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A POLYNOMIAL RING CONSTRUCTION FOR THE CLASSIFICATION OF DATA

Part of: Theory of error-correcting codes and error-detecting codes Rings and algebras arising under various constructions

Published online by Cambridge University Press:  13 March 2009

A. V. KELAREV ,
J. L. YEARWOOD  and
P. W. VAMPLEW
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.

Keywords

ring constructionsgroup ringsclassification

MSC classification

Secondary: 16S36: Ordinary and skew polynomial rings and semigroup rings 94B60: Other types of codes

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 79 , Issue 2 , April 2009 , pp. 213 - 225
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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