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A POLYNOMIAL RING CONSTRUCTION FOR THE CLASSIFICATION OF DATA

Published online by Cambridge University Press:  13 March 2009

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

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Drensky and Lakatos (Lecture Notes in Computer Science, 357 (Springer, Berlin, 1989), pp. 181–188) have established a convenient property of certain ideals in polynomial quotient rings, which can now be used to determine error-correcting capabilities of combined multiple classifiers following a standard approach explained in the well-known monograph by Witten and Frank (Data Mining: Practical Machine Learning Tools and Techniques (Elsevier, Amsterdam, 2005)). We strengthen and generalise the result of Drensky and Lakatos by demonstrating that the corresponding nice property remains valid in a much larger variety of constructions and applies to more general types of ideals. Examples show that our theorems do not extend to larger classes of ring constructions and cannot be simplified or generalised.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2009

Footnotes

The first author was supported by Discovery grant DP0449469 from the Australian Research Council. The second author was supported by a Queen Elizabeth II Fellowship and Discovery grant DP0211866 from the Australian Research Council. The third author was supported by two research grants of the University of Ballarat.

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