Radial Basis Functions (Model Browser User's Guide)

Model Browser User's Guide

How Many RBFs to Use

The main parameter that you must adjust in order to get a good fit with an RBF is the maximum number of centers. This is a parameter of the center selection algorithm, and is the maximum number of centers/RBFs that is chosen.
Usually the maximum number of centers is the number of RBFs that are actually selected. However, sometimes fewer RBFs are chosen because the (regularized) error has fallen below the tolerance before the maximum was reached.
You should use a number of RBFs that is significantly less than the number of data points, otherwise there are not enough degrees of freedom in the error to estimate the predictive quality of the model. That is, you cannot tell if the model is useful if you use too many RBFs. We would recommend an upper bound of 60% on the ratio of number of RBFs to number of data points. Having 80 centers when there are only 100 data points might seem to give a good value of PRESS, but when it comes to validation, it can sometimes become clear that the data has been overfitted, and the predictive capability is not as good as PRESS would suggest.
One strategy for choosing the number of RBFs is to fit more centers than you think are needed (say 70 out of 100), then use the (prune) toolbar button to reduce the number of centers in the model. After pruning the network, make a note of the reduced number of RBFs. Try fitting the model again with the maximum number of centers set to this reduced number. This recalculates the values of the nonlinear parameters (width and lambda) to be optimal for the reduced number of RBFs.
One strategy for the use of Stepwise is to use it to minimize PRESS as a final fine-tuning for the network, once pruning has been done. Whereas Prune only allows the last RBF introduced to be removed, Stepwise allows any RBF to be taken out.
Do not focus solely on PRESS as a measure of goodness of fit, especially at large ratios of RBFs to data points. Take log10(GCV) into account also.

Tips for Modeling with Radial Basis Functions Width Selection Algorithms