On the Number of Multilinear Partitions and the Computing Capacity of Multiple-Valued Multiple-Threshold Perceptrons.

Authors:
Alioune Ngom;Ivan Stojmenovic;Jovisa Zunic
Affiliations:
-;-;-
Venue:
ISMVL '99 Proceedings of the Twenty Ninth IEEE International Symposium on Multiple-Valued Logic
Year:
1999

Citing 0
Cited 5

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Abstract

We introduce the concept of multilinear partition of a point set V subset Rn and the concept of multilinear separability of a function f: V mapsto K = {0, \1dot, 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 K2. 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 Rn in general position and for V=K2. Finally, we describe a fast polynomial-time algorithm for counting the multilinear partitions of K2.