Performance comparison between the training method and the numerical method of the orthogonal neural network in function approximation

Abstract

The orthogonal neural network is a recently developed neural network based on the properties of orthogonal functions. It can avoid the drawbacks of traditional feedforward neural networks such as initial values of weights, number of processing elements, and slow convergence speed. Nevertheless, it needs many processing elements if a small training error is desired. Therefore, numerous data sets are required to train the orthogonal neural network. In the article, a least-squares method is proposed to determine the exact weights by applying limited data sets. By using the Lagrange interpolation method, the desired data sets required to solve for the exact weights can be calculated. An experiment in approximating typical continuous and discrete functions is given. The Chebyshev polynomial is chosen to generate the processing elements of the orthogonal neural network. The experimental results show that the numerical method in determining the weights gives as good performance in approximation error as the known training method and the former has less convergence time. © 2004 Wiley Periodicals, Inc. Int J Int Syst 19: 1257–1275, 2004.