Classifier conditional posterior probabilities

  • Robert P. W. Duin
  • David M. J. Tax
Statistical Classification Techniques
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1451)


Classifiers based on probability density estimates can be used to find posterior probabilities for the objects to be classified. These probabilities can be used for rejection or for combining classifiers. Posterior probabilities for other classifiers, however, have to be conditional for the classifier., i.e. they yield class probabilities for a given value of the classifier outcome instead for a given input feature vector. In this paper they are studied for a set of individual classifiers as well as for combination rules.


classification reliability reject combining classifiers 


  1. [1]
    R.P.W. Duin, On the choice of the smoothing parameters for Parzen estimators of probability density functions, IEEE Trans. Computers, vol. C-25, no. 11, 1976, Nov., 1175–1179.Google Scholar
  2. [2]
    J.R. Quinlan, Induction of decision trees, Machine Learning, vol. 1, pp. 81–106, 1986.Google Scholar
  3. [3]
    J.R. Quinlan, Simplifying decision trees, Int. J. Man-Machine Studies, vol. 27, pp. 221–234, 1987.Google Scholar
  4. [4]
    J. Kittler, M. Hatef, R.P.W. Duin, and J. Matas, On Combining Classifiers, IEEE Trans. on Pattern Analysis and Machine Intelligence, vol. 20, no. 3, 1998.Google Scholar
  5. [5]
    D.M.J. Tax, M. van Breukelen, R.P.W. Duin, and J. Kittler, Combining multiple classifiers by averaging or by multiplying?, submitted, september 1997.Google Scholar
  6. [6]
    J. A. Anderson, Logistic discrimination, in: P. R. Krishnaiah and L. N. Kanal (eds.), Handbook of Statistics 2: Classification, Pattern Recognition and Reduction of Dimensionality, North Holland, Amsterdam, 1982, 169–191.Google Scholar
  7. [7]
    R.P.W. Duin, PRTools, A Matlab toolbox for pattern recognition, version 2.1, 1997, see Scholar
  8. [8]
    A. Hoekstra, S.A. Tholen, and R.P.W. Duin, Estimating the reliability of neural network classifiers, in: C. von der Malsburg, W. von Seelen, J.C. Vorbruggen, B. Sendhoff (eds.), Artificial Neural Networks-ICANN'96, Proceedings of the 1996 International Conference on Artificial Neural Networks (Bochum, Germany, July 16–19, 1996), 53–58.Google Scholar
  9. [9]
    A. Hoekstra, R.P.W. Duin, and M.A. Kraaijveld, Neural Networks Applied to Data Analysis, in: C.T. Leondes (eds.), Neural Network Systems Techniques and Applications, Academic Press, in press.Google Scholar
  10. [10]
    Cox, L.H., M.M. Johnson, K. Kafadar (1982), Exposition of statistical graphics technology, ASA Proceedings Statistical Computation Section, page 55–56.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Robert P. W. Duin
    • 1
  • David M. J. Tax
    • 1
  1. 1.Pattern Recognition Group, Department of Applied SciencesDelft University of TechnologyThe Netherlands

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