Combining Rule-Based and Sample-Based Classifiers – Probabilistic Approach

  • Marek Kurzynski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3704)


The present paper is devoted to the pattern recognition methods for combining heterogeneous sets of learning data: set of training examples and the set of expert rules with unprecisely formulated weights understood as conditional probabilities. Adopting the probabilistic model two concepts of recognition learning are proposed. In the first approach two classifiers trained on homogeneous data set are generated and next their decisions are combined using local weighted voting combination rule. In the second method however, one set of data is transformed into the second one and next only one classifier trained on homogeneous set of data is used. Furthermore, the important problem of consistency of expert rules and the learning set is discussed and the method for checking it is proposed.


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  1. 1.
    Chen, D., Cheng, X.: An asymptotic analysis of some expert fusion methods. Pattern Recognition Letters 22, 901–904 (2001)zbMATHCrossRefGoogle Scholar
  2. 2.
    Czabanski, R.: Self-generating fuzzy rules from numerical data. Techn. Report Silesian Technical Univ. Gliwice (PhD Thesis) (2002) (in Polish)Google Scholar
  3. 3.
    Devroye, L., Gyorfi, P., Lugossi, G.: A Probabilistic Theory of Pattern Recognition. Springer, New York (1996)zbMATHGoogle Scholar
  4. 4.
    Dubois, D., Lang, J.: Possibilistic logic. In: Handbook of Logic in Artificial Intelligence and Logic Programming, pp. 439–513. Oxford Univ. Press, Oxford (1994)Google Scholar
  5. 5.
    Duda, R., Hart, P., Stork, D.: Pattern Classification. John Wiley and Sons, Chichester (2001)zbMATHGoogle Scholar
  6. 6.
    Halpern, J.: Reasoning about Uncertainty. MIT Press, Cambridge (2003)zbMATHGoogle Scholar
  7. 7.
    Jacobs, R.: Methods for combining experts probability assessments. Neural Computation 7, 867–888 (1995)CrossRefGoogle Scholar
  8. 8.
    Kittler, J., Duin, R., Matas, J.: On combining classifiers. IEEE Trans. on PAMI 20, 226–239 (1998)Google Scholar
  9. 9.
    Kuncheva, L.: Combining classifiers: Soft computing solutions. In: Pal, S., Pal, A. (eds.) Pattern Recognition: from Classical to Modern Approaches, pp. 427–451. World Scientific, Singapore (2001)CrossRefGoogle Scholar
  10. 10.
    Kurzynski, M., Sas, J., Blinowska, A.: Rule-Based Medical Decision-Making with Learning. In: Proc. 12th World IFAC Congress, Sydney, vol. 4, pp. 319–322 (1993)Google Scholar
  11. 11.
    Kurzynski, M., Wozniak, M.: Rule-Based Algorithms with Learning for Sequential Recognition Problem. In: Proc. 3rd Int. Conf. Fusion 2000, Paris, pp. 10–13 (2000)Google Scholar
  12. 12.
    Kurzynski, M., Puchala, E.: Hybrid Pattern Recognition Algorithms Applied to the Computer-Aided Medical Diagnosis. In: Crespo, J.L., Maojo, V., Martin, F. (eds.) ISMDA 2001. LNCS, vol. 2199, pp. 133–139. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  13. 13.
    Kurzynski, M.: Consistency Conditions of the Expert Rule Set in the Probabilistic Pattern Recognition. In: Zhang, J., He, J.-H., Fu, Y. (eds.) CIS 2004. LNCS, vol. 3314, pp. 831–836. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  14. 14.
    Mitchell, T.: Machine Learning. McGraw-Hill Science, New York (1997)zbMATHGoogle Scholar
  15. 15.
    Kuratowski, K., Mostowski, A.: Set Theory. Nort-Holland Publishing Co., Amsterdam (1986)Google Scholar
  16. 16.
    Sachs, L.: Applied Statistics. A Handbook of Techniques. Springer, Heidelberg (1982)zbMATHGoogle Scholar
  17. 17.
    Woods, K., Kegelmeyer, W.: Combination of multiple classifiers using local accuracy estimates. IEEE Trans. on PAMI 19, 405–410 (1997)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Marek Kurzynski
    • 1
    • 2
  1. 1.Faculty of Electronics, Chair of Systems and Computer NetworksWroclaw University of TechnologyWroclawPoland
  2. 2.The Witelon University of Applied SciencesLegnicaPoland

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