A novel Least Squares Support Vector Machine kernel for approximation

The support vector machine (SVM) is receiving considerable attention for its superior ability to solve nonlinear classification, function estimation and density estimation. Least squares support vector machines (LS-SVM) are re-formulations to the standard SVMs. Motivated by the theory of multi-scale representations of signals and wavelet transforms, this paper presents a way for building a wavelet-based reproducing kernel Hilbert spaces (RKHS) and its associate scaling kernel for least squares support vector machines (LS-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, approximation results illustrate that the LS-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.