ECM: An evidential version of the fuzzy c-means algorithm

Pattern Recognition

Volumn 41, Issue 4, 2008, Pages 1384-1397

  Masson, Marie Hélène ^a   Denoeux T ^a  

^a UNIVERSITÉ DE TECHNOLOGIE DE COMPIÈGNE   (France)

Author keywords

Belief functions; Cluster validity; Clustering; Dempster Shafer theory; Evidence theory; Robustness; Unsupervised learning

Indexed keywords

BAYESIAN NETWORKS; CLUSTERING ALGORITHMS; DATA PROCESSING; FUZZY SETS; ROBUSTNESS (CONTROL SYSTEMS);

BELIEF FUNCTIONS; CLUSTER VALIDITY; DEMPSTER-SHAFER THEORY; EVIDENCE THEORY;

UNSUPERVISED LEARNING;

EID: 36749023291     PISSN: 00313203     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.patcog.2007.08.014     Document Type: Article

References (34)

1. Bezdek J.C. Pattern Recognition with Fuzzy Objective Function Algorithms (1981), Plenum Press, New York
2. Dunn J.C. A fuzzy relative of the ISODATA process and its use in detecting compact, well-separated clusters. J. Cybern. (1974) 32-57
3. Hathaway R.J., Davenport J.W., and Bezdek J.C. Relational duals of the c-means clustering algorithms. Pattern Recognition 22 (1989) 205-212
4. Krishnapuram R., and Keller J. A possibilistic approach to clustering. IEEE Trans. Fuzzy Syst. 1 2 (1993) 98-110
5. Dubois D., and Prade H. Possibility Theory: An Approach to Computerized Processing of Uncertainty (1988), Plenum Press, New York
6. Davé R.N. Clustering relational data containing noise and outliers. Pattern Recognition Lett. 12 (1991) 657-664
7. Hathaway R.J., Bezdek J.C., and Davenport J.W. On relational versions of c-means algorithm. Pattern Recognition Lett. 17 (1996) 607-612
8. S. Sen, R.N. Davé, Clustering relational data containing noise and outliers, In: FUZZ'IEEE 98, 1998, pp. 1411-1416.
9. De Caceres M., Oliva F., and Font X. On relational possibilistic clustering. Pattern Recognition 39 (2006) 2010-2024
10. Denœux T., and Masson M.-H. Clustering of proximity data using belief functions. In: Bouchon-Meunier B., Foulloy L., and Yager R.R. (Eds). Intelligent Systems for Information Processing from Representation to Application (2003), Elsevier, Amsterdam 291-302
11. Denœux T., and Masson M.-H. EVCLUS: EVidential CLUStering of proximity data. IEEE Trans. Syst. Man Cybern. Part B 34 1 (2004) 95-109
12. Smets P. The transferable Belief Model for quantified belief representation. In: Gabbay D.M., and Smets P. (Eds). Hanbook of Defeasible Reasoning and Uncertainty Management Systems vol. 1 (1998), Kluwer Academic Publishers, Dordrecht 267-301
13. Shafer G. A Mathematical Theory of Evidence (1976), Princeton University Press, Princeton, NJ
14. Smets P., and Kennes R. The Transferable Belief Model. Artif. Intell. 66 (1994) 191-243
15. Smets P. The combination of evidence in the Transferable Belief Model. IEEE Trans. Pattern Anal. Mach. Intell. 12 5 (1990) 447-458
16. Cobb B.R., and Shenoy P.P. On the plausibility transformation method for translating belief function models to probability models. Int. J. Approximate Reasoning 41 3 (2006) 314-330
17. Smets P. Decision making in the TBM: the necessity of the pignistic transformation. Int. J. Approximate Reasoning 38 2 (2005) 133-147
18. Yager R.R. On the normalization of fuzzy belief structure. Int. J. Approximate Reasoning 14 (1996) 27-153
19. Döring C., Lesot M.-J., and Kruse R. Data analysis with fuzzy clustering methods. Comput. Data Anal. 51 (2006) 192-214
20. Barni M., Cappellini V., and Mecocci A. Comments on a possibilistic approach to clustering. IEEE Trans. Fuzzy Syst. 4 3 (1996) 393-396
21. Krishnapuram R., and Keller J. The possibilistic c-means algorithm: insights and recommendations. IEEE Trans. Fuzzy Syst. 4 3 (1996) 385-393
22. Masson M.-H., and Denœux T. Clustering interval-valued data using belief functions. Pattern Recognition Lett. 25 2 (2004) 163-171
23. Bezdek J.C., Keller J., Krishnapuram R., and Pal N.R. Fuzzy Models and Algorithms for Pattern Recognition and Image Processing (1999), Kluwer Academic Publishers, Boston
24. Ménard M., Demko C., and Loonis P. The fuzzy c + 2 means: solving the ambiguity rejection in clustering. Pattern Recognition 33 (2000) 1219-1237
25. Windham M.P. Numerical classification of proximity data with assignment measure. J. Classification 2 (1985) 157-172
26. Lingras P. Unsupervised rough set classification using GAs. J. Intelligent Inf. Syst. 16 (2001) 215-228
27. Bezdek J.C. Cluster validity with fuzzy sets. J. Cybern. 3 (1974) 58-73
28. Davé R.N. Validating fuzzy partition obtained through c-shell clustering. Pattern Recognition Lett. 17 (1996) 613-623
29. Ramer A. Uniqueness of information measure in the theory of evidence. Fuzzy Sets and Systems 24 (1987) 183-196
30. Klir G.J., and Wierman M.J. Uncertainty-based Information, Elements of Generalized Inf. Theory (1998), Springer, New York
31. Anderson E. The irises of the Gasp peninsula. Bull. Am. Iris Soc. 59 (1935) 2-5
32. Fisher R.A. The use of multiple measurements in taxonomic problems. Ann. Eugen. 7 (1936) 179-188
33. Bloch I. Some aspects of Dempster-Shafer evidence theory for classification of multi-modality medical images taking partial volume effect into account. Pattern Recognition Lett. 17 8 (1996) 905-919
34. I. Bloch, Defining belief functions using mathematical morphology-application to image fusion under imprecision, Int. J. Approximate Reasoning, 2007, in press, doi:10.1016/j.ijar.2007.07.008.