基于Riesz基的再生核及支持向量机

Riesz basis-based reproducing kernel and SVM

在支持向量机 (SVM)技术中 ,再生核的选择起着重要作用 .利用 L 2 (R)中的一组 Riesz基构造再生核 ,并将其推广到应用广泛的正交小波 .在基于正交小波的再生核 Hilbert空间中考虑函数的正则化逼近 ,对基于正交小波再生核的 SVM结合小波分析进行探讨 ,得到 SVM的离散逼近 。

The choice of the reproducing kernel is important in SVM technic. A reproducing kernel Hilbert space with a group of Riesz basis in L^2(R) is built, and generalized to widely used orthogonal wavelet. Considering regularized approximation of function in a reproducing kernel Hilbert space based on orthogonal wavelet, some studies on SVM have been done incorporating with wavelet analysis. It is proved that both the discrete approximation and discrete detail of SVM have something to do with support vectors.