Efficient algorithm for training interpolation RBF networks with equally spaced nodes

This brief paper proposes a new algorithm to train interpolation Gaussian radial basis function (RBF) networks in order to solve the problem of interpolating multivariate functions with equally spaced nodes. Based on an efficient two-phase algorithm recently proposed by the authors, Euclidean norm associated to Gaussian RBF is now replaced by a conveniently chosen Mahalanobis norm, that allows for directly computing the width parameters of Gaussian radial basis functions. The weighting parameters are then determined by a simple iterative method. The original two-phase algorithm becomes a one-phase one. Simulation results show that the generality of networks trained by this new algorithm is sensibly improved and the running time significantly reduced, especially when the number of nodes is large.