Skip to main content
SpringerLink
Log in

Optimization of classifiers for data mining based on combinatorial semigroups

  • RESEARCH ARTICLE
  • Published:
Semigroup Forum Aims and scope Submit manuscript

Abstract

The aim of the present article is to obtain a theoretical result essential for applications of combinatorial semigroups for the design of multiple classification systems in data mining. We consider a novel construction of multiple classification systems, or classifiers, combining several binary classifiers. The construction is based on combinatorial Rees matrix semigroups without any restrictions on the sandwich-matrix. Our main theorem gives a complete description of all optimal classifiers in this novel construction.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Auinger, K., Hall, T.E., Reilly, N.R., Zhang, S.: Congruences on the lattice of pseudovarieties of finite semigroups. Int. J. Algebra Comput. 7(4), 433–455 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  2. Cazaran, J., Kelarev, A.V., Quinn, S.J., Vertigan, D.: An algorithm for computing the minimum distances of extensions of BCH codes embedded in semigroup rings. Semigroup Forum 73, 317–329 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  3. Davey, B.A., Jackson, M., Maróti, M., McKenzie, R.N.: Principal and syntactic congruences in congruence-distributive and congruence-permutable varieties. J. Aust. Math. Soc. 85(1), 59–74 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  4. Easdown, D., Munn, W.D.: Trace functions on inverse semigroup algebras. Bull. Aust. Math. Soc. 52(3), 359–372 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  5. Hall, T.E.: The radical of the algebra of any finite semigroup over any field. J. Aust. Math. Soc. Ser. A 11, 350–352 (1970)

    Article  MATH  Google Scholar 

  6. Hall, T.E.: Biprefix codes, inverse semigroups and syntactic monoids of injective automata. Theor. Comput. Sci. 32(1–2), 201–213 (1984)

    Article  MATH  Google Scholar 

  7. Hall, T.E.: Amalgamation for inverse and generalized inverse semigroups. Trans. Am. Math. Soc. 310, 313–323 (1988)

    Article  MATH  Google Scholar 

  8. Hall, T.E., Imaoka, T.: Representations and amalgamation of generalized inverse ∗-semigroups. Semigroup Forum 58, 126–141 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  9. Howie, J.M.: Fundamentals of Semigroup Theory. Clarendon, Oxford (1995)

    MATH  Google Scholar 

  10. Jackson, M., Volkov, M.: Undecidable problems for completely 0-simple semigroups. J. Pure Appl. Algebra 213(10), 1961–1978 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  11. Kelarev, A.V.: Ring Constructions and Applications. World Scientific, Singapore (2002)

    MATH  Google Scholar 

  12. Kelarev, A.V.: Graph Algebras and Automata. Dekker, New York (2003)

    MATH  Google Scholar 

  13. Kelarev, A.V., Göbel, R., Rangaswamy, K.M., Schultz, P., Vinsonhaler, C.: Abelian Groups Rings and Modules. Contemporary Mathematics, vol. 273. American Mathematical Society, Providence (2001)

    MATH  Google Scholar 

  14. Kelarev, A.V., Passman, D.S.: A description of incidence rings of group automata. Contemp. Math. 456, 27–33 (2008)

    MathSciNet  Google Scholar 

  15. Kelarev, A.V., Praeger, C.E.: On transitive Cayley graphs of groups and semigroups. Eur. J. Comb. 24(1), 59–72 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  16. Kelarev, A., Ryan, J., Yearwood, J.: Cayley graphs as classifiers for data mining: The influence of asymmetries. Discrete Math. 309(17), 5360–5369 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  17. Kelarev, A.V., Sokratova, O.V.: On congruences of automata defined by directed graphs. Theor. Comput. Sci. 301, 31–43 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  18. Kelarev, A.V., Yearwood, J.L., Mammadov, M.A.: A formula for multiple classifiers in data mining based on Brandt semigroups. Semigroup Forum 78(2), 293–309 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  19. Kelarev, A.V., Watters, P., Yearwood, J.L.: Rees matrix construction for clustering of data. J. Aust. Math. Soc. 87, 377–393 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  20. Kelarev, A.V., Yearwood, J.L., Vamplew, P.W.: A polynomial ring construction for classification of data. Bull. Aust. Math. Soc. 79, 213–225 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  21. Okniński, J.: Semigroup Algebras. Dekker, New York (1991)

    Google Scholar 

  22. Witten, I.H., Frank, E.: Data Mining: Practical Machine Learning Tools and Techniques. Elsevier/Morgan Kaufman, Amsterdam/San Mateo (2005)

    MATH  Google Scholar 

  23. Yearwood, J.L., Mammadov, M.A.: Classification Technologies: Optimization Approaches to Short Text Categorization. Idea Group Inc., Hershey (2010)

    Google Scholar 

  24. Yearwood, J., Webb, D., Vamplew, P., Ma, L., Ofoghi, B., Kelarev, A.: Applying clustering and ensemble clustering approaches to phishing profiling. In: Eighth Australasian Data Mining Conference, AusDM 2009, Melbourne, Australia, December 2009. Conferences in Research and Practice in Information Technology, vol. 101, pp. 25–34 (2009)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Science, Information Technology and Engineering, University of Ballarat, P.O. Box 663, Ballarat, Victoria, 3353, Australia

    A. V. Kelarev, J. L. Yearwood & P. A. Watters

Authors
  1. A. V. Kelarev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. L. Yearwood
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. A. Watters
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. V. Kelarev.

Additional information

Communicated by Thomas E. Hall.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kelarev, A.V., Yearwood, J.L. & Watters, P.A. Optimization of classifiers for data mining based on combinatorial semigroups. Semigroup Forum 82, 242–251 (2011). https://doi.org/10.1007/s00233-011-9298-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00233-011-9298-6

Keywords

Search

Navigation