Radial basis functions: Normalised or un-normalised?

In this paper a simple and robust combination of architecture and training strategy is proposed for a radial basis function network (RBFN). The proposed network uses a normalised Gaussian kernel architecture with kernel centres randomly selected from a training data set. The output layer weights are adapted using the numerically robust Householder transform. The application of this normalised radial basis function network (NRBFN) to the prediction of chaotic signals is reported. NRBFN´s are shown to perform better than un-normalised equivalent networks for the task of chaotic signal prediction. Chaotic signal prediction is also used to demonstrate that a NRBFN is less sensitive to basis function parameter selection than an equivalent un-normalised network. Normalisation is found to be a simple alternative to regularisation for the task of using a RBFN to recursively predict, and thus to capture the dynamics of, a chaotic signal corrupted by additive white Gaussian noise.