Algorithm for building a neural network for function approximation

Abstract

A technique for constructing a multilayer tree-structured neural network, which provides a continuous, piece-wise linear function approximation, is presented. The method uses a growth network with linear threshold neurons. Neurons are added to a binary tree until the approximation error at all sampling points is brought down to within a specified ±Δ. The number of neurons in the constructed network depends on the samples provided as well as the specified tolerance Δ, thus enabling a trade-off between accuracy and network size. In comparison to approaches such as backpropagation, the proposed technique requires no assumptions regarding the number of neurons, learning rate, momentum term, or initial weight values. It also does not suffer from problems of local minima. Examples are presented to illustrate the effectiveness of the technique.