RBF Neural Network, Basis Functions And Genetic Algorithm - Neural Networks,1997., International Conference on

Radial Basis Funct ion ( R B F ) network i s a n e f i c i e n t func t ion approximator. Theoretical researches focus o n the capabilities of the network t o reach a n optimal solution. Unfortunately, f e w results concerning the design and training of the network are available. W h e n dealing with a specific application, the performances of the network dramatically depend o n the number of neurons and o n the distribution o f the hidden neurons in the input space. Generally, the network resulting f r o m learning applied t o a predetermined architecture, i s either insu f ic ien t or over-complicated. In this study, we focus o n genetic learning f o r the R B F network applied to prediction of chaotic t i m e series. The centers and widths of the hidden layer neurons basis func t ion defined as the barycenter and distance between two input patterns are coded in to a chromosome. I t i s shown that the basis funct ions which are also coded as a paramater of the neurons provide a n additional degree of freedom resulting in a smaller optimal network. A direct inversion of matr ix provides the weights between the hidden layer and the output layer and avoids the risk of getting stuck in to a local m i n i m u m . T h e performances of a network wi th Gaussian basis func t ions i s compared with those of a network with genetic determinat ion of the basis func t ions o n the MackeyGlass delay differential equation.