Characterising complexity in a radial basis function network

Attempting to match the complexity of a neural network to the complexity of a data set is difficult as there is no method to determine the effective total degrees of freedom of a network. In this paper we introduce a method for characterising the degrees of freedom of a Radial Basis Function network by exploiting a relationship to the theory of linear smoothers. Specifically, complexity of the model is demonstrated theoretically and empirically to be determined by a spectral analysis of the space spanned by the outputs of the hidden layer.