Supervised RBFNN Centers and Radii Initialization for Function Approximation Problems

Radial basis function neural networks (RBFNNs) have been applied to solve problems of classification, function approximation and time series prediction. In the design of an RBFNN it is necessary to set the values for the positions of the centers and the radii for each RBF. In the literature it is usually performed an initialization step to set the positions of the centers and, once they are placed, the radii are calculated using a heuristic. In this paper, a new algorithm to set the value of those two parameters is presented. This new algorithm uses a supervised learning in such a way that the position of the centers will be constrained by the output of the function to be approximated. Since each center represents a neuron that is activated by the input vectors, the radii are initialized using the center´s positions and their activation grades. In this way, the calculation of the radii is also influenced by the output of the target function, not like in other heuristics where only the positions of the centers or the input vectors are considered. As the experiments show, the new algorithm outperforms other algorithms previously used for this problem.