Non-euclidean c-means clustering algorithms

Intelligent Data Analysis

Volumn 7, Issue 5, 2003, Pages 405-425

  Karayiannis, Nicolaos B ^a   Randolph Gips, Mary M ^b  

^a UNIVERSITY OF HOUSTON   (United States)

^b UNIVERSITY OF HOUSTON CLEAR LAKE   (United States)

Author keywords

c means clustering; generalized mean; non Euclidean norm; reformulation; weighted norm

Indexed keywords

CONSTRAINED OPTIMIZATION; ITERATIVE METHODS; VECTOR SPACES;

C-MEANS CLUSTERING; GENERALIZED MEAN; NON-EUCLIDEAN NORM; REFORMULATION; WEIGHTED NORM;

CLUSTERING ALGORITHMS;

EID: 48249118292     PISSN: 1088467X     EISSN: 15714128     Source Type: Journal    
DOI: 10.3233/ida-2003-7503     Document Type: Article

References (27)

1. E. Anderson, The IRISes of the Gaspe Peninsula, Bulletin of the American IRIS Society, 59 (1939), 2-5.
2. J.C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum, New York, 1981.
3. J.C. Bezdek and N.R. Pal, Two soft relatives of learning vector quantization, Neural Networks 8(5) (1995), 729-743.
4. L. Bobrowski and J.C. Bezdek, c-means clustering with the 1 and ? norms, IEEE Transactions on Systems, Man, and Cybernetics 21(3) (1991), 545-554.
5. D. Dubois and H. Prade, A review of fuzzy set aggregation connectives, Information Sciences 36(1-2) (1985), 85-121.
6. H. Dyckhoff and W. Pedrycz, Generalized means as a model of compensative connectives, Fuzzy Sets and Systems 14(2) (1984), 143-154.
7. D.E. Gustafson and W. Kessel, Fuzzy clustering with a fuzzy covariance matrix, in Proceedings of IEEE Conference on Decision and Control, San Diego, CA, 1979, pp. 761-766.
8. R.J. Hathaway and J.C. Bezdek, NERF c-means: Non-Euclidean relational fuzzy clustering, Pattern Recognition 27(3) (1994), 429-437.
9. R.J. Hathaway and J.C. Bezdek, Optimization of clustering criteria by reformulation, IEEE Transactions on Fuzzy Systems 3 (1995), 241-246.
10. R.J. Hathaway, J.C. Bezdek and Y. Hu, Generalized fuzzy c-means clustering strategies using Lp norm distances, IEEE Transactions on Fuzzy Systems 8(5) (2000), 576-582.
11. K. Jajuga, L1-norm based fuzzy clustering, Fuzzy Sets and Systems 39 (1991), 43-50.
12. N.B. Karayiannis, Fuzzy partition entropies and entropy constrained fuzzy clustering algorithms, Journal of Intelligent and Fuzzy Systems 5(2) (1997), 103-111.
13. N.B. Karayiannis, Reformulating learning vector quantization and radial basis neural networks, Fundamenta Informaticae 37(1999), 137-175.
14. N.B. Karayiannis, An axiomatic approach to soft learning vector quantization based on reformulation, IEEE Transactions on Neural Networks 10(5) (1999), 1153-1165.
15. N.B. Karayiannis, From aggregation operators to soft learning vector quantization and clustering algorithms, in Kohonen Maps, E. Oja and S. Kaski, eds, Elsevier, Amsterdam, 1999, pp. 47-56.
16. N.B. Karayiannis, Generalized fuzzy c-means algorithms, Journal of Intelligent and Fuzzy Systems 8(1) (2000), 63-81.
17. N.B. Karayiannis, Soft learning vector quantization and clustering algorithms based on ordered weighted aggregation operators, IEEE Transactions on Neural Networks 11(5) (2000), 1093-1105.
18. N.B. Karayiannis, Soft learning vector quantization and clustering algorithms based on mean-type aggregation operators, International Journal of Fuzzy Systems 4(3) (2002), 739-751.
19. N.B. Karayiannis and J.C. Bezdek, An integrated approach to fuzzy learning vector quantization and fuzzy c-means clustering, IEEE Transactions on Fuzzy Systems 5(4) (1997), 622-628.
20. N.B. Karayiannis, J.C. Bezdek, N.R. Pal, R.J. Hathaway and P.-I. Pai, Repairs to GLVQ: A new family of competitive learning schemes, IEEE Transactions on Neural Networks 7(5) (1996), 1062-1071.
21. N.B. Karayiannis and M.M. Randolph-Gips, Soft learning vector quantization and clustering algorithms based on non-Euclidean norms: Single-norm algorithms, Proceedings of Fourth International Conference on Neural Networks and Expert Systems in Medicine and Health Care, Milos Island, Greece, June 20-22, 2001, pp. 134-141.
22. N.B. Karayiannis and M.M. Randolph-Gips, Soft learning vector quantization and clustering algorithms based on non-Euclidean norms: Multi-norm algorithms, IEEE Transactions on Neural Networks 14(1) (2003), 89-102.
23. N.B. Karayiannis and N. Zervos, Entropy-constrained learning vector quantization algorithms and their application in image compression, Journal of Electronic Imaging 9(4) (2000), 495-508.
24. G.J. Klir and B. Yuan, Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice Hall, Upper Saddle River, NJ, 1995.
25. R. Krishnapuram and J. Kim, Anote on the Gustafson-Kessel and adaptive fuzzy clustering algorithms, IEEE Transactions on Fuzzy Systems 7(4) (1999), 453-461.
26. J.T. Tou and R.C. Gonzalez, Pattern Recognition Principles, Addison-Wesley, Reading, MA, 1974.
27. E.C.-K. Tsao, J.C. Bezdek and N.R. Pal, Fuzzy Kohonen clustering networks, Pattern Recognition 27(5) (1994), 757-764.