An adaptive wavelet network for function learning

Abstract

In this article, a wavelet neural network (WNN) model is proposed for approximating arbitrary nonlinear functions. Our WNN model structure comes from the idea of adaptive neuro-fuzzy inference system (ANFIS) which is used for obtaining fuzzy rule base from the input-output data of an unknown function. The WNN model which is called in this study as adaptive wavelet network (AWN) consists of wavelet scaling functions in its processing units whereas in an ANFIS, mostly Gaussian-type membership functions are used for a function approximation. We present to train an AWN by a hybrid-learning method containing least square estimation (LSE) with gradient-based optimization algorithm to obtain the optimal translation and dilation parameters of our AWN for model accuracy. Simulation examples are also given to illustrate the effectiveness of the method.