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Decoding of Ternary Error Correcting Output Codes

  • Sergio Escalera
  • Oriol Pujol
  • Petia Radeva
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4225)

Abstract

Error correcting output codes (ECOC) represent a successful extension of binary classifiers to address the multiclass problem. Lately, the ECOC framework was extended from the binary to the ternary case to allow classes to be ignored by a certain classifier, allowing in this way to increase the number of possible dichotomies to be selected. Nevertheless, the effect of the zero symbol by which dichotomies exclude certain classes from consideration has not been previously enough considered in the definition of the decoding strategies. In this paper, we show that by a special treatment procedure of zeros, and adjusting the weights at the rest of coded positions, the accuracy of the system can be increased. Besides, we extend the main state-of-art decoding strategies from the binary to the ternary case, and we propose two novel approaches: Laplacian and Pessimistic Beta Density Probability approaches. Tests on UCI database repository (with different sparse matrices containing different percentages of zero symbol) show that the ternary decoding techniques proposed outperform the standard decoding strategies.

References

  1. 1.
    Vapnik, V.: Estimation of dependences based on empirical data. Springer, Heidelberg (1982)zbMATHGoogle Scholar
  2. 2.
    Vapnik, V.: The nature of statistical learning theory. Springer, Heidelberg (1995)zbMATHGoogle Scholar
  3. 3.
    Breiman, L., Friedman, J.: Classification and Regression Trees, Wadsworth (1984)Google Scholar
  4. 4.
    Friedman, J., Hastie, T., Tibshirani, R.: Additive logistic regression: a statistical view of boosting (38), 337–374 (1998)Google Scholar
  5. 5.
    Allwein, E., Schapire, R., Singer, Y.: Reducing multiclass to binary: A unifying approach for margin classifiers (1), 113–141 (2002)Google Scholar
  6. 6.
    Dietterich, T., Bakiri, G.: Solving multiclass learning problems via error-correcting output codes (2), 263–286 (1995)Google Scholar
  7. 7.
    Windeatt, T., Ghaderi, R.: Coding and decoding for multi-class learning problems (4), 11–21 (2003)Google Scholar
  8. 8.
    Dietterich, T., Bakiri, G.: Error-correcting output codes: A general method for improving multiclass inductive learning programs. In: Press, A. (ed.) Ninth National Conference on Artificial Intelligence, pp. 572–577 (1991)Google Scholar
  9. 9.
    Hastie, T., Tibshirani, R.: Classification by pairwise grouping (26), 451–471 (1998)Google Scholar
  10. 10.
    Crammer, K., Singer, Y.: On the learnability and design of output codes for multi-class problems (47), 201–233 (2002)Google Scholar
  11. 11.
    Pujol, O., Radeva, P., Vitrià, J.: Discriminant ECOC: A heuristic method for application dependent design of error correcting output codes (28), 1001–1007 (2006)Google Scholar
  12. 12.
    Escalera, S., Pujol, O., Radeva, P.: ECOC-ONE: A novel coding and decoding strategy. In: ICPR, Hong Kong, China (in press, 2006)Google Scholar
  13. 13.
    Escalera, S., Pujol, O., Radeva, P.: Forest extension of error correcting output codes and boosted landmarks. In: ICPR, Hong Kong, China (in press, 2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Sergio Escalera
    • 1
  • Oriol Pujol
    • 2
  • Petia Radeva
    • 1
  1. 1.Computer Vision Center, Dept. Computer ScienceUABBellaterraSpain
  2. 2.Dept. Matemàtica Aplicada i AnàlisiUBBarcelonaSpain

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