Radial basis function neural networks: Theory and applications

Essential theory and main applications of feed-forward connectionist structures termed radial basis function (RBF) neural networks are given. Universal approximation and Cover's theorems are outlined that justify powerful RBF network capabilities in function approximation and data classification tasks. The methods for regularising RBF generated mappings are addressed also. Links of these networks to kernel regression methods, density estimation, and nonlinear principal component analysis are pointed out. Particular attention is put on discussing different RBF network training schemes, e.g. the constructive method incorporating orthogonalisation of RBF kernels. Numerous, successful RBF networks applications in diverse fields such as signal modelling, non-linear time series prediction, identification of dynamic systems, pattern recognition, and knowledge discovery are outlined.