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Pattern Classification Based on a Piecewise Multi-linear Model for the Class Probability Densities

  • Edgard Nyssen
  • Luc Van Kempen
  • Hichem Sahli
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1876)

Abstract

When a Bayesian classifier is designed, a model for the class probability density functions (PDFs) has to be chosen. This choice is determined by a trade-off between robustness and low complexity — which is usually satisfied by simple parametric models, based on a restricted number of parameters — and the model’s ability to fit a large class of PDFs — which usually requires a high number of model parameters.

In this paper, a model is introduced, where the class PDFs are approximated as piecewise multi-linear functions (a generalisation of bilinear functions for an arbitrary dimensionality). This model is compared with classical parametric and non-parametric models, from a point of view of versatility, robustness and complexity. The results of classification and PDF estimation experiments are discussed.

Keywords

Quadratic Discriminant Analysis Orthogonal Expansion Localise Base Function Orthonormal Base Function Simple Parametric Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Richard O. Duda and Peter E. Hart. Pattern Classification and Scene Analysis. John Wiley & Sons, 1973.Google Scholar
  2. 2.
    Julius T. Tou and Raphael C. Gonzales. Pattern Recognition Principles. Addison Wesley Publishing Company, 1979.Google Scholar
  3. 3.
    Robert Schalkoff. Pattern Recognition — Statistical, Structural and Neural Approaches. John Wiley & Sons, 1992.Google Scholar
  4. 4.
    Fang Sun, Shin’ichiro Omachi, and Hirotomo Aso. An algorithm for estimating mixture distributions of high dimensional vectors and its application to character recognition. In Proc. 11th Scandinavian Conference on Image Analysis, pages 267–274, 1999.Google Scholar
  5. 5.
    David L. Donoho, Iain M. Johnstone, Gérard Kerkyacharian, and Dominique Picard. Density estimation by wavelet thresholding. The Annals of Statistics, 24(2):508–539, 1996.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    N. Balakrishnan. Introduction and historical remarks. In N. Balakrishnan, editor, Handbook of the Logistic Distribution. Marcel Dekker, Inc, 1992.Google Scholar
  7. 7.
    W. J. Dixon, M. B. Brown, L. Engelman, J. W. Frane, M. A. Hill, R. I. Jennrich, and J. D. Toporek. BMDP Statistical Software 1981, 1981.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Edgard Nyssen
    • 1
  • Luc Van Kempen
    • 1
  • Hichem Sahli
    • 1
  1. 1.Vakgroep Elektronica en Informatieverwerking (ETRO)Vrije Universiteit BrusselBrusselBelgium

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