Bulletin of the Australian Mathematical Society

Research Article

A POLYNOMIAL RING CONSTRUCTION FOR THE CLASSIFICATION OF DATA

A. V. KELAREVa1 c1, J. L. YEARWOODa2 and P. W. VAMPLEWa3

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

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

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

Abstract

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.

(Received February 11 2008)

2000 Mathematics subject classification

  • primary 16S36; secondary 20M25;
  • 94B60

Keywords and phrases

  • ring constructions;
  • group rings;
  • classification

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 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.