Calibrating Margin-Based Classifier Scores into Polychotomous Probabilities

  • Martin Gebel
  • Claus Weihs
Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)


Margin-based classifiers like the SVM and ANN have two drawbacks. They are only directly applicable for two-class problems and they only output scores which do not reflect the assessment uncertainty. K-class assessment probabilities are usually generated by using a reduction to binary tasks, univariate calibration and further application of the pairwise coupling algorithm. This paper presents an alternative to coupling with usage of the Dirichlet distribution.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. ALLWEIN, E. L. and SHAPIRE, R. E. and SINGER, Y. (2000): Reducing Multiclasss to Binary: A Unifying Approach for Margin Classifiers. Journal of Machine Learning Re-search 1, 113-141.CrossRefGoogle Scholar
  2. DEGROOT, M. H. and FIENBERG, S. E. (1983): The Comparison and Evaluation of Fore-casters. The Statistician 32, 12-22.CrossRefGoogle Scholar
  3. GEBEL, M. and WEIHS, C. (2007): Calibrating classifier scores into probabilities. In: R. Decker and H. Lenz (Eds.): Advances in Data Analysis. Springer, Heidelberg, 141-148.CrossRefGoogle Scholar
  4. HASTIE, T. and TIBSHIRANI, R. (1998): Classification by Pairwise Coupling. In: M. I. Jordan, M. J. Kearns and S. A. Solla (Eds.): Advances in Neural Information Processing Systems 10. MIT Press, Cambridge.Google Scholar
  5. HEILEMANN, U. and MÜNCH, J. M. (1996): West german business cycles 1963-1994: A multivariate discriminant analysis. CIRET-Conference in Singapore, CIRET-Studien 50.Google Scholar
  6. JOHNSON, N. L. and KOTZ, S. and BALAKRISHNAN, N. (2002): Continuous Multivariate Distributions 1, Models and Applications, 2nd edition. John Wiley & Sons, New York.Google Scholar
  7. NEWMAN, D.J. and HETTICH, S. and BLAKE, C.L. and MERZ, C.J. (1998): UCI Reposi-tory of machine learning databases [∼learn/MLRepository.html]. University of California, Department of Information and Computer Science, Irvine.
  8. SUYKENS, J. A. K. and VANDEWALLE, J. P. L. (1999): Least Squares Support Vector Machine classifiers. Neural Processing Letters 9:3,93-300.CrossRefMathSciNetGoogle Scholar
  9. ZHANG, T. (2004): Statistical behavior and consitency of classification methods based on convex risk minimization. Annals of Statistics 32:1, 56-85.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Martin Gebel
    • 1
  • Claus Weihs
    • 2
  1. 1.Graduiertenkolleg Statistische Modellbildung, Lehrstuhl für Computergestützte StatistikUniversitÄt DortmundDortmundGermany
  2. 2.Lehrstuhl für Computergestützte StatistikUniversitÄt DortmundDortmundGermany

Personalised recommendations