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We Use A Gaussian Function As A Kernel Function

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In order to specify the middle layer of an RBF we have to decide the number of neurons of the layer and their kernel functions which are usually Gaussian functions. In this paper we use a Gaussian function as a kernel function. A Gaussian function is specified by its center and width. The simplest and most general method to decide the middle layer neurons is to create a neuron for each training pattern. However the method is usually not practical since in most applications there are a large number of training patterns and the dimension of the input space is fairly large. Therefore it is usual and practical to first cluster the training patterns to a reasonable number of groups by using a clustering algorithm such as K-means or SOFM and then to assign a neuron to each cluster. A simple way, though not always effective, is to choose a relatively small number of patterns randomly among the training patterns and create only that many neurons. A clustering algorithm is a kind of an unsupervised learning algorithm and is used when the class of each training pattern is not known. But an RBFN is a supervised learning network. And we know at least the class of each training pattern. So we’d better take advantage of the information of these class memberships when we cluster the training patterns. Namely we cluster the training patterns class by class instead of the entire patterns at the same time (Moody and Darken, 1989; Musavi et al., 1992). In this way we can reduce at least the

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