Abstract
A regularization method using an entropy function is studied and contrasted with the ordinary fuzzy c-means. The way in which two algorithms lead to similar formulas is discussed. Classification functions derived from the two methods, which are naturally obtained when the algorithm of clustering is convergent, are compared. Theoretical properties of the two classification functions are studied.
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References
Bezdek, J.C. (1981). Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum.
Dunn, J.C. (1974). A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters, J. of Cybernetics, 3, 32–57.
Li, R.-P. and Mukaidono, M. (1995). A maximum entropy approach to fuzzy clustering, Proc. of the 4th IEEE Intern. Conf on Fuzzy Systems (FUZZ- IEEE/IFES’95), Yokohama, Japan, March 20-24, 1995, 2227–2232.
Keller, J.M., Gray, M.R., and Givens, J.A. (1985). A fuzzy k - nearest neighbor algorithm, IEEE Trans., on Syst., Man, and Cybern., 15, 580–585.
Masulli, F., Artuso, M., Bogus, P., and Schenone, A. (1997). Fuzzy clustering methods for the segmentation of multivariate medical images, Proc. of the 7th International Fuzzy Systems Association World Congress (IFSA;91% June 25-30, 1997, Prague, Chech, 123–128.
Preparata, F.P. and Shamos, M.I. (1985). Computational Geometry: An Introduction, Springer, New York.
Rose, K., Gurewitz, E., and Fox, G. (1990). A deterministic annealing ap-proach to clustering, Pattern Recognition Letters, 11, 589–594.
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© 1998 Springer-Verlag Berlin · Heidelberg
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Miyamoto, S., Umayahara, K. (1998). Two Methods of Fuzzy c-Means and Classification Functions. In: Rizzi, A., Vichi, M., Bock, HH. (eds) Advances in Data Science and Classification. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-72253-0_14
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DOI: https://doi.org/10.1007/978-3-642-72253-0_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-64641-9
Online ISBN: 978-3-642-72253-0
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