A Wavelet Neural Network for the Approximation of Nonlinear Multivariable Functions

Abstract

Wavelet transformation has the ability of representing a function and revealing the properties of the func-tion in both the localized time domain and frequency domain. Wavelet neural networks employing the wavelet function as the activation function of the units of the neural networks have been proposed as an alternative approach to nonlinear mapping problems. In this paper, we propose a novel wavelet neural network which can be employed as a useful tool for learning a mapping between an input and an output space. The activa-tion function of the units of the proposed network is compact supported non-orthogonal function which has been described by Yamakawa et al. as convex wavelet in their paper. We present the theoretical proof about the function approximation ability of the proposed network. The experimential results of solving function approximation problems and the two-spirals classification problem indicate the better performance of the proposed network.