Combining space-filling curves and radial basis function networks

Abstract

We propose here to use a space-filling curve (SPC) as a tool to introduce a new metric in Id denned as a distance along the space-filling curve. This metric is to be used inside radial functions instead of the Euclidean or the Mahalanobis distance. This approach is equivalent to using SFC to pre-process the input data before training the RBF net. All the network tuning operations are performed in one dimension. Furthermore, we introduce a new method of computing the weights of linear output neuron, which is based on connection between RBF net and Nadaraya-Watson kernel regression estimators.