Skip to main content
SpringerLink
Log in

MAD Loss in Pattern Recognition and RBF Learning

  • Conference paper
Artificial Intelligence and Soft Computing – ICAISC 2008 (ICAISC 2008)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5097))

Included in the following conference series:

Abstract

We consider a multi-class pattern recognition problem with linearly ordered labels and a loss function, which measures absolute deviations of decisions from true classes. In the bayesian setting the optimal decision rule is shown to be the median of a posteriori class probabilities. Then, we propose three approaches to constructing an empirical decision rule, based on a learning sequence. Our starting point is the Parzen-Rosenblatt kernel density estimator. The second and the third approach are based on radial bases functions (RBF) nets estimators of class densities.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

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.

References

  1. Bors, A.G., Pitas, I.: Median Radial Basis Function Neural Network. IEEE Trans. on Neural Networks I, 1351–1364 (1996)

    Article  Google Scholar 

  2. Allwein, A., Schapire, R., Singer, Y.: Reducing multiclass to binary: A unifying approach for margin classifiers. J. Machine Learning Research 1, 113–141 (2000)

    Article  MathSciNet  Google Scholar 

  3. Bishop, C.: Neural Networks for Pattern Recognition. Oxford University Press, Oxford (1995)

    Google Scholar 

  4. Chow, Y.S., Teicher, H.: Probability Theory. Springer, New York (1988)

    MATH  Google Scholar 

  5. Devroye, L., Györfi, L.: Nonparametric Density Estimation. The L 1 View. Wiley, New York (1985)

    MATH  Google Scholar 

  6. Devroye, L., Györfi, L., Lugosi, G.: Probabilistic Theory of Pattern Recognition. Springer, New York (1996)

    MATH  Google Scholar 

  7. Dietterich, T., Bakiri, G.: Solving Multiclass Learning Problems via Error-Correcting Output Codes. J. Artificial Intelligence Research 2, 263–286 (1995)

    MATH  Google Scholar 

  8. 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)

    Article  MATH  Google Scholar 

  9. Hastie, T., Tibshirani, R.: Classification by Pairwise Coupling. The Annals of Statistics 26, 451–471 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  10. 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)

    Article  Google Scholar 

  11. 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)

    Google Scholar 

  12. Lugosi, G., Zeger, K.: Nonparametric Estimation via Empirical Risk Minimization. IEEE Trans. on Information Theory 41, 677–687 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  13. Pawlak, M., Siu, D.: Classification with Noisy Features. Advances in Pattern Recognition 1451, 845–852 (1999)

    Article  Google Scholar 

  14. Rafajłowicz, E.: RBF Nets in Faults Localization. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Żurada, J.M. (eds.) ICAISC 2006. LNCS (LNAI), vol. 4029, Springer, Heidelberg (2006)

    Google Scholar 

  15. Rafajłowicz, E.: Improving the efficiency of counting defects by learning RBF nets with MAD loss. ICAISC 2008 (to appear)

    Google Scholar 

  16. Rafajłowicz, E., Pawla, M., Steland, A.: Nonlinear Image Filtering and Reconstruction: A Unified Approach Based on Vertically Weighted Regression. Int. J. Apll. Math. Comp. Sci (to appear, 2008)

    Google Scholar 

  17. Skubalska-Rafajłowicz, E.: Pattern Recognition Algorithms Based on Space-Filling Curves and Orthogonal Expansions. IEEE Trans. Information Theory 47, 1915–1927 (2001)

    Article  Google Scholar 

  18. Skubalska-Rafajłowicz, E., Krzyżak, A.: Fast k-NN Classification Rule Using Metric on Space-Filling Curves. In: Proceedings of the 13th International Conference on Pattern Recognition, Vienna, vol. 2, pp. 121–125 (1996)

    Google Scholar 

  19. Skubalska-Rafajłowicz, E.: Data Compression for Pattern Recognition Based on Space-Filling Curve Pseudo-Inverse Mapping. Nonlinear Analysis, Theory, Methods and Applications 47, 315–326

    Google Scholar 

  20. 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, pp. 133–141. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  21. Skubalska-Rafajłowicz, E.: Local correlation and entropy maps as tools for detecting defects in industrial images. Int. J. Apll. Math. Comp. Sci (to appear, 2008)

    Google Scholar 

  22. 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)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Computer Engineering, Control and Robotics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50 370, Wrocław, Poland

    Ewaryst Rafajłowicz & Ewa Skubalska-Rafajłowicz

Authors
  1. Ewaryst Rafajłowicz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ewa Skubalska-Rafajłowicz
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Leszek Rutkowski Ryszard Tadeusiewicz Lotfi A. Zadeh Jacek M. Zurada

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Rafajłowicz, E., Skubalska-Rafajłowicz, E. (2008). MAD Loss in Pattern Recognition and RBF Learning. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds) Artificial Intelligence and Soft Computing – ICAISC 2008. ICAISC 2008. Lecture Notes in Computer Science(), vol 5097. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69731-2_65

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-69731-2_65

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-69572-1

  • Online ISBN: 978-3-540-69731-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation