Journal of the Australian Mathematical Society

Research Article

REES MATRIX CONSTRUCTIONS FOR CLUSTERING OF DATA

A. V. KELAREVa1 c1, P. WATTERSa2 and J. L. YEARWOODa3

a1 Graduate School of Information Technology and Mathematical Sciences, University of Ballarat, PO Box 663, Ballarat, Victoria 3353, Australia (email: a.kelarev@ballarat.edu.au)

a2 Graduate School of Information Technology and Mathematical Sciences, University of Ballarat, PO Box 663, Ballarat, Victoria 3353, Australia (email: p.watters@ballarat.edu.au)

a3 Graduate School of Information Technology and Mathematical Sciences, University of Ballarat, PO Box 663, Ballarat, Victoria 3353, Australia (email: j.yearwood@ballarat.edu.au)

Abstract

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.

(Received July 07 2008)

(Accepted March 21 2009)

2000 Mathematics subject classification

  • primary 16S36;
  • 20M35; secondary 20M25;
  • 68T

Keywords and phrases

  • Rees matrix semigroups;
  • clustering;
  • data mining

Correspondence:

c1 For correspondence; e-mail: a.kelarev@ballarat.edu.au

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.