Effects of moving the centers in an RBF network

In radial basis function networks, placement of centers has been one of the problems addressed and has a significant effect on the performance of the network. Supervised learning of center locations in some applications show that they are superior to the networks whose centers are located using unsupervised methods. Supervised learning of centers seem to offset the advantages achieved by the two stage learning of the RBF networks. One way to overcome this may be to train the network with a set of centers selected by unsupervised methods and then to fine tune the centers. This can be done by evaluating whether moving the centers would decrease the error. In this paper we have calculated bounds for the gradient and Hessian of the error considered as a function of centers for networks of fixed size. Using these bounds it is possible to know by how much one can reduce the error by changing the centers. Furthermore, step size can be specified to achieve a guaranteed amount of reduction in error