Approximation with polynomial kernels and SVM classifiers

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

114 Scopus Citations
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Author(s)

  • Ding-Xuan Zhou
  • Kurt Jetter

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)323-344
Journal / PublicationAdvances in Computational Mathematics
Volume25
Issue number1-3
Publication statusPublished - Jul 2006

Abstract

This paper presents an error analysis for classification algorithms generated by regularization schemes with polynomial kernels. Explicit convergence rates are provided for support vector machine (SVM) soft margin classifiers. The misclassification error can be estimated by the sum of sample error and regularization error. The main difficulty for studying algorithms with polynomial kernels is the regularization error which involves deeply the degrees of the kernel polynomials. Here we overcome this difficulty by bounding the reproducing kernel Hilbert space norm of Durrmeyer operators, and estimating the rate of approximation by Durrmeyer operators in a weighted L 1 space (the weight is a probability distribution). Our study shows that the regularization parameter should decrease exponentially fast with the sample size, which is a special feature of polynomial kernels. © Springer 2006.

Research Area(s)

  • Approximation by Durrmeyer operators, Classification algorithm, Misclassification error, Polynomial kernel, Regularization scheme, Support vector machine

Citation Format(s)

Approximation with polynomial kernels and SVM classifiers. / Zhou, Ding-Xuan; Jetter, Kurt.
In: Advances in Computational Mathematics, Vol. 25, No. 1-3, 07.2006, p. 323-344.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review