Constructing a wavelet-based RKHS and its associated scaling kernel for support vector approximation

Many of characteristics of support vector machine (SVM) are determined by the type of kernels used. Traditional kernels such as polynomial kernel and radial basis function kernel have many limitations. It is valuable to investigate the problem of whether a better performance could be obtained if we construct a scaling kernel by using the scaling function. This paper presents a way for building a wavelet-based reproducing kernel Hilbert spaces (RKHS) and its associate scaling kernel for SVM. The RKHS built is a multiresolution scale subspace, and the scaling kernel is constructed by using a scaling function with its different dilations and translations. Compared to the traditional kernels, results on two approximation problems illustrate that the SVM with scaling kernel enjoys two advantages: (1) it can approximate arbitrary signal and owns better approximation performance; (2) it can implement multi-scale approximation.