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Exact Classification with Two-Layer Neural Nets

✍ Scribed by Gavin J. Gibson

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 559 KB
Volume: 52
Category: Article
ISSN: 0022-0000
DOI: 10.1006/jcss.1996.0026

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✦ Synopsis

This paper considers the classification properties of two-layer networks of McCulloch Pitts units from a theoretical point of view. In particular we consider their ability to realise exactly, as opposed to approximate, bounded decision regions in R 2 . The main result shows that a two-layer network can realise exactly any finite union of bounded polyhedra in R 2 whose bounding lines lie in general position, except for some well-characterised exceptions. The exceptions are those unions whose boundaries contain a line which is ``inconsistent,'' as described in the text. Some of the results are valid for R n , n 2, and the problem of generalising the main result to higher-dimensional situations is discussed.

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