Implementation of RBF type networks by MLP networks

Simple transformations of input patterns onto a hypersphere in augmented space are presented and experimentally verified. This approach allows the multilayer perceptron (MLP) networks to perform the same functions as radial basis function (RBF) networks. Two transformations are described. In the first one, the dimensionality is increased by one, and only one additional variable has to be computed. In the second approach the dimensionality is doubled. But this leads to a simple implementation of the transformation with sigmoidal type neurons. The modified network has a relatively simple structure, and it is able to perform very complicated nonlinear operations. The power of this network is demonstrated with examples including the two spiral problem.