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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, normalisation of the basis functions can lead to other effects which are sometimes less desirable for modelling applications. This paper describes some side effects 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 'reactivate', i.e. re-appear far from the basis function centre. This paper examines how these phenomena occur, discusses their relevance for non-linear function approximation and examines the effect of normalisation on the network condition number and weights.
|Glasgow Author(s):||Murray-Smith, Prof Roderick|
|Authors:||Shorten, R., and Murray-Smith, R.|
|Subjects:||Q Science > QA Mathematics > QA75 Electronic computers. Computer science|
|College/School:||College of Science and Engineering > School of Computing Science|
|Journal Name:||International Journal of Neural Systems|