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REES MATRIX CONSTRUCTIONS FOR CLUSTERING OF DATA

Part of: Rings and algebras arising under various constructions Semigroups

Published online by Cambridge University Press:  15 December 2009

A. V. KELAREV ,
P. WATTERS  and
J. L. YEARWOOD
A. V. KELAREV*
Affiliation:
Graduate School of Information Technology and Mathematical Sciences, University of Ballarat, PO Box 663, Ballarat, Victoria 3353, Australia (email: a.kelarev@ballarat.edu.au)
P. WATTERS
Affiliation:
Graduate School of Information Technology and Mathematical Sciences, University of Ballarat, PO Box 663, Ballarat, Victoria 3353, Australia (email: p.watters@ballarat.edu.au)
J. L. YEARWOOD
Affiliation:
Graduate School of Information Technology and Mathematical Sciences, University of Ballarat, PO Box 663, Ballarat, Victoria 3353, Australia (email: j.yearwood@ballarat.edu.au)
*
✉For correspondence; e-mail: a.kelarev@ballarat.edu.au
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Abstract

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This paper continues the investigation of semigroup constructions motivated by applications in data mining. We give a complete description of the error-correcting capabilities of a large family of clusterers based on Rees matrix semigroups well known in semigroup theory. This result strengthens and complements previous formulas recently obtained in the literature. Examples show that our theorems do not generalize to other classes of semigroups.

Keywords

Rees matrix semigroupsclusteringdata mining

MSC classification

Secondary: 16S36: Ordinary and skew polynomial rings and semigroup rings 20M35: Semigroups in automata theory, linguistics, etc.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 87 , Issue 3 , December 2009 , pp. 377 - 393
Copyright
Copyright © Australian Mathematical Publishing Association, Inc. 2009

Footnotes

The first author was supported by Discovery Grant DP0449469 from the Australian Research Council. The second author was supported by Linkage Grant LP0776267 from the Australian Research Council. The third author was supported by a Queen Elizabeth II Fellowship and Discovery Grant DP0211866 from the Australian Research Council.

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