Skip to main content

Statistical and Possibilistic Methodology for the Evaluation of Classification Algorithms

  • Conference paper
Software and Data Technologies (ICSOFT 2011)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 303))

Included in the following conference series:

Abstract

In the paper we consider the problem of the statistical evaluation and comparison of different classification algorithms. For this purpose we apply the methodology of statistical tests for testing independence in the case the multinomial distribution. We propose to use two-sample tests for the comparison of different classification algorithms. In the paper we consider only the case of the supervised classification when an external ‘expert’ evaluates the correctness of classification. The results of the proposed statistical tests are interpreted using possibilistic methodology based on indices of dominance introduced by [7].

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Agresti, A.: Categorical Data Analysis, 2nd edn. J. Wiley, Hoboken (2006)

    Google Scholar 

  2. Berthold, M., Hand, D.J. (eds.): Intelligent Data Analysis. An Introduction, 2nd edn. Springer, Berlin (2007)

    Google Scholar 

  3. Breiman, L., Friedman, J., Olshen, R., Stone, C.: Classification and Regression Trees. CRC Press, Boca Raton (1984)

    MATH  Google Scholar 

  4. Charytanowicz, M., Niewczas, J., Kulczycki, P., Kowalski, P.A., Łukasik, S., Żak, S.: Complete Gradient Clustering Algorithm for Features Analysis of X-Ray Images. In: Piętka, E., Kawa, J. (eds.) Information Technologies in Biomedicine. AISC, vol. 69, pp. 15–24. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  5. Desu, M.M., Raghavarao, D.: Nonparametric Statistical Methods for Complete and Censored Data. Chapman & Hall, Boca Raton (2004)

    MATH  Google Scholar 

  6. Dubois, D., Prade, H.: Ranking Fuzzy Numbers in the Setting of Possibility Theory. Information Science 30, 183–224 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  7. Gil, M.A., Hryniewicz, O.: Statistics with Imprecise Data. In: Meyers, R.A. (ed.) Encyclopedia of Complexity and Systems Science, pp. 8679–8690. Springer, Heidelberg (2009)

    Google Scholar 

  8. Hryniewicz, O.: Possibilistic Interpretation of the Results of Statistical Tests. In: Proceedings of Eight International Conference on Information Processing and Management of Uncertainty in Knowledge-based Systems, IPMU 2000, Madrid, pp. 215–219 (2000)

    Google Scholar 

  9. Hryniewicz, O.: Possibilistic decisions and fuzzy statistical tests. Fuzzy Sets and Systems 157, 2665–2673 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  10. Hryniewicz, O.: Possibilistic methodology for the evaluation of classification algorithms. In: Proceedings of the 6th International Conference on Software and data Technology, ICSOFT 2011, Seville (July 2011)

    Google Scholar 

  11. Krzanowski, W.J.: Principles of Multivariate Analysis: A User’s Perspective. Oxford University Press, New York (1988)

    MATH  Google Scholar 

  12. Kulczycki, P., Kowalski, P.A.: Bayes classification of imprecise information of interval type. Control and Cybernetics 40, 101–123 (2011)

    Google Scholar 

  13. Mehta, C.R., Patel, N.R.: Network algorithm for performing Fisher’s exact test in r × c contingency tables. Journ. Amer. Stat. Assoc. 78, 427–434 (1983)

    MathSciNet  MATH  Google Scholar 

  14. Mehta, C.R., Patel, N.R.: ALGORITHM 643: FEXACT: a FORTRAN subroutine for Fisher’s exact test on unordered r × c contingency tables. ACM Transactions on Mathematical Software (TOMS) 12, 154–161 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  15. Nisbet, R., Elder, J., Miner, G.: Statistical Analysis and Data Mining. Applications. Elsevier Inc., Amsterdam (2009)

    MATH  Google Scholar 

  16. Yarnold, J.K.: The Minimum Expectation in X2 Goodness of fit test and the Accuracy of Approximations for the Null Distribution. Journ. Amer. Stat. Assoc. 70, 864–886 (1970)

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hryniewicz, O. (2013). Statistical and Possibilistic Methodology for the Evaluation of Classification Algorithms. In: Escalona, M.J., Cordeiro, J., Shishkov, B. (eds) Software and Data Technologies. ICSOFT 2011. Communications in Computer and Information Science, vol 303. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36177-7_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-36177-7_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-36176-0

  • Online ISBN: 978-3-642-36177-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics