Radial basis function (RBF) networks have a static Gaussian function as the nonlinearity for the hidden layer processing elements. The Gaussian function responds only to a small region of the input space where the Gaussian is centered. The key to a successful implementation of these networks is to find suitable centers for the Gaussian functions. This can be done with supervised learning, but an unsupervised approach usually produces better results. For this reason, NeuroSolutions implements RBF networks as a hybrid supervised-unsupervised topology.
The simulation starts with the training of an unsupervised layer. Its function is to derive the Gaussian centers and the widths from the input data. These centers are encoded within the weights of the unsupervised layer using competitive learning. During the unsupervised learning, the widths of the Gaussians are computed based on the centers of their neighbors. The output of this layer is derived from the input data weighted by a Gaussian mixture.
Once the unsupervised layer has completed its training, the supervised segment then sets the centers of Gaussian functions (based on the weights of the unsupervised layer) and determines the width (standard deviation) of each Gaussian. Any supervised topology (such as a MLP) may be used for the classification of the weighted input.
The advantage of the radial basis function network is that it finds the input to output map using local approximators. Usually the supervised segment is simply a linear combination of the approximators. Since linear combiners have few weights, these networks train extremely fast and require fewer training samples.
