A Growing and Pruning Method for Radial Basis Function Networks

A recently published generalized growing and pruning (GGAP) training algorithm for radial basis function (RBF) neural networks is studied and modified. GGAP is a resource-allocating network (RAN) algorithm, which means that a created network unit that consistently makes little contribution to the network's performance can be removed during the training. GGAP states a formula for computing the significance of the network units, which requires a d-fold numerical integration for arbitrary probability density function
p
(
x
) of the input data
x
(
x
isin
R

d
) . In this work, the GGAP formula is approximated using a Gaussian mixture model (GMM) for
p
(
x
) and an analytical solution of the approximated unit significance is derived. This makes it possible to employ the modified GGAP for input data having complex and high-dimensional
p
(
x
), which was not possible in the original GGAP. The results of an extensive experimental study show that the modified algorithm outperforms the original GGAP achieving both a lower prediction error and reduced complexity of the trained network.