IEEE Systems, Man and Cybernetics Magazine - April 2020 - 9

SC yields a higher cluster coverage than FCM, which indicates a better suitability for finding many clusters in data.
SP is a useful method to find clusters in delay data that can
be modeled as mixtures of Poisson distributions.
Due to limited space, many areas of fuzzy clustering
research have not been considered here, such as nonpoint
prototypes, relational clustering, cluster validity, (visual)
tendency assessment, fuzzy rules generation, kernelized
clustering, clustering for big data, and many more. The diagram in Figure 1 includes many interesting instances of
ACE and SCE, but the remaining white boxes indicate that
there is still rich potential for future research, including
ACE/SCE instances with other membership function
shapes, theory (such as properties and convergence), and
further applications.

[9] R. Krishnapuram and J. M. Keller, "A possibilistic approach to clustering," IEEE

About the Author
Thomas A. Runkler (thomas.runkler@siemens.com) earned
his M.S. and Ph.D. degrees in electrical engineering from the
Technical University of Darmstadt, Germany, in 1992 and
1995, respectively, and was a postdoctoral researcher at the
University of West Florida, Pensacola, from 1996 to 1997. He
has taught computer science at the Technical University of
Munich since 1999 and was appointed adjunct professor in
2011. Since 1997, he has worked at the Research and Development Center of Siemens AG in various expert and management functions, currently as a senior principal research scientist. He is a speaker for the Fuzzy Systems and Soft Computing group of the German Association for Computer Science, a
member of the IEEE Computational Intelligence Society (CIS)
Fuzzy Systems technical committee, and a member of the
IEEE CIS Industry Liaison Committee. He is a Senior Member
of the IEEE.

Approx. Reason., vol. 32, nos. 2-3, pp. 217-236, Feb. 2003. doi: 10.1016/S0888-613X

Trans. Fuzzy Syst., vol. 1, no. 2, pp. 98-110, May 1993. doi: 10.1109/91.227387.
[10] T. A. Runkler and J. C. Bezdek, "Function approximation with polynomial membership functions and alternating cluster estimation," Fuzzy Sets Syst., vol. 101, no. 2,
pp. 207-218, 1999. doi: 10.1016/S0165-0114(98)00164-X.
[11] T. A. Runkler and J. C. Bezdek, "Regular alternating cluster estimation," in Proc.
European Congr. Intelligent Techniques and Soft Computing, Aachen, Germany, Sept.
1998, pp. 1355-1359.
[12] T. A. Runkler and J. C. Bezdek, "RACE: Relational alternating cluster estimation
and the wedding table problem," in Proc. Artificial Intelligence Fuzzy-Neuro--
Systems '98, München, W. Brauer, Ed. Mar. 1998, vol. 7, pp. 330-337.
[13] T. A. Runkler, J. Hollatz, H. Furumoto, E. Jünnemann, and K. Villforth, "Compression of industrial process data using fast alternating cluster estimation (FACE),"
in Proc. GI Jahrestagung Informatik (Workshop Data Mining), Magdeburg, Sept.
1998, pp. 71-80.
[14] T. A. Runkler and J. C. Bezdek, "Web mining with relational clustering," Int. J.
(02)00084-1.
[15] T. A. Runkler and J. C. Bezdek, "Automatic keyword extraction with relational
clustering and Levenshtein distances," in Proc. IEEE Int. Conf. Fuzzy Systems, San
Antonio, TX, May 2000, pp. 636-640. doi: 10.1109/FUZZY.2000.839067.
[16] T. A. Runkler and J. C. Bezdek, "Classification of internet newsgroup articles
using RACE," in Proc. Joint IFSA World Congr. and NAFIPS Int. Conf., Vancouver,
Canada, July 2001, pp. 1437-1442. doi: 10.1109/NAFIPS.2001.943760.
[17] T. A. Runkler and J. C. Bezdek, "Relational clustering for the analysis of internet
newsgroups," in Exploratory Data Analysis in Empirical Research (Studies in Classification, Data Analysis, and Knowledge Organization), O. Opitz and M. Schwaiger,
Eds. New York: Springer-Verlag, 2002, pp. 291-299.
[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, 1996. doi:
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and recommendations," IEEE Trans. Fuzzy Syst., vol. 4, no. 3, pp. 385-393, 1996. doi:
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IEEE Systems, Man and Cybernetics Magazine - April 2020

Table of Contents for the Digital Edition of IEEE Systems, Man and Cybernetics Magazine - April 2020
