Call for Paper

CAE solicits original research papers for the July 2019 Edition. Last date of manuscript submission is June 30, 2019.

Read More

Selecting Parameters of the Fuzzy Possibilistic Clustering Algorithm

Mohamed Fadhel Saad, Adel M. Alimi. Published in Fuzzy Systems.

Communications on Applied Electronics
Year of Publication: 2016
Publisher: Foundation of Computer Science (FCS), NY, USA
Authors: Mohamed Fadhel Saad, Adel M. Alimi

Mohamed Fadhel Saad and Adel M Alimi. Selecting Parameters of the Fuzzy Possibilistic Clustering Algorithm. Communications on Applied Electronics 5(10):42-52, September 2016. BibTeX

	author = {Mohamed Fadhel Saad and Adel M. Alimi},
	title = {Selecting Parameters of the Fuzzy Possibilistic Clustering Algorithm},
	journal = {Communications on Applied Electronics},
	issue_date = {September 2016},
	volume = {5},
	number = {10},
	month = {Sep},
	year = {2016},
	issn = {2394-4714},
	pages = {42-52},
	numpages = {11},
	url = {},
	doi = {10.5120/cae2016652389},
	publisher = {Foundation of Computer Science (FCS), NY, USA},
	address = {New York, USA}


Clustering has been widely used in pattern recognition, image processing, and data analysis. It aims to organize a collection of data items into clusters, such that items within a cluster are more similar to each other than they are in other clusters. The Fuzzy Possibilistic C-Means (FPCM) is one of the most popular clustering methods based on minimization of a criterion function. So the implementation of this algorithm requires a priori selection of some parameters: the fuzzy and the typical exponent, initialization of cluster centers. But the definition of these parameters at the moment is fixed in advanced and the initialization of centers is random; so the algorithm can give results not consistent. The determination of an optimal value for these parameters and the cluster centers at the beginning are problematic and remains an open problem. New procedures for choice of the optimal values of parameters and for initialization of centers were developed. Numerical results using data sets are used to illustrate the simplicity and effectiveness of the proposed procedures.


  1. Borgelt, C. Prototype-based classification and clustering. Habilitation, University of Magdeburg Germany, June 2005.
  2. Saad, M. F. and Alimi, A. M. A New Improved Fuzzy Possibilistic C-Means Algorithm Based On Weight Degree. Intelligent Automation and Computer Engineering, 90-104, 2010.
  3. Zadeh, L.A. Fuzzy Sets. Inf. control, vol. 8, 338-352, 1965.
  4. Bezdek, J.C. Fuzzy mathematics in pattern classification. PH.D dissertation, Cornell Univ. Ithaca, NY, 1973.
  5. Bezdek, J.C. Pattern recognition with fuzzy objective function algorithms. Plenum, New York, 1981.
  6. Krishnapuram, R. and Keller, J. A possibilistic Approch to Clustering. IEEE Trans. on Fuzzy Systems, vol. 1, no. 2, May 1993.
  7. Pal, N.R. Pal, K. and Bezdek, J. C. A mixed c-means clustering model. Proceedings of the Sixth IEEE International Conference on Fuzzy Systems, vol. 1, 11-21, Jul. 1997.
  8. Forgy, E.W. Cluster analysis of multivariate data: Efficiency versus interpretability of classification. Biometrics, vol. 21, 768-769, 1965.
  9. Saad, M. F. and Alimi, A. M. Modified Fuzzy Possibilistic C-means. Proceedings of the International MultiConference of Engineers and Computer Scientists, vol. 1, 177-182, 2009.
  10. Pena, J., Lozano, J. and Larranaga, P. An empirical Comparison of four Initialization Methods for the k-means Algorithm. Pattern Recognition Letters, vol. 20, 1027-1040, 1999.
  11. Kaufman, L. and Rousseeuw, P.J. Finding Groups in Data, an Introduction to Cluster Analysis. Wiley, Canada, 1990.
  12. Velthuizen, R., Hall, L. and Clarke, L. Unsupervised fuzzy segmentation of 3D magnetic resonance brain images. In Proceedings International Symposium on Electronic Images: Science and Technology, 627-635, Jan 31-Feb 4, 1993.
  13. Bahman, B., Benjamin, M., Andrea, V., Ravi, K., Sergei, V. Scalable k-means++, Proceedings of the VLDB Endowment, vol. 5, 622-633, March 2012.
  14. Shanthi, R. and Suganya, R. Enhancement of Fuzzy Possibilistic C-Means Algorithm using EM Algorithm. International Journal of Computer Applications, vol. 61, no. 12, 10-15, January 2013.  
  15. Cannon, R. L., Dave, J. V. and Bezdek, J.C. Efficient Implementation of the Fuzzy C-Means Clustering Algorithms. IEEE Trans. Pattern Anal. Mach. Intell. vol. 8, no. 2, 248-255, 1986.
  16. Eef, M., Marc, V.M. Philippe, D.S., Timothy, S. Mohammad, M.I., Fun, M., Ellen, V. and Gunther, G. Imaging a Polygonal Network of Ice-Wedge Casts with an Electromagnetic Induction Sensor. Soil Science Society of America Journal, vol. 75, no. 6, 2095-2100, 2011.
  17. Choe, H. and Jordan, J.B. On the optimal choice of parameters in Fuzzy C-Means Algorithm. Proc of the IEEE International Conference on fuzzy systems, 349-354, 1992.
  18. Foody, G.M. and Cox, D.P. Sub-Pixel and cover composition estimation using mixture model and fuzzy set membership. International Journal of Remote Sensing, vol. 10, 1823-1842, 1989.
  19. Deer, P.J. and Eklund, P. A study of parameter values for a Mahalanobis distance fuzzy classifier. Fuzzy Sets and Systems, vol. 137, no. 2, 191-213, 2003.
  20. Okeke, F. and Karnieli, A. Linear mixture approach for selecting fuzzy exponent value in fuzzy c-means algorithm. Ecological informatics, vol. 1, 117-124, 2006.
  21. Barni, M., Cappellini, V. and Mecocci, A. Comments on A possibilistic approach to clustering. IEEE Trans. Fuzzy Systems, vol. 4, 393-396, 1996.
  22. Barra, V. Fusion 3D Images of the Brain: Study of Models and Applications. thesis: University Blaise Pascal and University Auvergne, France, July 2000.
  23. Saad, M. F. and Alimi, A. M. Validity Index and number of clusters. International Journal of Computer Science Issues, vol. 9, no. 3, January 2012.
  24. Belton, V. and Stewart, T.J. Multiple criteria approach: an integrated perspective. Kluwer Academics Publishers, Netherlands, 2001.
  25. Bezdek, J.C., Popescu, M. , Keller, J.M. Comparing Fuzzy, Probabilistic, and Possibilistic Partitions. IEEE Transactions on Fuzzy Systems. vol. 18, no. 5, 906-918, 2010.
  26. Blake, C.L. and Merz, C.J. UCI Repository of Machine Learning Databases. University of California, Irvine, CA, USA, 1998.


Fuzzy c-means, Possibilistic c-means, Fuzzy possibilistic c-means, K-means++.