On Normalising Radial Basis Function

Normalisation of the basis function activations in a radial basis function (RBF) network is a common way of achieving the partition of unity often desired for modelling applications. It results in the basis functions covering the whole of the input space to the same degree. However, normalisa-tion of the basis functions can lead to other eeects which are sometimes less desireable for modelling applications. This paper describes some side eeects of normalisation which fundamentally alter properties of the basis functions, e.g. the shape is no longer uniform, maxima of basis functions can be shifted from their centres, and the basis functions are no longer guaranteed to decrease monotonically as distance from their centre increases { in many cases basis functions can reappear far from the basis function centre. This paper examines how these phenomena occur, and analyses theoretically and experimentally the eeect of normalisation on the least squares solution to the weights problem.