Abstract
Figure 2.1 portrays cluster analysis. This field comprises three problems: tendency assessment, clustering and validation. Given an unlabeled data set, ① is there substructure in the data? This is clustering tendency — should you look for clusters at all? Very few methods — fuzzy or otherwise — address this problem. Panayirci and Dubes (1983), Smith and Jain (1984), Jain and Dubes (1988), Tukey (1977) and Everitt (1978) discuss statistical and informal graphical methods (visual displays) for deciding what — if any — substructure is in unlabeled data.
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Bell, E. T. (1966). Men of mathematics, 5th printing, Simon and Schuster, NY.
Duda, R. and Hart, P. (1973). Pattern Classification and Scene Analysis, Wiley Interscience, NY.
Thorndike, R. L. (1953). Who belongs in the family?, Psychometrika, 18, 267–276.
Gersho, A. and Gray, R. (1992). Vector Quantization and Signal Compression, Kluwer, Boston.
Geva, A. B. and Pratt, H. (1994). Unsupervised clustering of evoked potentials by waveform, Med. and Bio. Engineering and Computing, 543–550.
Dunn, J. C. (1974a). A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters, J. Cyberns., 3 (3), 32–57.
Bezdek, J. C. (1973). Fuzzy mathematics in pattern classification, Ph. D. Thesis, Cornell U., Ithaca, NY.
Bezdek, J. C. (1974a). Numerical taxonomy with fuzzy sets, J. Math. Bio., 1 (1), 57–71.
Krishnapuram, R. and Keller, J. M. (1993). A possibilistic approach to clustering, IEEE Trans. Fuzzy Syst., 1 (2), 98–110.
Yang, M. S. (1993). A survey of fuzzy clustering, Math. Comput. Modeling, 18 (11), 1–16.
Duda, R. and Hart, P. (1973). Pattern Classification and Scene Analysis, Wiley Interscience, NY.
Dunn, J. C. (1974a). A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters, J. Cyberns., 3 (3), 32–57.
Clark, M., Hall, L. O., Goldgof, D, Velthuizen, R., Murtaugh, F.R. and Silbiger, M. (1998). Automatic tumor segmentation using knowledge-based techniques, IEEE Trans. Med. Imaging, 17 (2), 187–201.
Sato, M., Sato, Y. and Jain, L.C. (1997). Fuzzy Clustering Models and Applications, Physica-Verlag, Heidelberg, Germany.
Bezdek, J. C. (1997). Computational intelligence and edge detection, Proc. AI 5: Fuzzy Neuro Syst. ‘87: Computational Intelligence, eds. A. Grauel, W. Becker and F. Belli, Infix Press, Zoest, Germany, 1–31.
Bezdek, J. C. (1998). Computational intelligence defined–by everyone!, Computational Intelligence: Soft Computing and Fuzzy-Neuro Integration with Applications, eds. O. Kaynak, L.A. Zadeh, B. Turksen and I. J. Rudas, Physica-Verlag, Heidelberg, Germany, 10–37.
Redner, R., Hathaway, R. J. and Bezdek, J. C. (1987). Estimating the parameters of mixture models with modal estimators, Comm. in Stat. (A), 16 (9), 2639–2660.
Bezdek, J. C., Hathaway, R. J. and Windham, M. (1991). Numerical comparison of the RFCM and AP algorithms for clustering relational data, Patt. Recog., 24 (8), 783–791.
Simpson, P. (1992). Fuzzy min-max neural networks I: classification, IEEE Trans. Neural Networks, 3 (5), 776–786.
Yager, R. R. and and Filev, D.P. (1994a). Approximate clustering by the mountain method, IEEE Trans. Syst., Man and Cyberns., 24 (8), 1279–1283.
Chiu, S. L. (1994). Fuzzy model identification based on cluster estimation, J. Intell. and Fuzzy Syst., 2, 267–278.
Backer, E. and Jain, A.K. (1981). A clustering performance measure based on fuzzy set decomposition, IEEE Trans. Patt. Anal. and Machine Intell., 3, 66–75.
Duda, R. and Hart, P. (1973). Pattern Classification and Scene Analysis, Wiley Interscience, NY.
Hall, D. (1992). Mathematical Techniques in Multisensor Data Fusion, Artech House, Norwood, MA.
Tou, J. T. (1979). DYNOC–A dynamic optimum cluster-seeking technique, Int. J. Comp. Syst. Science, 8, 541–547.
Vaidyanathan, M., Clarke, L.P., Velthuizen, R. P., Phuphanich, S., Bensaid, A. M., Hall, L. O., Bezdek, J. C., Greenberg, H., Trotti, A. and Silbiger, M. (1995). Comparison of supervised MRI segmentation methods for tumor volume determination during therapy, Mag. Res. Imaging, 13 (5), 719–728.
Velthuizen, R. P., Hall, L. O. and Clarke, L. P. (1996). Feature extraction with genetic algorithms for fuzzy clustering, Biomed. Engineering Appl., Basis and Communications, 8 (6), 496–517.
Velthuizen, R. P., Hall, L. O., Clarke, L. P. and Silbiger, M. L. (1997). An investigation of mountain method clustering for large data sets, Patt. Recog., 30 (7), 1121–1135.
Wang L., Wang M., Yamada M., Seki H., and Itoh H. (1996). Fuzzy reasoning for image compression using adaptive triangular plane patches, Proc, Int. Conf. on Soft Computing, 2, eds. T. Yamakawa G. Matsumoto, World Scientific, Singapore, 753–756
Wang, D., Keller, J., Carson, C.A., McAdoo, K., and Bailey, Ce (1998). Use of fuzzy logic-inspired features to improve bacterial recognition through classifier fusion, IEEE Trans. Syst., Man and Cyberns., 28 (4), 583–591.
Runkler, T. A. (1995). Improved cluster validity measures for the fuzzy c-elliptotypes algorithms, Proc. European Congress on Intelligent Techniques and Soft Computing, Aachen, Germany, 1331–1335.
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Bezdek, J.C., Keller, J., Krisnapuram, R., Pal, N.R. (1999). Cluster Analysis for Object Data. In: Fuzzy Models and Algorithms for Pattern Recognition and Image Processing. The Handbooks of Fuzzy Sets Series, vol 4. Springer, Boston, MA. https://doi.org/10.1007/0-387-24579-0_2
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