Wavelet Support Vector Machine With Universal Approximation and its Application

Abstract

Wavelet support vector machines (WSVM) using the Mexican Hat wavelet kernel has been used for nonlinear system identification successfully, but its universal approximation property has never been proved in theory. Based on the Stone-Weierstrass theorem, the universal approximation property of the WSVM to arbitrary functions on a compact set is proved with arbitrary accuracy. These simulations show that WSVM is very effective in nonlinear system identification, and can deduce the noise of the system, so WSVM has great potential applications in function estimation, nonlinear system identification, signal processing and control