Risk Estimation for Hierarchical Classifier

  • I. T. Podolak
  • A. Roman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6678)


We describe the Hierarchical Classifier (HC), which is a hybrid architecture [1] built with the help of supervised training and unsupervised problem clustering. We prove a theorem giving the estimation \(\hat{R}\) of HC risk. The proof works because of an improved way of computing cluster weights, introduced in this paper. Experiments show that \(\hat{R}\) is correlated with HC real error. This allows us to use \(\hat{R}\) as the approximation of HC risk without evaluating HC subclusters. We also show how \(\hat{R}\) can be used in efficient clustering algorithms by comparing HC architectures with different methods of clustering.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Corchado, E., Abraham, A., Carvalo, A.C.: Hybrid intelligent algorithms and applications. Information Science 180(14), 2633–2634 (2010)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Haykin, S.: Neural networks: a comprehensive foundation. Prentice-Hall, Englewood Cliffs (2009)zbMATHGoogle Scholar
  3. 3.
    Christiani, N., Shawe-Taylor, J.: Support vector machines and other kernel-based learning methods. Cambridge University Press, Cambridge (2000)CrossRefGoogle Scholar
  4. 4.
    Bishop, C.: Pattern recognition and machine learning. Springer, Heidelberg (2006)zbMATHGoogle Scholar
  5. 5.
    Hastie, T., Tibshirani, R., Friedman, J.: The Elements of Statistical Learning. Springer, Heidelberg (2001)CrossRefzbMATHGoogle Scholar
  6. 6.
    Tresp, V.: Committee Machines. In: Handbook for Neural network Signal Processing. CRC Press, Boca Raton (2001)Google Scholar
  7. 7.
    Kearns, M., Valiant, L.: Cryptographic limitations on learning Boolean formulae and finite automata. Journal of the ACM 41(1), 67–95 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Shapire, R.E.: The strength of weak learnability. Machine Learning 5, 197–227 (1990)Google Scholar
  9. 9.
    Freund, Y., Shapire, R.E.: A decision theoretic generalization of online learning and an application to boosting. Journal of Computer and System Sciences 55, 119–139 (1997)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Podolak, I.T., Roman, A.: Theoretical foundations and practical results for the hierarchical classifier. Submitted to Computational IntelligenceGoogle Scholar
  11. 11.
    Podolak, I.T.: Hierarchical Classifier with Overlapping Class Groups. Expert Systems with Applications 34(1), 673–682 (2008)CrossRefGoogle Scholar
  12. 12.
    Podolak, I.T.: Hierarchical rules for a hierarchical classifier. In: Beliczynski, B., Dzielinski, A., Iwanowski, M., Ribeiro, B. (eds.) ICANNGA 2007. LNCS, vol. 4431, pp. 749–757. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  13. 13.
    Wozniak, M., Zmyslony, M.: Designing Fusers on the Basis of Discriminants – Evolutionary and Neural Methods of Training. In: Graña Romay, M., Corchado, E., Garcia Sebastian, M.T. (eds.) HAIS 2010. LNCS (LNAI), vol. 6076, pp. 590–597. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  14. 14.
    Shipp, C.A., Kuncheva, L.I.: Relationships between combination methods and measures of diversity in combining classifiers. Information Fusion 3, 135–148 (2002)CrossRefGoogle Scholar
  15. 15.
    Podolak, I., Roman, A.: Fusion of supervised and unsupervised training methods for a multi-class classification problem. Accepted for publication in Pattern Analysis and ApplicationsGoogle Scholar
  16. 16.
    Frank, A., Asuncion, A.: UCI Machine Learning Repository. University of California, School of Information and Computer Science, Irvine, CA,
  17. 17.
    Efron, B.: Estimating the error rate of a prediction rule: some improvements on cross-validation. Journal of the American Statistical Association 78, 316–331 (1983)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • I. T. Podolak
    • 1
  • A. Roman
    • 1
  1. 1.Institute of Computer ScienceJagiellonian UniversityPoland

Personalised recommendations