General structures for classification

The problem of classifying signals is of interest in several application areas. Typically, we are given a finite number m of pairwise disjoint sets C₁,…,C_m of signals, and we would like to synthesize a system that maps the elements of each C_j into a real number a_j, such that the numbers a₁ ,…,a_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_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 Rⁿ using sigmoidal functions