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  • Bulletin of the Australian Mathematical Society, Volume 79, Issue 2
  • April 2009, pp. 213-225

A POLYNOMIAL RING CONSTRUCTION FOR THE CLASSIFICATION OF DATA

  • A. V. KELAREV (a1), J. L. YEARWOOD (a2) and P. W. VAMPLEW (a3)
  • DOI: http://dx.doi.org/10.1017/S0004972708001111
  • Published online: 01 April 2009
Abstract
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.

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Copyright
Corresponding author
For correspondence; e-mail: a.kelarev@ballarat.edu.au
Footnotes
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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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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]R. Alfaro and A. V. Kelarev , ‘Recent results on ring constructions for error-correcting codes’, Contemp. Math. 376 (2005), 112.

[3]I. M. Araújo , A. V. Kelarev and A. Solomon , ‘An algorithm for commutative semigroup algebras which are principal ideal rings with identity’, Comm. Algebra 32(4) (2004), 12371254.

[4]A. M. Bagirov , A. M. Rubinov and J. Yearwood , ‘A global optimization approach to classification’, Optim. Eng. 3 (2002), 129155.

[5]J. Cazaran and A. V. Kelarev , ‘Generators and weights of polynomial codes’, Arch. Math. (Basel) 69 (1997), 479486.

[6]J. Cazaran , A. V. Kelarev , S. J. Quinn and D. Vertigan , ‘An algorithm for computing the minimum distances of extensions of BCH codes embedded in semigroup rings’, Semigroup Forum 73 (2006), 317329.

[17]A. V. Kelarev and D. S. Passman , ‘A description of incidence rings of group automata’, Contemp. Math. 456 (2008), 2733.

[21]H. N. Ward , ‘Visible codes’, Arch. Math. (Basel) 54 (1990), 307312.

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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