Analytically tractable case of fuzzy c-means clustering

Pattern Recognition

Volumn 39, Issue 1, 2006, Pages 35-46

  Pianykh, Oleg S ^a,b,c  

^a LOUISIANA STATE UNIVERSITY SCHOOL OF MEDICINE   (United States)

^b LOUISIANA STATE UNIVERSITY HEALTH SCIENCES CENTER   (United States)

^c Central Cardio Institute   (Russian Federation)

Author keywords

Clustering; Fuzzy c means; Hankel matrix; Optimization

Indexed keywords

CLUSTERING; FUZZY C-MEANS; HANKEL MATRIX; OPTIMAL CLUSTERING;

ALGORITHMS; CLOSED LOOP CONTROL SYSTEMS; FUNCTIONS; OPTIMAL CONTROL SYSTEMS; PATTERN RECOGNITION; PROBLEM SOLVING;

FUZZY SETS;

EID: 27344448931     PISSN: 00313203     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.patcog.2005.06.005     Document Type: Article

References (21)

1. J.C. Dunn A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters J. Cybern. 3 1973 32 57
2. J.C. Bezdek Pattern Recognition with Fuzzy Objective Function Algorithms 1981 Plenum Press New York
3. B.C. Everitt Cluster Analysis 3rd ed. 1993 Halsted Press
4. H. Hellendoorn, and D. Driankov Fuzzy Model Identification 1997 Springer Heidelberg
5. U. Mailik, and S. Bandyopadhyay Performance evaluation of some clustering algorithms and validity indices IEEE Trans. Pattern Anal. Mach. Intell. 24 12 2002 1650 1654
6. R.J. Hathaway, and J.C. Bezdek Local convergence of the fuzzy c-means algorithms IEEE Trans. Pattern Anal. Mach. Intell. 19 6 1986 477 480
7. J.A. Hartigan Clustering Algorithms 1975 Wiley New York
8. L. Kaufman, and P.J. Rousseeuw Finding groups in Data: An Introduction to Cluster Analysis 1990 Wiley New York
9. B. Mirkin Mathematical Classification and Clustering 1996 Kluwer Dordrecht, The Netherlands
10. A. Baraldi, and P. Blonda A survey of fuzzy clustering algorithms for pattern recognition IEEE Trans. Syst. Man Cybern. 29 1999 778 801
11. E. Gockay, and J.C. Principe Information theoretic clustering IEEE Trans. Pattern Anal. Mach. Intell. 24 12 2002 158 170
12. S. Eschrich, J. Ke, L.O. Hall, and D.B. Goldrof Fast accurate fuzzy clustering through data reduction IEEE Trans. Fuzzy Syst. 11 2003 262 270
13. V. Castelli, A. Thomasian, and C-S. Li CSVD: clustering and singular value decomposition for approximate similarity search in high-dimensional spaces IEE Trans. Knowl. Data Eng. 18 2003 671 685
14. C.C. Aggarwal, and P.S. Yu Redefining clustering for high-dimensional applications IEE Trans. Knowl. Data Eng. 14 2002 210 224
15. P.E. Gill, W. Murray, and M.H. Wright Numer. Linear Algebra Optim. 1 1991 356
16. E. Tyrtyshnikov How Bad are Hankel Matrices? Numer. Math. 67 1994 261 269
17. F. Chatelin, Eigenvalues of Matrices, Wiley, 1993, pp. 56, 332.
18. H.G. Golub, P. Milanfar, and J. Varah A stable numerical method for inverting shape from moments SIAM J. Sci. Comput. 21 4 1999 1222 1243
19. L.H. Bezerra, and F.S.V. Bazan Eigenvalue localization of generalized companion predictor matrices SIAM J. Matrix Anal. Appl. 19 4 1998 886 897
20. F.S.V. Bazan Conditioning of rectangular Vandermonde matrices with nodes in the unit disk SIAM J. Matrix Anal. Appl. 21 2 1999 679 693
21. E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, D. Sorensen, LAPACK User's Guide (http://www.netlib.org/lapack/lug/lapack_lug.html ), third ed., SIAM, Philadelphia, 1999.