Generalized radial basis function networks for classification and novelty detection: self-organization of optimal Bayesian decision.

By adding reverse connections from the output layer to the central layer it is shown how a generalized radial basis functions (GRBF) network can self-organize to form a Bayesian classifier, which is also capable of novelty detection. For this purpose, three stochastic sequential learning rules are introduced from biological considerations which pertain to the centers, the shapes, and the widths of the receptive fields of the neurons and allow ajoint optimization of all network parameters. The rules are shown to generate maximum-likelihood estimates of the class-conditional probability density functions of labeled data in terms of multivariate normal mixtures. Upon combination with a hierarchy of deterministic annealing procedures, which implement a multiple-scale approach, the learning process can avoid the convergence problems hampering conventional expectation-maximization algorithms. Using an example from the field of speech recognition, the stages of the learning process and the capabilities of the self-organizing GRBF classifier are illustrated.