Neural Networks for Classification

In many applications, ranging from character recognition to signal detection to automatic target identification, the problem of signal classification is of interest. Often, for example, a signal is known to belong to one of a family of sets C sub 1..., C sub n and the goal is to classify the signal according to the set to which it belongs. The main purpose of this thesis is to show that under certain conditions placed on the sets, the theory of uniform approximation can be applied to solve this problem. Specifically, if we assume that sets C sub j are compact subsets of a normed linear space, several approaches using the Stone-Weierstrass theorem give us a specific structure for classification. This structure is a single hidden layer feedforward neural network. We then discuss the functions which comprise the elements of this neural network and give an example of an application.