Advertisement

Abstract

The task of faults localization is discussed in a model-free setting. As a tool for its solution we consider a multiclass pattern recognition problem with a metric in the label space. Then, this problem is approximately solved, providing hints on selecting appropriate RBF nets. It was shown that the approximate solution is the exact one in several important cases. Finally, we propose the algorithm for learning the proposed RBF net. The results of its testing are briefly reported.

Keywords

Decision Rule Radial Basis Function Neural Network Learning Sequence Pattern Recognition Problem Quadratic Loss Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Allwein, A., Schapire, R., Singer, Y.: Reducing multiclass to binary: A unifying approach for margin classifiers. J. Machine Learning Research 1, 113–141 (2000)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Bishop, C.: Neural Networks for Pattern Recognition. Oxford University Press, Oxford (1995)Google Scholar
  3. 3.
    Devroye, L., Györfi, L.: Nonparametric Density Estimation. In: The L 1 View, Wiley, New York (1985)Google Scholar
  4. 4.
    Devroye, L., Györfi, L., Lugosi, G.: Probabilistic Theory of Pattern Recognition. Springer, New York (1996)MATHGoogle Scholar
  5. 5.
    Dietterich, T., Bakiri, G.: Solving Multiclass Learning Problems via Error-Correcting Output Codes. J. Artificial Intelligence Research 2, 263–286 (1995)MATHGoogle Scholar
  6. 6.
    Greblicki, W., Pawlak, M.: Necessary and Sufficient Conditions for Bayes Risk Consistency of Recursive Kernel Classification Rule. IEEE Trans. Information Theory 33, 408–412 (1987)MATHCrossRefGoogle Scholar
  7. 7.
    Hastie, T., Tibshirani, R.: Classification by Pairwise Coupling. The Annals of Statistics 26, 451–471 (1998)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Karayiannis, N.B., Randolph-Gips, M.M.: On the Construction and Training of Reformulated Radial Basis Function Neural Networks. IEEE Trans. on Neural Networks 14, 835–846 (2003)CrossRefGoogle Scholar
  9. 9.
    Korbicz, J., Kocielny, J.M., Kowalczuk, Z., Cholewa, W. (eds.): Fault Diagnosis. Models, Artificial Intelligence, Applications. Springer, Heidelberg (2004)MATHGoogle Scholar
  10. 10.
    Krzyżak, A., Skubalska-Rafajłowicz, E.: Combining Space-Filling Curves and Radial Basis Function Networks. In: Rutkowski, L., Siekmann, J.H., Tadeusiewicz, R., Zadeh, L.A. (eds.) ICAISC 2004. LNCS (LNAI), vol. 3070, pp. 229–234. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  11. 11.
    Pawlak, M., Siu, D.: Classification with Noisy Features. Advances in Pattern Recognition 1451, 845–852 (1999)CrossRefGoogle Scholar
  12. 12.
    Skubalska-Rafajłowicz, E.: Pattern Recognition Algorithms Based on Space-Filling Curves and Orthogonal Expansions. IEEE Trans. Information Theory 47, 1915–1927 (2001)MATHCrossRefGoogle Scholar
  13. 13.
    Skubalska-Rafajłowicz, E., Krzyżak, A.: Fast k-NN Classification Rule Using Metric on Space-Filling Curves. Proceedings of the 13th International Conference on Pattern Recognition, Vienna 2, 121–125 (1996)CrossRefGoogle Scholar
  14. 14.
    Skubalska-Rafajłowicz, E.: Data Compression for Pattern Recognition Based on Space-Filling Curve Pseudo-Inverse Mapping. Nonlinear Analysis, Theory, Methods and Applications 47, 315–326Google Scholar
  15. 15.
    Skubalska-Rafajłowicz, E.: RBF Neural Network for Probability Density Function Estimation and Detecting Changes in Multivariate Processes. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Żurada, J.M. (eds.) ICAISC 2006. LNCS (LNAI), vol. 4029, Springer, Heidelberg (in print, 2006)Google Scholar
  16. 16.
    Xu, L., Krzyżak, A., Yuille, A.: On Radial Basis Function Nets and Kernel Regression: Statistical Consistency, Convergence Rates and Receptive Field Size. Neural Networks 4, 609–628 (1994)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Ewaryst Rafajłowicz
    • 1
  1. 1.Institute of Computer Engineering, Control and RoboticsWrocław University of TechnologyWrocławPoland

Personalised recommendations