Authors: Ngom, Alioune
Stojmenović, Ivan
Žunić, Joviša 
Title: On the number of multilinear partitions and the computing capacity of multiple-valued multiple-threshold perceptrons
Journal: IEEE Transactions on Neural Networks
Volume: 14
Issue: 3
First page: 469
Last page: 477
Issue Date: 1-May-2003
Rank: M21
ISSN: 1045-9227
DOI: 10.1109/TNN.2003.810598
We introduce the concept of multilinear partition of a point set V ⊂ Rn and the concept of multilinear separability of a function f : V → K = {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 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 ⊂ Rn in general position and for V = K2. Finally, we describe a fast polynomial-time algorithm for counting the multilinear partitions of K2.
Keywords: (k, k)-grid | Complexity | Farey sequence | General position | k-valued s-threshold perceptron | Minimal pair | Multiple-valued logic | Partition | Separability
Publisher: IEEE
Project: NSERC, Grants RGPIN22811700 and OGPIN007

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