Possibilistic and probabilistic fuzzy clustering: Unification within the framework of the non-extensive thermostatistics

Pattern Recognition

Volumn 36, Issue 6, 2003, Pages 1325-1342

  Ménard, Michel ^a   Courboulay, Vincent ^a   Dardignac, Pierre André ^a  

^a UNIVERSITÉ DE LA ROCHELLE   (France)

Author keywords

Extreme physical information; Fisher information; Fuzzy c means; Measures of information; Non extensive thermostatistics; Possibilistic algorithm; Possibilistic and probabilistic fuzzy clustering

Indexed keywords

FUNCTIONS; FUZZY SETS; PROBABILITY;

FUZZY CLUSTERING;

PATTERN RECOGNITION;

FUZZY MATHEMATICS;

EID: 0037410622     PISSN: 00313203     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0031-3203(02)00049-3     Document Type: Article

References (32)

1. F. Hoppner, F. Klawonn, R. Kruse, T. Runler, Fuzzy Cluster Analysis, Wiley, New York.
2. A. Kandel, Fuzzy Mathematical Techniques with Applications, Addison-Wesley Publishing Company, Reading, MA, 1986.
3. M. Ma, et al., Fuzzy partition and fuzzy rule base, Inform. Sci. 108 (1998) 109-121.
4. G. Xinbo, Advances in theory and applications of fuzzy clustering, Chin. Sci. Bull. 45 (11) (2000) 961-970.
5. M. Friedman, A. Kandel, Introduction to pattern recognition. Statistical, structural, neural and fuzzy logic approaches, Machine Perception Artificial Intelligence, Vol. 32, World Scientific Publishers, Singapore, 1999.
6. J. Bezdek, S. Pal, Fuzzy Models for Pattern Recognition, IEEE Press, Piscataway, NY.
7. J.C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum Press, New York, 1981.
8. A. Bensaid, L. Hall, J. Bezdek, L. Clarke, M. Silbiger, J. Arrington, R. Murtagh, Validity-guided (re) clustering with applications to image segmentation, IEEE Trans. Fuzzy Systems, 4(2).
9. R. Krishnapuram, A possibilistic approach to clustering, IEEE Trans. Fuzzy Systems 1 (2) (1993) 98-110.
10. R. Davé, R. Krishnapuram, Robust clustering methods: a unified view, IEEE Trans. Fuzzy Systems 5 (2) (1997) 270-292.
11. R. Krishnapuram, J. Keller, The possibilistic c-means algorithm: Insights and recommendations, IEEE Trans. Fuzzy Systems 4 (3) (1996) 148-158.
12. R. Hathaway, J. Bezdek, Optimization of clustering criteria by reformulation, IEEE Trans. Fuzzy Systems 3 (2) 241-245.
13. E. Ruspini, A new approach to clustering, Inform. and Control 15 (1969) 22-32.
14. R. Hathaway, J. Bezdek, Switching regression models and fuzzy clustering, IEEE Trans. Fuzzy Systems 1 (3) (1993) 195-203.
15. M. Ménard, C. Demko, P. Loonis, The fuzzy c+2-means: solving the ambiguity reject in clustering, Pattern Recognition 33 (7) (2000) 1219-1237.
16. M. Ménard, Fuzzy clustering and switching regression models using ambiguity and distance rejects, Fuzzy Sets and Systems 122 (3) (2001) 363-400.
17. A. Schneider, Weighted possibilistic c-means, clustering algorithms, Fuzz'IEEE 2000; 7 May 2000, Texas, USA.
18. R. Li, M. Mukaidono, A maximum entropy approach to fuzzy clustering, Conference on Fuzzy Systems (Fuzz'IEEE), Yokohama, Japan.
19. S. Miyamoto, M. Mukaidono, Fuzzy c-means as a regularization and maximum entropy approach, Proceedings of the Seventh International Fuzzy Systems Association World Congress (IFSA'97), Vol. 2, Prague, Chech., 1997, pp. 86-92.
20. K. Rose, E. Gurewitz, G. Fox, A determininistic annealing approach to clustering, Pattern Recognition Lett. 11 (1990) 589-594.
21. S. Miyamoto, An overview and new methods in fuzzy clustering, Conference on Knowledge-Based Intelligent Electronic, Systems, Adelaide, Australia, 1998, pp. 33-40.
22. S. Miyamoto, K. Umayahara, Fuzzy clustering by quadratic regularization, Proceedings of FUZZ-IEEE'98, Anchorage, Alaska.
23. H. Ichihashai, K. Honda, N. Tani, Gaussian mixture pdf approximation and fuzzy c-means clustering with entropy regularization, Proceedings of the Fourth Asian Fuzzy System Symposium, Tsukuba, Japan, 2000, pp. 217-221.
24. M. Ménard, M. Eboueya, Extreme physical information and objective functions in fuzzy clustering, Fuzzy Sets and Systems 27pp, A paraitre.
25. B. Frieden, Physics from Fisher information. A Unification, Cambridge University Press, Cambridge, 1999.
26. B. Frieden, Fisher information as a measure of time, in: Astrophysics and Space Sciences, Vol. 244, Kluwer Academic Publishers, Dordrecht, 1996, pp. 387-391.
27. V. Kreinovich, H. Nguyen, Y. Yam, Optimal choices of potential functions in fuzzy clustering, Technical Report CUHK-MAE-98-001, The Chinese University of Hong Kong.
28. S. Chiu, J. Cheng, Fuzzy model identification based on cluster estimation, J. Intell. Fuzzy Systems 2 (3) (1994) 267-268.
29. C. Tsallis, Entropic nonextensivity: a possible measure of complexity, Fractal 6, 539.
30. C. Tsallis, Possible generalisation of Boltzmann-Gibbs statistics, J. Statist. Phys. 52(479).
31. L. Chimento, F. Pennini, A. Plastino, The Frieden-soffer extreme physical information principle in a non-extensive setting, Phys. Lett. A 257, 275-282.
32. A. Plastino, A. Plastino, H. Miller, Tsallis non-extensive thermostatistics and Fisher's information measure, Physica A 235, 577-588.