Skip to main content
SpringerLink
Log in

Estimating time-varying densities using a stochastic learning automaton

  • Original Paper
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

The popular Expectation Maximization technique suffers a major drawback when used to approximate a density function using a mixture of Gaussian components; that is the number of components has to be a priori specified. Also, Expectation Maximization by itself cannot estimate time-varying density functions. In this paper, a novel stochastic technique is introduced to overcome these two limitations. Kernel density estimation is used to obtain a discrete estimate of the true density of the given data. A Stochastic Learning Automaton is then used to select the number of mixture components that minimizes the distance between the density function estimated using the Expectation Maximization and discrete estimate of the density. The validity of the proposed approach is verified using synthetic and real univariate and bivariate observation data.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Poznyak AS, Najim K, Gomez-Ramirez E (1994) Learning automata: theory and applications. Self-learning control of finite Marker chains. Pergamon, New York

    Google Scholar 

  2. Poznyak AS, Najim K (1997) Learning automata and stochastic optimization. Lecture Notes in Control and Information Sciences 225. Springer

  3. Abd-Almageed W, Smith CE (2002) Mixture models for dynamix statistical pressure snakes. In: Proceedings of IEEE internation conference on pattern recognition, pp 721-724

  4. Abu-Naser A, Galatsanos NP, Wernick MN, Schonfeld D (1998) Object recognition based on impulse restoration with use of the expectation-maximization algorithm. J Opti Soc Am A (Optics Image Science and Vision) 15(9):2327–2340

    Article  Google Scholar 

  5. Bensmail H, Celeus G, Rafetry A, Robert C (1997) Inference in model-based cluster analysis. Stat Comput 7:1–10

    Article  Google Scholar 

  6. Biernacki C, Celeux G, Govaert G (2000) Assessing a Mixture Model for Clustering with the Integrated Classification Likelihood. IEEE Trans Pattern Anal Mach Intell 22(7):719–725

    Article  Google Scholar 

  7. Campbell J, Fraley C, Murtagh F, Raftery A (1997) Linear Flaw Detection in Woven Textiles Using Model-Based clustering. Pattern Recognit Lett 18:1539–1548

    Article  Google Scholar 

  8. Dasgupta A, Rafetry A (1998) Detecting Features ni Spatial Point Patterns with Clutter Via Model-Based Clustering. J Am Stat Assoc 93:294–302

    Article  MATH  Google Scholar 

  9. Dempster AP, Laird NM, Rubin DB (1977) Maximum Likelihood from Incomplete Data via the EM Algorithm. J R Stat Soc B-39:1–38

    MATH  MathSciNet  Google Scholar 

  10. Elgammal A, Duraiswami R, Davis L (2003) Efficient kernel density estimation using the fast gauss transform with applications to color modeling and tracking. IEEE Trans Pattern Anal Mach Intell 25(11):1499–1504

    Article  Google Scholar 

  11. Figueirdeo M, Jain A (2002) Unsupervised learning of finite mixture models. IEEE Trans Pattern Anal Mach Intell 24(3):381–396

    Article  Google Scholar 

  12. Greengard L, Strain J (1991) The Fast Gauss Transform. SIAM J Sci Comput 12(1):79–94

    Article  MATH  MathSciNet  Google Scholar 

  13. Johnson D, Sinanovic S (2001) Symmetrizing the Kullback-Leibler Distance. IEEE Trans Inf Theory (Submitted)

  14. Fu KS, McMurtry GJ (1966) A study of stochastic automata as a model for learning and adaptive controllers. IEEE Trans Autom Control 11:379–387

    Article  Google Scholar 

  15. Narendra KS, Thathachar MAL (1974) Learning automata: a survey. IEEE Trans Syst Man Cybern 14:323–334

    MathSciNet  Google Scholar 

  16. Kullback S (1968) Information theory and statistics. Dover, New York

    Google Scholar 

  17. Thathachar MAL, Sastry PS (2002) Varieties of learning automata: an overview. IEEE Trans Syst Man Cybern 32(6):711–722

    Article  Google Scholar 

  18. Neal R (1992) Bayesian mixture modeling. In: Proceedings of 11th International workshop on maximum entropy and bayesian methods of statistical analysis, pp 197–211

  19. Nefian AV, Liang L, Pi X, Xiaoxiang L, Mao C, Murphy K (2002) A coupled HMM for audio-visual speech recognition. In: International conference on acoustics speech and signal processing (CASSP’02) Orlando FL, pp 13–17

  20. Parzen E (1962) On the Estimation of a Probability Density Function and the Mode. Ann Math Stat 33:1065–1076

    Article  MathSciNet  Google Scholar 

  21. Richardson S, Green P (1997) On Bayesian analysis of mixturtes with unknown number of componenets. J R Stat Soc 59:731–792

    Article  MATH  MathSciNet  Google Scholar 

  22. Tsetlin ML (1962) On The Bahavior of Finit Automata in Random Media. Autom Remote Control 22:1210-1219

    MATH  Google Scholar 

  23. Yang C, Duraiswami R, Gumerov N, Davis L (2003) Improved fast gauss transform and efficient kernel density estimation. In: Proc IEEE international conference computer vision

Download references

Author information

Authors and Affiliations

  1. Computer Vision Laboratory, Institute for Advanced Computer Studies, University of Maryland, College Park, MD, 20742, USA

    Wael Abd-Almageed

  2. Department of Electrical Engineering, New Mexico Tech., Socorro, NM, 87801, USA

    Aly I. El-Osery

  3. Department of Electrical and Computer Engineering, University of New Mexico, Albuquerque, NM, 87131, USA

    Christopher E. Smith

Authors
  1. Wael Abd-Almageed
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Aly I. El-Osery
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Christopher E. Smith
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wael Abd-Almageed.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Abd-Almageed, W., El-Osery, A.I. & Smith, C.E. Estimating time-varying densities using a stochastic learning automaton. Soft Comput 10, 1007–1020 (2006). https://doi.org/10.1007/s00500-005-0028-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-005-0028-4

Keywords

Search

Navigation