CLASSIFIERS ON RELATIVELY COMPACT-SETS

The problem of classifying signals is of interest in several applicati on areas. Typically we are given a finite number m of pairwise disjoin t sets C1,...,C(m) 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. In a recent paper it is shown that this classification can be performed by certain simple structure s involving linear functionals and memoryless nonlinear elements, assu ming that the C(j) are compact subsets of a real normed linear space. Here we give a similar solution to the problem under the considerably weaker assumption that the C(j) are relatively compact and are of posi tive distance from each other. An example is given in which the C(j) a re subsets of L(p)(a, b), 1 less-than-or-equal-to p < infinity.