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IEEE Transactions on Neural NetworksVolume 18, Issue 5, September 2007, Pages 1356-1363

Separating points by parallel hyperplanes-characterization problem(Article)

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  • aFaculty of Engineering, University of Novi Sad, 21000 Novi Sad
  • bDepartment of Computer Science, University of Exeter, Exeter EX4 4QF, United Kingdom
  • cMathematical Institute, Serbian Academy of Arts and Sciences, Belgrade 11001

Abstract

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. © 2007 IEEE.

Author keywords

Discrete momentsEncodingMultilevel threshold functionMultilinear partitionsNeural networksStorage complexity

Indexed keywords

Engineering controlled terms:Bit error rateComputational complexityImage codingMany valued logics
Engineering uncontrolled terms:Discrete momentsMultilevel threshold functionMultilinear partitions
Engineering main heading:Neural networks
EMTREE medical terms:algorithmarticleartificial intelligenceautomated pattern recognitioncomputer simulationmethodologyreproducibilitysensitivity and specificitysignal processingtheoretical model
MeSH:AlgorithmsArtificial IntelligenceComputer SimulationModels, TheoreticalPattern Recognition, AutomatedReproducibility of ResultsSensitivity and SpecificitySignal Processing, Computer-Assisted
  • ISSN: 10459227
  • CODEN: ITNNE
  • Source Type: Journal
  • Original language: English
  • DOI: 10.1109/TNN.2007.891678
  • PubMed ID: 18220185
  • Document Type: Article

  Ghilezan, S.; Faculty of Engineering, University of Novi Sad, Serbia;
© Copyright 2008 Elsevier B.V., All rights reserved.

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