On Global–Local Artificial Neural Networks for Function Approximation

We present a hybrid radial basis function (RBF) sigmoid neural network with a three-step training algorithm that utilizes both global search and gradient descent training. The algorithm used is intended to identify global features of an input–output relationship before adding local detail to the approximating function. It aims to achieve efficient function approximation through the separate identification of aspects of a relationship that are expressed universally from those that vary only within particular regions of the input space. We test the effectiveness of our method using five regression tasks; four use synthetic datasets while the last problem uses real-world data on the wave overtopping of seawalls. It is shown that the hybrid architecture is often superior to architectures containing neurons of a single type in several ways: lower mean square errors are often achievable using fewer hidden neurons and with less need for regularization. Our global–local artificial neural network (GL-ANN) is also seen to compare favorably with both perceptron radial basis net and regression tree derived RBFs. A number of issues concerning the training of GL-ANNs are discussed: the use of regularization, the inclusion of a gradient descent optimization step, the choice of RBF spreads, model selection, and the development of appropriate stopping criteria.