Skip to main content

A new approach for determining the prior probabilities in the classification problem by Bayesian method


In this article, we suggest a new algorithm to identify the prior probabilities for classification problem by Bayesian method. The prior probabilities are determined by combining the information of populations in training set and the new observations through fuzzy clustering method (FCM) instead of using uniform distribution or the ratio of sample or Laplace method as the existing ones. We next combine the determined prior probabilities and the estimated likelihood functions to classify the new object. In practice, calculations are performed by Matlab procedures. The proposed algorithm is tested by the three numerical examples including bench mark and real data sets. The results show that the new approach is reasonable and gives more efficient than existing ones.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5


  1. Bora DJ, Gupta AK (2014) Impact of exponent parameter value for the partition matrix on the performance of fuzzy C means Algorithm. arXiv:1406.4007 (arXiv preprint)

  2. Cannon RL, Dave JV, Bezdek JC (1986) Efficient implementation of the fuzzy c-means clustering algorithms. IEEE Trans Pattern Anal Mach Intell 2:248–255

    Article  MATH  Google Scholar 

  3. Fadili MJ et al (2001) On the number of clusters and the fuzziness index for unsupervised FCA application to BOLD fMRI time series. Med Image Anal 5(1):55–67

    Article  Google Scholar 

  4. Ghosh AK, Chaudhuri P, Sengupta D (2006) Classification using Kernel density estimates. Technometrics 48(1):120–132

    MathSciNet  Article  Google Scholar 

  5. Hall LO et al (1992) A comparison of neural network and fuzzy clustering techniques in segmenting magnetic resonance images of the brain. IEEE Trans Neural Netw 3(5):672–682

    Article  Google Scholar 

  6. Inman HF, Bradley EL Jr (1989) The overlapping coefficient as a measure of agreement between probability distributions and point estimation of the overlap of two normal densities. Commun Stat Theory Methods 18(10):3851–3874

    MathSciNet  Article  MATH  Google Scholar 

  7. Mardia KV, Kent JT, Bibby JM (1979) Multivariate analysis. Academic Press, Cambridge

    MATH  Google Scholar 

  8. Martinez WL, Martinez AR (2007) Computational statistics handbook with MATLAB. CRC Press, Boca Raton

    MATH  Google Scholar 

  9. McLachlan GJ, Basford KE (1988) Mixture models: inference and applications to clustering. Statistics: textbooks and monographs. Dekker, New York

  10. Miller G et al (2001) Bayesian prior probability distributions for internal dosimetry. Radiat Prot Dosim 94(4):347–352

    Article  Google Scholar 

  11. Pal NR, Bezdek JC (1995) On cluster validity for the fuzzy c-means model. IEEE Trans Fuzzy Syst 3(3):370–379

    Article  Google Scholar 

  12. Pham-Gia T, Turkkan N, Vovan T (2008) Statistical discrimination analysis using the maximum function. Commun Stat Simul Comput 37(2):320–336

    MathSciNet  Article  MATH  Google Scholar 

  13. Scott DW (1992) Multivariate density estimation: theory, practice, and visualization. Wiley

  14. Silverman BW (1986) Density estimation for statistics and data analysis, vol 26. CRC Press, Boca Raton

    Book  MATH  Google Scholar 

  15. Van Vo T, Pham-Gia T (2010) Clustering probability distributions. J Appl Stat 37(11):1891–1910

    MathSciNet  Article  Google Scholar 

  16. Webb AR (2003) Statistical pattern recognition. Wiley, New York

    MATH  Google Scholar 

  17. Yu J, Cheng Q, Huang H (2004) Analysis of the weighting exponent in the FCM. IEEE Trans Syst Man Cybern Part B Cybern 34(1):634–639

    Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Thao Nguyen-Trang.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Nguyen-Trang, T., Vo-Van, T. A new approach for determining the prior probabilities in the classification problem by Bayesian method. Adv Data Anal Classif 11, 629–643 (2017).

Download citation


  • Classification
  • Bayes error
  • BayesC
  • Prior probability

Mathematics Subject Classification

  • 62H30
  • 68T10