RBF neural network center selection based on Fisher ratio class separability measure

Abstract

For classification applications, the role of hidden layer neurons of a radial basis function (RBF) neural network can be interpreted as a function which maps input patterns from a nonlinear separable space to a linear separable space. In the new space, the responses of the hidden layer neurons form new feature vectors. The discriminative power is then determined by RBF centers. In the present study, we propose to choose RBF centers based on Fisher ratio class separability measure with the objective of achieving maximum discriminative power. We implement this idea using a multistep procedure that combines Fisher ratio, an orthogonal transform, and a forward selection search method. Our motivation of employing the orthogonal transform is to decouple the correlations among the responses of the hidden layer neurons so that the class separability provided by individual RBF neurons can be evaluated independently. The strengths of our method are double fold. First, our method selects a parsimonious network architecture. Second, this method selects centers that provide large class separation.