The paper is related to the error analysis of Support Vector Machine (SVM) classifiers based on reproducing kernel Hilbert spaces. We choose the polynomial kernels as the Mercer kernel and give the error estimate with De La Vallée Poussin means which improve the approximation error. On the other hand, the distortion is replaced by the uniformly boundedness of the Cesàro means. We also introduce the standard estimation of the sample error, and derive the explicit learning rate.
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