Radial Basis Functions Networks

The solution of complex mapping problems with artificial neural networks normally demands the use of a multi-layer network structure. This multi-layer topology process data into consecutive steps in each one of the layers. Radial Basis Functions networks are a particular neural network structure that uses radial functions in the intermediate, or hidden, layer. It has been shown in the literature that feed-forward neural networks, such as Multi-Layer Perceptrons and Radial Basis Functions Networks, are universal multi-variable function approximators. Since forecasting problems can be treated as a general function approximation problem in the form y(k) = f(y(k− 1), y(k− 2), …, u(k), u(k− 1), …) (uand yare, respectively, system input and output) it can be easily understood that these network structures can be directly applied to forecasting problems.A general introduction to Radial Basis Functions is given in this chapter. Training this network structure consists on two phases: center and radius selection for the radial functions of the hidden layer and weights determination for the output linear layer. Several methods for both phases of training are presented throughout the chapter. In the end, an example of using Radial Basis Functions for non-linear time series forecasting is given, in order to show its applicability to solve complex forecasting problems.