Multiple Models Book: Side effect of Normalising Basis Functions
Normalisation of the basis functions in a local model 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 can lead to other effects which are
sometimes less desirable for modelling applications. This chapter describes
some of these side-effects 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, the entire input space can be covered, 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. reappear far from the basis
function centre, thereby having more than one region of significant activity.
The effect of normalisation on the least squares solution for the local model parameters is then discussed.
R Murray-Smith
Last modified: Tue Mar 25 16:30:08 GMT