Abstract
Four methods of c-regression are compared. Two of them are methods of fuzzy clustering: (a) the fuzzy c-regression methods, and (b) an entropy method proposed by the authors. Two others are probabilistic methods of (c) the deterministic annealing, and (d) the mixture distribution method using the EM algorithm. It is shown that the entropy method yields the same formula as that of the deterministic annealing. Clustering results as well as classification functions are compared. The classification functions for fuzzy clustering are fuzzy rules interpolating cluster memberships, while those for the latter two are probabilistic rules. Theoretical properties of the classification functions are studied. A numerical example is shown.
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References
Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum, New York (1981)
Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via the EM algorithm. J. of the Royal Statistical Society, B. 39, 1–38 (1977)
Dunn, J.C.: A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters. J. of Cybernetics 3, 32–57 (1974)
Hathaway, R.J., Bezdek, J.C.: Switching regression models and fuzzy clustering. IEEE Trans. on Fuzzy Syst. 1, 195–204 (1993)
Li, R.-P., Mukaidono, M.: A maximum entropy approach to fuzzy clustering. In: Proc. of the 4th IEEE Intern. Conf. on Fuzzy Systems, Yokohama, Japan, March 20-24, pp. 2227–2232 (1995)
Masulli, F., Artuso, M., Bogus, P., Schenone, A.: Fuzzy clustering methods for the segmentation of multivariate medical images. In: Proc. of the 7th International Fuzzy Systems Association World Congress, Prague, Chech, June 25-30, pp. 123–128 (1997)
Miyamoto, S., Mukaidono, M.: Fuzzy c - means as a regularization and maximum entropy approach. In: Proc. of the 7th International Fuzzy Systems Association World Congress, Prague, Chech, June 25-30, vol. II, pp. 86–92 (1997)
Miyamoto, S., Umayahara, K.: Fuzzy clustering by quadratic regularization. In: Proc. of FUZZ-IEEE 1998, Anchorage, Alaska, May 4-9, pp. 791–795 (1998)
Miyamoto, S., Umayahara, K.: Two methods of fuzzy c-means and classiication functions. In: Proc. of 6th Conf. of the International Federation of Classiication Societies, Roma, Italy, July 21-24, pp. 105–110 (1998)
Redner, R.A., Walker, H.F.: Mixture densities, maximum likelihood and the EM algorithm. SIAM Review 26(2), 195–239 (1984)
Rose, K., Gurewitz, E., Fox, G.: A deterministic annealing approach to clustering. Pattern Recognition Letters 11, 589–594 (1990)
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© 1999 Springer-Verlag Berlin Heidelberg
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Miyamoto, S., Umayahara, K., Nemoto, T. (1999). Four c-Regression Methods and Classification Functions. In: Zhong, N., Skowron, A., Ohsuga, S. (eds) New Directions in Rough Sets, Data Mining, and Granular-Soft Computing. RSFDGrC 1999. Lecture Notes in Computer Science(), vol 1711. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-48061-7_25
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DOI: https://doi.org/10.1007/978-3-540-48061-7_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66645-5
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