A Novel Least Squares Support Vector Machine Kernel for Approximation
Xiangyang Mu, Weixin Gao, Nan Tang, Yatong Zhou · 2008
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.