authors and Affiliations

  1. Department of Mathematical Sciences, Chongqing Normal University, Chongqing, 401331, China

    Linxi Yang, Guoquan Li & Zhiyou Wu

  2. Chongqing Center for Applied Mathematics, Chongqing, 401331, China

    Guoquan Li & Zhiyou Wu

  3. School of Management, Guangzhou University, Guangzhou, 510006, China

    Changzhi Wu

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  1. Linxi Yang
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  2. Guoquan Li
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Correspondence to Guoquan Li.

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Yang, L., Li, G., Wu, Z. et al. Robust truncated L\(_2\)-norm twin support vector machine. Int. J. Mach. Learn. & Cyber. 12, 3415–3436 (2021). https://doi.org/10.1007/s13042-021-01368-8

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  • DOI: https://doi.org/10.1007/s13042-021-01368-8

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