Skip to main content
SpringerLink
Log in

Novel Mixtures Based on the Dirichlet Distribution: Application to Data and Image Classification

  • Conference paper
  • First Online:
Machine Learning and Data Mining in Pattern Recognition (MLDM 2003)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2734))

Abstract

The Dirichlet distribution offers high flexibility for modeling data. This paper describes two new mixtures based on this density: the GDD (Generalized Dirichlet Distribution) and the MDD (Multinomial Dirichlet Distribution) mixtures. These mixtures will be used to model continuous and discrete data, respectively. We propose a method for estimating the parameters of these mixtures. The performance of our method is tested by contextual evaluations. In these evaluations we compare the performance of Gaussian and GDD mixtures in the classification of several pattern-recognition data sets and we apply the MDD mixture to the problem of summarizing image databases.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Amari, S. Natural Gradient Works Efficiently in Learning. Neural Computation, 10:251–276, 1998.

    Article  Google Scholar 

  2. Bouguila, N., Ziou, D. and Vaillancourt, J. The Introduction of Dirichlet Mixture into Image Processing Applications. Submitted to. IEEE Transactions on Image Processing.

    Google Scholar 

  3. Crawford, S.L. An Application of the Laplace Method to Finite Mixture Distributions. Journal of the American Statistical Association, 89:259–267, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  4. Dempster, A.P., Laird, N.M. and Rubin, D.B. Maximum Likelihood from Incomplete Data via the EM Algorithm. Journal of the Royal Statistical Society, B, 39:1–38, 1977.

    MATH  MathSciNet  Google Scholar 

  5. Duda, R.O. and Hart, P.E. Pattern Classification and Scene Analysis. Wiley, New York, 1973.

    MATH  Google Scholar 

  6. Everitt, B.S. and Hand, D.J. Finite mixture Distributions. Chapman and Hall, London, UK, 1981.

    MATH  Google Scholar 

  7. Fielitz, B.D and Myers, B.L. Estimation of Parameters in the Beta Distribution. Decision Sciences, 6:1–13, 1975.

    Article  Google Scholar 

  8. Ikeda, S. Acceleration of the EM algorithm. Systems and Computers in Japan, 31(2):10–18, February 2000.

    Article  Google Scholar 

  9. Kaufman, L. and Rousseeuw, P.J. Finding Groups in Data. John Wiley, New York, 1990.

    Google Scholar 

  10. Kherfi, M.L., Ziou, D. and Bernardi, A. Content-Based Image Retrieval Using Positive and Negative Examples. To appear, 2002.

    Google Scholar 

  11. Kotz, S. and Ng, K.W. and Fang, K. Symmetric Multivariate and Related Distributions. London/New York: Chapman and Hall, 1990.

    MATH  Google Scholar 

  12. Raftery, A.E. and Banfield, J.D. Model-Based Gaussian and Non-Gaussian Clustering. Biometrics, 49:803–821, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  13. Rao, C.R. Advanced Statistical Methods in Biomedical Research. New York: John Wiley and Sons, 1952.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. DMI, Faculté des Sciences, Université de Sherbrooke, Sherbrooke, Qc, Canada, J1K 2R1

    Nizar Bouguila, Djemel Ziou & Jean Vaillancourt

Authors
  1. Nizar Bouguila
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Djemel Ziou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jean Vaillancourt
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Computer Vision and Applied Computer Sciences, Arndtstr. 4, 04275, Leipzig, Germany

    Petra Perner

  2. Center for Automation Research, University of Maryland, College Park, Maryland, 20742-3275, USA

    Azriel Rosenfeld

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bouguila, N., Ziou, D., Vaillancourt, J. (2003). Novel Mixtures Based on the Dirichlet Distribution: Application to Data and Image Classification. In: Perner, P., Rosenfeld, A. (eds) Machine Learning and Data Mining in Pattern Recognition. MLDM 2003. Lecture Notes in Computer Science, vol 2734. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45065-3_15

Download citation

  • DOI: https://doi.org/10.1007/3-540-45065-3_15

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40504-7

  • Online ISBN: 978-3-540-45065-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation