General structures for classification

Abstract

The problem of classifying signals is of interest in several application areas. Typically, we are given a finite number m of pairwise disjoint sets C/sub 1/,...,C/sub m/ of signals, and we would like to synthesize a system that maps the elements of each C/sub j/ into a real number a/sub j/, such that the numbers a/sub 1/,...,a/sub m/ are distinct. The main purpose of this paper is to show that this classification can be performed by certain simple structures. Involving linear functionals and memoryless nonlinear elements, assuming only that the C/sub j/ are compact subsets of a real normed linear space. The results on which this conclusion is based have applications other than to classification problems. For example, one result provides a relatively simple completion of a proof of a well-known proposition concerning approximations in R/sup n/ using sigmoidal functions.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>