Learning rates for SVM classifiers with polynomial kernels

The polynomial kernel is one of the most important kernels used in the learning theory. This paper provides an error analysis for the support vector machine (SVM) soft margin classifier with polynomial kernels. The learning rate is estimated by the sum of sample error and regularization error. As an important tool, so-called modified Durrmeyer polynomials are introduced. The norm of reproducing kernel Hilbert space generated by the polynomial kernels and the approximation properties of the operators play key roles in the analysis of the regularization error. Also, the explicit learning rates for the SVM regularized classifiers are derived.