Critical Vector Learning for RBF Networks

Abstract

One of the most popular neural network models, the radial basis function (RBF) network attracts a lot of attention due to its improved approximation ability as well as the construction of its architecture. Bishop (1991) concluded that an RBF network can provide a fast, linear algorithm capable of representing complex nonlinear mappings. Park and Sandberg (1993) further showed that an RBF network can approximate any regular function. In a statistical sense, the approximation ability is a special case of statistical consistency. Hence, Xu et al. (1994) presented upper bounds for the convergence rates of the approximation error of RBF networks, and constructively proved the existence of a consistent point-wise estimator for RBF networks. Their results can be a guide to optimize the construction of an RBF network, which includes the determination of the total number of radial basis functions along with their centers and widths. This is an important problem to address because the performance and training of an RBF network depend very much on these parameters.