首页 | 本学科首页   官方微博 | 高级检索  
     检索      


Approximation with polynomial kernels and SVM classifiers
Authors:Ding-Xuan Zhou  Kurt Jetter
Institution:001. Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China
002. Institut für Angewandte Mathematik und Statistik, Universit?t Hohenheim, D-70593, Stuttgart, Germany
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 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. Dedicated to Charlie Micchelli on the occasion of his 60th birthday Mathematics subject classifications (2000) 68T05, 62J02. Ding-Xuan Zhou: The first author is supported partially by the Research Grants Council of Hong Kong (Project No. CityU 103704).
Keywords:classification algorithm  regularization scheme  polynomial kernel  approximation by Durrmeyer operators  support vector machine  misclassification error
本文献已被 SpringerLink 等数据库收录!
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号