The fuzzy c+2-means: Solving the ambiguity rejection in clustering

Pattern Recognition

Volumn 33, Issue 7, 2000, Pages 1219-1237

  Ménard, Michel ^a   Demko, Christophe ^a   Loonis, Pierre ^a  

^a UNIVERSITÉ DE LA ROCHELLE   (France)

Author keywords

Ambiguity rejection; Distance rejection; Fuzzy c means; Fuzzy clustering

Indexed keywords

ALGORITHMS; FUZZY SETS; MEMBERSHIP FUNCTIONS;

FUZZY CLUSTERING;

PATTERN RECOGNITION;

EID: 0033735084     PISSN: 00313203     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0031-3203(99)00110-7     Document Type: Article

References (29)

1. J. MacQueen, Some methods of classification and analysis of multivariate observations, Proceedings of the 5th Berkeley Symposium on Math. Stat. and Prob. U, California Press, Berkeley, CA, 1967.
2. M.R. Andenberg, Cluster Analysis for Applications, Academic Press, New York, 1973.
3. S.K. Pal, D.D. Majumber, Fuzzy sets and decision making approaches in vowel and speaker recognition, IEEE. Trans. Systems Man Cybernet. 7 (1977) 625-629.
4. S.K. Pal, Fuzzy tools in the management of uncertainty in pattern recognition, image analysis, vision and expert systems, Int. J. Systems Sci. 22 (1991) 511-549.
5. J.C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum Press, New York, 1987.
6. E. Ruspini, A new approach to clustering, Inform. Control 15 (1969) 22-32.
7. J.C. Bezdek, R.J. Hathaway, M.J. Sabin, W.T. Tucker, Convergence theory for fuzzy c-means: Counter examples and repairs, IEEE Trans. Systems Man Cybernet. 17 (5) (1987) 873-877.
8. D.E. Gustafson, W.C. Kessel, Fuzzy clustering with a fuzzy covariance matrix, Proceedingds of IEEE CDC, San Diego, CA, January 10-12 1979, pp. 761-766.
9. R. Krishnapuram, A possibilistic approach to clustering, IEEE Trans. Fuzzy Systems 1 (2) (1993) 98-110.
10. N.B. Karayiannis, M. Ravuri, An Integrated Approach to Fuzzy Learning Vector Quantization and Fuzzy c-Means Clustering, in: C.H. Dagli et al. (Eds), Vol. 4, ASME Press, New York, USA, March 1997, pp. 247-252.
11. N.B. Karayiannis, Generalized fuzzy k-means algorithms and their application in image compression, SPIE Proceedings: Applications of Fuzzy Logic Technology II, Vol. 2493, Orlando, Florida, April 1995, pp. 206-217.
12. R.N. Dave, Generalized fuzzy c-shells clustering and detection of circular and elliptical boundaries, Pattern recognition 25 (1992) 713-721.
13. B. Dubuisson, Decision with reject option, European Signal Processing Conference, Barcelona, Spain, 1990.
14. B. Dubuisson, M.H. Masson, A statistical decision rule with incomplete knowledge about classes, Pattern Recognition 26 (1993) 155-165.
15. J.C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum Press, New York, 1981.
16. N.R. Pal, K. Pal, J.C. Bezdek, A mixed c-means clustering model; Proceedings of the Sixth IEEE International Conference on Fuzzy Systems, Barcelona, July 1997, pp. 11-21.
17. C. Demko, M. Menard, P. Loonis, The fuzzy c + 1-means: introduction of reject in clustering, IEEE Trans. Pattern Anal. Mach. Intell. Under review.
18. C. Demko, P. Loonis, M. Michel, Les c + 1-moyennes floues: introduction du rejet en classification, Actes des sixièmes rencontres de la société francophone de classification, Montpellier, France, September 1998.
19. C. Demko, Les c + 1-moyennes floues: élimination du bruit en classification. In Actes des rencontres francophone sur la logique floue et ses applications, Rennes, France, November 1998.
20. C.K. Chow, On optimum recognition error and reject tradeoff, IEEE Trans. Inform. Theory 16 (1990) 41-46.
21. C.K. Chow. Recognition error and reject trade-off, in: Proceedings of the Third Annual Symposium Document Analysis and Information Retrieval, Vol. 13, Univ. of Nevada, Las Vegas, USA, April 1994, pp. 1-8.
22. T.M. Ha, The optimum class-selective rejection rule, IEEE Trans. Pattern Anal. Mach. Intell. Vol. 19, No. 6, Yokohama, Japan, March 1997, pp. 608-614.
23. Z. Pawlack, Rough sets, Theoritical Aspects of Reasoning About Data, Kluwer Academic Publishers, Dordrecht, Boston, London, 1991.
24. T. Pavlidis, A critical survey of image analysis methods, ICPR (1986) 502-511.
25. A. Black, A. Zisserman, Visual reconstruction, MIT Press, Cambridge, MA, 1987.
26. I. Bloch, H. Maitre, Fuzzy mathematical morphologies: a comparative study, Pattern Recognition 28 (9) (1995) 1341-1387.
27. R. Dave, Characterization and detection of noise in clustering, Pattern recognition Lett. 12 (1991) 657-664.
28. R. Dave, Robust fuzzy clustering algorithms, IEEE International Conference on Fuzzy Systems, San Francisco Vol. 2 (1993) 1281-1286.
29. R.A. Fisher, The statistical utilisation of multiple measurements, Ann. Eugen. 8 (1938) 376-386.