title: On the number of multilinear partitions and the computing capacity of multiple-valued multiple-threshold perceptrons.
abstract: We introduce the concept of multilinear partition of a point set V/spl sub/R/sup n/ and the concept of multilinear separability of a function f:Vtwo head right arrowK={0,...,k-1}. Based on well-known relationships between linear partitions and minimal pairs, we derive formulae for the number of multilinear partitions of a point set in general position and of the set K(2). The (n,k,s)-perceptrons partition the input space V into s+1 regions with s parallel hyperplanes. We obtain results on the capacity of a single (n,k,s)-perceptron, respectively, for V subset R(n) in general position and for V=K(2). Finally, we describe a fast polynomial-time algorithm for counting the multilinear partitions of K(2).
authors.affiliation: Comput. Sci. Dept., Univ. of Windsor, Ont., Canada.
authors.forename: A
authors.initials: A
authors.lastname: Ngom
authors.forename: I
authors.initials: I
authors.lastname: Stojmenovic
authors.forename: J
authors.initials: J
authors.lastname: Zunic