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SVM-Maj: a majorization approach to linear support vector machines with different hinge errors

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  • Groenen, P.J.F.
  • Nalbantov, G.I.
  • Bioch, J.C.

Abstract

Support vector machines (SVM) are becoming increasingly popular for the prediction of a binary dependent variable. SVMs perform very well with respect to competing techniques. Often, the solution of an SVM is obtained by switching to the dual. In this paper, we stick to the primal support vector machine (SVM) problem, study its effective aspects, and propose varieties of convex loss functions such as the standard for SVM with the absolute hinge error as well as the quadratic hinge and the Huber hinge errors. We present an iterative majorization algorithm that minimizes each of the adaptations. In addition, we show that many of the features of an SVM are also obtained by an optimal scaling approach to regression. We illustrate this with an example from the literature and do a comparison of different methods on several empirical data sets.

Suggested Citation

  • Groenen, P.J.F. & Nalbantov, G.I. & Bioch, J.C., 2007. "SVM-Maj: a majorization approach to linear support vector machines with different hinge errors," Econometric Institute Research Papers EI 2007-49, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:12011
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    References listed on IDEAS

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    3. van der Kooij, Anita J. & Meulman, Jacqueline J. & Heiser, Willem J., 2006. "Local minima in categorical multiple regression," Computational Statistics & Data Analysis, Elsevier, vol. 50(2), pages 446-462, January.
    4. Kiers, Henk A. L., 2002. "Setting up alternating least squares and iterative majorization algorithms for solving various matrix optimization problems," Computational Statistics & Data Analysis, Elsevier, vol. 41(1), pages 157-170, November.
    5. Jan Leeuw & Forrest Young & Yoshio Takane, 1976. "Additive structure in qualitative data: An alternating least squares method with optimal scaling features," Psychometrika, Springer;The Psychometric Society, vol. 41(4), pages 471-503, December.
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