The key point in design of radial basis function networks is to specify the
number and the locations of the centers. Several heuristic hybrid learning
methods, which apply a clustering algorithm for locating the centers and s
ubsequently a linear least-squares method for the linear weights, have been
previously suggested. These hybrid methods can be put into two groups, whi
ch will be called as input clustering (IC) and input-output clustering (IOC
), depending on whether the output vector is also involved in the clusterin
g process, The idea of concatenating the output vector to the input vector
in the clustering process has independently been proposed by several papers
in the literature although none of them presented a theoretical analysis o
n such procedures, but rather demonstrated their effectiveness in several a
pplications. The main contribution of this paper is to present an approach
for investigating the relationship between clustering process on input-outp
ut training samples and the mean squared output error in the context of a r
adial basis function network (RBFN), We may summarize our investigations in
that matter as follows: 1) A weighted mean squared input-output quantizati
on error, which is to be minimized by IOC, yields an upper bound to the mea
n squared output error. 2) This upper bound and consequently the output err
or can be made arbitrarily small (zero in the limit case) by decreasing the
quantization error which can be accomplished through increasing the number
of hidden units.