GENERAL STRUCTURES FOR CLASSIFICATION

The problem of classifying signals is of interest in several applicati on areas. Typically, we are given a finite number m of pairwise disjoi nt sets C1,..., Cm of signals, and we would like to synthesize a syste m that maps the elements of each C(j) into a real number a(j), such th at the numbers a1,..., a(m) are distinct. The main purpose of this pap er is to show that this classification can be performed by certain sim ple structures, involving linear functionals and memoryless nonlinear elements, assuming only that the C(j) are compact subsets of a real no rmed linear space. The results on which this conclusion is based have applications other than to classification problems. For example, one r esult provides a relatively simple completion of a proof of a well-kno wn proposition concerning approximations in R(n) using sigmoidal funct ions.