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OPTIMAL REES MATRIX CONSTRUCTIONS FOR ANALYSIS OF DATA

Part of: Semigroups

Published online by Cambridge University Press:  08 December 2011

A. V. KELAREV ,
J. L. YEARWOOD  and
LIFANG ZI
A. V. KELAREV*
Affiliation:
School of Science, Information Technology and Engineering, University of Ballarat, PO Box 663, Ballarat, Victoria 3353, Australia (email: a.kelarev@ballarat.edu.au)
J. L. YEARWOOD
Affiliation:
School of Science, Information Technology and Engineering, University of Ballarat, PO Box 663, Ballarat, Victoria 3353, Australia (email: j.yearwood@ballarat.edu.au)
LIFANG ZI
Affiliation:
School of Science, Information Technology and Engineering, University of Ballarat, PO Box 663, Ballarat, Victoria 3353, Australia (email: l.zi@ballarat.edu.au)
*
✉For correspondence; e-mail: a.kelarev@ballarat.edu.au
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Abstract

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We introduce a new construction involving Rees matrix semigroups and max-plus algebras that is very convenient for generating sets of centroids. We describe completely all optimal sets of centroids for all Rees matrix semigroups without any restrictions on the sandwich matrices.

Keywords

Rees matrix semigroupssets of centroidsclassification and clustering

MSC classification

Secondary: 20M25: Semigroup rings, multiplicative semigroups of rings
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 92 , Issue 3 , June 2012 , pp. 357 - 366
Copyright
Copyright © 2011 Australian Mathematical Publishing Association Inc.

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