caa a22 4500 467939519 CHVBK 20180406153008.0 cr unu---uuuuu 170328e20060701xx s 000 0 eng 10.1007/s10444-004-7206-2 doi (NATIONALLICENCE)springer-10.1007/s10444-004-7206-2 Approximation with polynomial kernels and SVM classifiers [Elektronische Daten] [Ding-Xuan Zhou, Kurt Jetter] 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 L1 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 classification algorithm nationallicence regularization scheme nationallicence polynomial kernel nationallicence approximation by Durrmeyer operators nationallicence support vector machine nationallicence misclassification error nationallicence Zhou Ding-Xuan Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China aut Jetter Kurt Institut für Angewandte Mathematik und Statistik, Universität Hohenheim, D-70593, Stuttgart, Germany aut Advances in Computational Mathematics Kluwer Academic Publishers 25/1-3(2006-07-01), 323-344 1019-7168 25:1-3<323 2006 25 10444 https://doi.org/10.1007/s10444-004-7206-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10444-004-7206-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Zhou Ding-Xuan Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China aut NATIONALLICENCE 700 1- Jetter Kurt Institut für Angewandte Mathematik und Statistik, Universität Hohenheim, D-70593, Stuttgart, Germany aut NATIONALLICENCE 773 0- Advances in Computational Mathematics Kluwer Academic Publishers 25/1-3(2006-07-01), 323-344 1019-7168 25:1-3<323 2006 25 10444 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer