Applying the possibilistic c-means algorithm in kernel-induced spaces

IEEE Transactions on Fuzzy Systems

Volumn 18, Issue 3, 2010, Pages 572-584

  Filippone, Maurizio ^a   Masulli, Francesco ^b   Rovetta, Stefano ^b  

^a UNIVERSITY OF GLASGOW   (United Kingdom)

^b UNIVERSITY OF GENOA   (Italy)

Author keywords

Kernel methods; Outlier detection; Possibilistic clustering; Regularization

Indexed keywords

GENERIC SHAPES; HIGH DIMENSIONAL SPACES; HIGH STABILITY; INDUCED SPACES; INPUT PATTERNS; INPUT SPACE; KERNEL DENSITY ESTIMATION; KERNEL METHODS; ONE-CLASS SUPPORT VECTOR MACHINE; OUTLIER DETECTION; POSSIBILISTIC; POSSIBILISTIC C-MEANS; POSSIBILISTIC CLUSTERING; POSSIBILISTIC CLUSTERING ALGORITHMS; REAL DATA SETS;

CLUSTER ANALYSIS; LEARNING ALGORITHMS;

CLUSTERING ALGORITHMS;

EID: 77953110999     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2010.2043440     Document Type: Article

References (26)

1. R. O. Duda and P. E. Hart, Pattern Classification and Scene Analysis. New York: Wiley, 1973.
2. J. C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms. Norwell, MA: Kluwer, 1981.
3. R. Krishnapuram and J. M. Keller. (1993, May). A possibilistic approach to clustering. IEEE Trans. Fuzzy Syst. [Online]. vol.1, no.2, pp. 98-110. Available: http://ieeexplore.ieee.org/xpls/abs-all.jsp?arnumber=227387
4. M. Filippone, F. Camastra, F. Masulli, and S. Rovetta, "A survey of kernel and spectral methods for clustering," Pattern Recognit., vol.41, no.1, pp. 176-190, Jan. 2008.
5. M. Filippone, F. Masulli, and S. Rovetta, "Possibilistic clustering in feature space," in WILF, (Lecture Notes in Computer Science). New York: Springer-Verlag, 2007.
6. R. Krishnapuram and J. M. Keller. (1996, Aug.). The possibilistic c-means algorithm: Insights and recommendations. IEEE Trans. Fuzzy Syst. [Online]. vol.4, no.3, pp. 385-393. Available: http://ieeexplore.ieee.org/xpls/abs-all. jsp?arnumber=531779
7. D.Q.Zhang and S.C.Chen, "Kernel-based fuzzy and possibilistic c-means clustering," in Proc. Int. Conf. Artif. Neural Netw., Istanbul, Turkey, 2003, pp. 122-125.
8. B. Schölkopf, J. C. Platt, J. S. Taylor, A. J. Smola, and R. C. Williamson, "Estimating the support of a high-dimensional distribution," Neural Comput., vol.13, no.7, pp. 1443-1471, 2001.
9. D. M. J. Tax and R. P. W. Duin, "Support vector domain description," Pattern Recognit. Lett., vol.20, no.11-13, pp. 1191-1199, 1999.
10. T. Lange, V. Roth, M. L. Braun, and J.M. Buhmann, "Stability-based validation of clustering solutions," Neural Comput., vol.16, no.6, pp. 1299- 1323, 2004.
11. M. Filippone. (2009, Feb.). Dealing with non-metric dissimilarities in fuzzy central clustering algorithms. Int. J. Approx. Reason. [Online]. vol.50, no.2, pp. 363-384, Available: http://dx.doi.org/10.1016/j.ijar.2008.08.006
12. F. Höppner and F. Klawonn. (2003, Oct.). A contribution to convergence theory of fuzzy c-means and derivatives. IEEE Trans. Fuzzy Syst. [Online]. vol.11, no.5, pp. 682-694, Available: http://ieeexplore.ieee.org/xpls/ abs-all.jsp?arnumber=1235994
13. N. Aronszajn, "Theory of reproducing kernels," Trans. Amer. Math. Soc., vol.68, no.3, pp. 337-404, 1950.
14. M. Aizerman, E. Braverman, and L. Rozonoer, "Theoretical foundations of the potential function method in pattern recognition learning," Autom. Remote Control, vol.25, pp. 821-837, 1964.
15. B. Schölkopf and A. J. Smola, Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond. Cambridge,MA: MIT Press, 2001.
16. D. Q. Zhang and S. C. Chen. (2002)., "Fuzzy clustering using kernel method," in Proc. 2002 Int. Conf. Control Autom. (ICCA). [Online]. pp. 162-163, Available: http://ieeexplore.ieee.org/xpls/abs-all.jsp?arnumber=1229535
17. B. Schölkopf, S.Mika,C. J.C.Burges, P. Knirsch, K. R.Müller,G.Rätsch, and A. J. Smola, "Input space versus feature space in kernel-based methods," IEEE Trans. Neural Netw., vol.10, no.5, pp. 1000-1017, Sep. 1999.
18. M. Barni, V. Cappellini, and A. Mecocci, "Comments on a possibilistic approach to clustering," IEEE Trans. Fuzzy Syst., vol.4, no.3, pp. 393- 396, Aug. 1996.
19. C.-C. Chang and C.-J. Lin. (2001). LIBSVM: A library for support vector machines (software). [Online]. Available: www.csie.ntu.edu.tw/?cjlin/
20. B.W. Silverman. (1986, Apr.). Density Estimation for Statistics and Data Analysis. London, U.K./Boca Raton, FL: Chapman&Hall/CRC. [Online]. Available: http://www.worldcat.org/isbn/0412246201
21. A. B. Hur, D. Horn, H. T. Siegelmann, and V. Vapnik, "Support vector clustering," J. Mach. Learning Res., vol.2, pp. 125-137, 2001.
22. P. Hall, G. S. Watson, and J. Cabrera, "Kernel density estimation with spherical data," Biometrika, vol.74, no.4, pp. 751-762, 1987.
23. A. Asuncion and D. J. Newman. (2007). "UCI machine learning repository," [Online]. Available: http://www.ics.uci.edu/ $sim$mlearn/MLRepository.html
24. W. H. Wolberg and O. L. Mangasarian, "Multisurface method of pattern separation for medical diagnosis applied to breast cytology," Proc. Nat. Acad. Sci., U.S.A., vol.87, pp. 9193-9196, 1990.
25. V. G. Sigillito, S. P.Wing, L. V. Hutton, and K. B. Baker, "Classification of radar returns from the ionosphere using neural networks," Johns Hopkins APL Tech. Dig., vol.10, pp. 262-266, 1989.
26. R. A. Fisher, "The use of multiple measurements in taxonomic problems," Ann. Eugenics, vol.7, pp. 179-188, 1936.