Introducing the Separability Matrix for Error Correcting Output Codes Coding

  • Miguel Ángel Bautista
  • Oriol Pujol
  • Xavier Baró
  • Sergio Escalera
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6713)

Abstract

Error Correcting Output Codes (ECOC) have demonstrate to be a powerful tool for treating multi-class problems. Nevertheless, predefined ECOC designs may not benefit from Error-correcting principles for particular multi-class data. In this paper, we introduce the Separability matrix as a tool to study and enhance designs for ECOC coding. In addition, a novel problem-dependent coding design based on the Separability matrix is tested over a wide set of challenging multi-class problems, obtaining very satisfactory results.

Keywords

Error Correcting Output Codes Problem-dependent designs Separability matrix Ensemble Learning 

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References

  1. [AN07]
    Asuncion, A., Newman, D.J.: UCI machine learning repository. University of California, Irvine, School of Information and Computer Sciences (2007), http://www.ics.uci.edu/~mlearn/MLRepository.html
  2. [ASS02]
    Allwein, E., Schapire, R., Singer, Y.: Reducing multiclass to binary: A unifying approach for margin classifiers. In: JMLR, vol. 1, pp. 113–141 (2002)Google Scholar
  3. [CMP+04]
    Casacuberta, J., Miranda, J., Pla, M., Sanchez, S., Serra, A., Talaya, J.: On the accuracy and performance of the GeoMobil system. In: International Society for Photogrammetry and Remote Sensing (2004)Google Scholar
  4. [CS02]
    Crammer, K., Singer, Y.: On the learnability and design of output codes for multi-class problems. Machine Learning 47, 201–233 (2002)CrossRefMATHGoogle Scholar
  5. [DB95]
    Dietterich, T., Bakiri, G.: Solving multiclass learning problems via error-correcting output codes. In: JAIR, vol. 2, pp. 263–286 (1995)Google Scholar
  6. [Dem06]
    Demsar, J.: Statistical comparisons of classifiers over multiple data sets. In: JMLR, vol. 7, pp. 1–30 (2006)Google Scholar
  7. [DK95]
    Dietterich, T., Kong, E.: Error-correcting output codes corrects bias and variance. In: Prieditis, S., Russell, S. (eds.) ICML, pp. 313–321 (1995)Google Scholar
  8. [Hol75]
    Holland,J.H.: Adaptation in natural and artificial systems: An analysis with applications to biology, control, and artificial intelligence. University of Michigan Press (1975)Google Scholar
  9. [BEB10]
    Bautista, M.A., Escalera, S., Baro, X.: Compact Evolutive Design of Error-Correcting Output Codes. In: Supervised and Unsupervised Ensemble methods and applications - European Conference on Machine Learning, pp. 119–128 (2010)Google Scholar
  10. [LdC08]
    Lorena, A.C., de Carvalho, A.C.P.L.F.: Evolutionary tuning of svm parameter values in multiclass problems. Neurocomputing 71(16-18), 3326–3334 (2008)CrossRefGoogle Scholar
  11. [MB98]
    Martinez, A., Benavente, R.: The AR face database. In: Computer Vision Center Technical Report # 24 (1998)Google Scholar
  12. [MP]
  13. [PRV06]
    Pujol, O., Radeva, P., Vitrià, J.: Discriminant ECOC: A heuristic method for application dependent design of error correcting output codes. Trans. on PAMI 28, 1001–1007 (2006)CrossRefGoogle Scholar
  14. [RK04]
    Rifkin, R., Klautau, A.: In defense of one-vs-all classification. In: JMLR, vol. 5, pp. 101–141 (2004)Google Scholar
  15. [TR98]
    Hastie, T., Tibshirani, R.: Classification by pairwise grouping. In: NIPS, vol. 26, pp. 451–471 (1998)Google Scholar
  16. [EOR08]
    Escalera, S., Pujol, O., Radeva, P.: Sub-class error-correcting output codes. In: Proceedings of the 6th international conference on Computer vision systems, pp. 494–504 (2008)Google Scholar
  17. [BEV09]
    Baro, X., Escalera, S., Vitria, J., Pujol, O., Radeva, P.: Traffic Sign Recognition Using Evolutionary Adaboost Detection and Forest-ECOC Classification. IEEE Transactions on Intelligent Transportation Systems 10(1), 113–126 (2009)CrossRefGoogle Scholar
  18. [BGV92]
    Boser, B.E., Guyon, I.M., Vapnik, V.N.: A training algorithm for optimal margin classifiers. In: Proceedings of the Fifth Annual Workshop on Computational Learning Theory (COLT 1992), pp. 144–152. ACM Press, New York (1992)CrossRefGoogle Scholar
  19. [FS95]
    Freund, Y., Schapire, R.E.: A decision-theoretic generalization of on-line learning and an application to boosting. In: Proceedings of the Second European Conference on Computational Learning Theory, UK pp. 23–37 (1995)Google Scholar
  20. [CC01a]
    Chang, C.-C., Lin, C.-J.: LIBSVM: a library for support vector machines., http://www.csie.ntu.edu.tw/~cjlin/libsvm

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Miguel Ángel Bautista
    • 1
    • 2
  • Oriol Pujol
    • 1
    • 2
  • Xavier Baró
    • 1
    • 2
    • 3
  • Sergio Escalera
    • 1
    • 2
  1. 1.Applied Math and Analisis DeptUniversity of BarcelonaBarcelonaSpain
  2. 2.Computer Vision CenterCampus UABBellaterraSpain
  3. 3.Computer Science, Multimedia, and Telecommunications DeptUniversitat Oberta de Catalunya.BarcelonaSpain

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