Approximation of continuous and discontinuous mappings by a growing neural RBF-based algorithm

In this paper a neural network for approximating continuous and discontinuous mappings is described. The activation functions of the hidden nodes are the Radial Basis Functions (RBF) whose variances are learnt by means of an evolutionary optimization strategy. A new incremental learning strategy is used in order to improve the net performances. The learning strategy is able to save computational time because of the selective growing of the net structure and the capability of the learning algorithm to keep the effects of the activation functions local. Further, it does not require high order derivatives. An analysis of the learning capabilities and a comparison of the net performances with other approaches reported in literature have been performed. It is shown that the resulting network improves the approximation results reported for continuous mappings and for those exhibiting a finite number of discontinuities.