Authors: Ghilezan, Silvia 
Pantović, Jovanka
Žunić, Joviša 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Separating points by parallel hyperplanes-characterization problem
Journal: IEEE Transactions on Neural Networks
Volume: 18
Issue: 5
First page: 1356
Last page: 1363
Issue Date: 1-Sep-2007
Rank: M21a
ISSN: 1045-9227
DOI: 10.1109/TNN.2007.891678
This paper deals with partitions of a discrete set S of points in a d-dimensional space, by h parallel hyperplanes. Such partitions are in a direct correspondence with multilinear threshold functions which appear in the theory of neural networks and multivalued logic. The characterization (encoding) problem is studied. We show that a unique characterization (encoding) of such multilinear partitions of S = {0, 1,..., m -1}d is possible within O(h · d2 · log m) bit rate per encoded partition. The proposed characterization (code) consists of (d+1) · (h+1) discrete moments having the order no bigger than 1. The obtained bit rate is evaluated depending on the mutual relations between h; d, and m. The optimality is reached in some cases.
Keywords: Discrete moments | Encoding | Multilevel threshold function | Multilinear partitions | Neural networks | Storage complexity
Publisher: IEEE

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