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Robust energy-based least squares twin support vector machines

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Abstract

Twin support vector machine (TSVM), least squares TSVM (LSTSVM) and energy-based LSTSVM (ELS-TSVM) satisfy only empirical risk minimization principle. Moreover, the matrices in their formulations are always positive semi-definite. To overcome these problems, we propose in this paper a robust energy-based least squares twin support vector machine algorithm, called RELS-TSVM for short. Unlike TSVM, LSTSVM and ELS-TSVM, our RELS-TSVM maximizes the margin with a positive definite matrix formulation and implements the structural risk minimization principle which embodies the marrow of statistical learning theory. Furthermore, RELS-TSVM utilizes energy parameters to reduce the effect of noise and outliers. Experimental results on several synthetic and real-world benchmark datasets show that RELS-TSVM not only yields better classification performance but also has a lower training time compared to ELS-TSVM, LSPTSVM, LSTSVM, TBSVM and TSVM.

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Acknowledgments

The authors gratefully acknowledge the helpful comments and suggestions of the reviewers, which have improved the presentation.

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Authors and Affiliations

  1. School of Computer Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore, 639798, Singapore

    Mohammad Tanveer & Shen-Shyang Ho

  2. Department of Electronics and Communication Engineering, The LNM Institute of Information Technology, Jaipur, 302 031, India

    Mohammad Asif Khan

Authors
  1. Mohammad Tanveer
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  2. Mohammad Asif Khan
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  3. Shen-Shyang Ho
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Correspondence to Mohammad Tanveer.

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Tanveer, M., Khan, M.A. & Ho, SS. Robust energy-based least squares twin support vector machines. Appl Intell 45, 174–186 (2016). https://doi.org/10.1007/s10489-015-0751-1

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