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Sample Reduction Using\(\ell _1\)-Norm Twin Bounded Support Vector Machine

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Abstract

Twin support machine (TSVM) has a lower time complexity than support vector machine (SVM), but it has a poor ability to perform sample reduction. In order to improve the ability of TSVM to reduce sample, we propose an\(\ell _1\)-norm twin bounded support machine (\(\ell _1\)-TBSVM) inspired by the sparsity of\(\ell _1\)-norm in feature space. The objective function of\(\ell _1\)-TBSVM contains the hinge loss and the\(\ell _1\)-norm terms, both which can induce sparsity. We solve the primal programming problems of\(\ell _1\)-TBSVM to prevent the disappearance of sparsity and avoid the situation that the inverse of matrix does not exist. Thus,\(\ell _1\)-TBSVM has a good sparsity, or a good ability to reduce sample. Experimental results on synthetic and UCI datasets indicate that\(\ell _1\)-TBSVM has a good ability to perform sample reduction and simultaneously enhances the classification performance.

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Acknowledgment

This work was supported in part by the Natural Science Foundation of the Jiangsu Higher Education Institutions of China under Grant No. 19KJA550002, by the Six Talent Peak Project of Jiangsu Province of China under Grant No. XYDXX-054, by the Priority Academic Program Development of Jiangsu Higher Education Institutions, and by the Collaborative Innovation Center of Novel Software Technology and Industrialization.

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Authors and Affiliations

  1. School of Computer Science and Technology, Joint International Research Laboratory of Machine Learning and Neuromorphic Computing, Soochow University, Suzhou, 215006, China

    Xiaohan Zheng, Li Zhang & Leilei Yan

  2. Provincial Key Laboratory for Computer Information Processing Technology, Soochow University, Suzhou, 215006, China

    Li Zhang

Authors
  1. Xiaohan Zheng

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  2. Li Zhang

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  3. Leilei Yan

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Correspondence toLi Zhang.

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Editors and Affiliations

  1. Harbin Institute of Technology, Shenzhen, China

    Haijun Zhang

  2. Nanfang College of Sun Yat-sen University, Guangzhou, China

    Zhi Yang

  3. Hefei University of Technology, Hefei, China

    Zhao Zhang

  4. Chongqing University, Chongqing, China

    Zhou Wu

  5. South China Normal University, Guangzhou, China

    Tianyong Hao

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Zheng, X., Zhang, L., Yan, L. (2021). Sample Reduction Using\(\ell _1\)-Norm Twin Bounded Support Vector Machine. In: Zhang, H., Yang, Z., Zhang, Z., Wu, Z., Hao, T. (eds) Neural Computing for Advanced Applications. NCAA 2021. Communications in Computer and Information Science, vol 1449. Springer, Singapore. https://doi.org/10.1007/978-981-16-5188-5_11

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