RBF networks with mixed radial basis functions

After the introduction to neural network technology as multivariable function approximation, radial basis function (RBF) networks have been studied in many different aspects in recent years. From the theoretical viewpoint, approximation and uniqueness of the interpolation is studied and it has been established that RBF network can approximate arbitrarily well any multivariate continuous function provided enough radial basis functions are employed. For the number of hidden nodes, type of radial base functions, width of the basis functions, cluster centres of the basis functions are some example issues on which numerous research works appeared in the literature. In contrast with this, however, there is remarkably only a few papers pointing out the functional approximation from the frequency domain view-point. They identify that basis functions basically behave as low pass filters. Due to this over filtering effect the RBF networks are not favourable for high frequencies unless relatively high number of hidden nodes is used. Therefore, for approximations that have only low frequency components, RBF networks provide satisfactory results and this is presumably the case in many favourable RBF applications reported in literature and vice versa. However, considering the filtering characteristics of different radial basis functions, one can improve the performance of RBF networks with mixture of radial basis functions.