Configuring radial basis function network using fractal scaling process with application to chaotic time series prediction

Abstract

This paper introduces a novel algorithm for determining the structure of a radial basis function (RBF) network (the number of hidden units) while it is used for dynamic modeling of chaotic time series. It can be seen that the hidden units in the RBF network can form hyperplanes to partition the input space into various regions in each of which it is possible to approximate the dynamics with a basis function. The number of regions corresponds to the number of hidden units. The basic idea of the proposed algorithm is to partition the input space by fractal scaling of the chaotic time series being modeled. By fractal scaling process, the number of basis functions (hidden units) as well as the number of input variables can be specified. Accordingly, the network topology is efficiently determined based on the complexity of the underlying dynamics as reflected in the observed time series. The feasibility of the proposed scheme is examined through dynamic modeling of the well-known chaotic time series. The results show that the new method can improve the predictability of chaotic time series with a suitable number of hidden units compared to that of reported in the literature.