Unsupervised Optimal Fuzzy Clustering
July 1989 (vol. 11 no. 7)
pp. 773-780
DOI Bookmark:
http://doi.ieeecomputersociety.org/10.1109/34.192473
This study reports on a method for carrying out fuzzy classification without a priori assumptions on the number of clusters in the data set. Assessment of cluster validity is based on performance measures using hypervolume and density criteria. An algorithm is derived from a combination of the fuzzy K-means algorithm and fuzzy maximum-likelihood estimation. The unsupervised fuzzy partition-optimal number of classes algorithm performs well in situations of large variability of cluster shapes, densities, and number of data points in each cluster. The algorithm was tested on different classes of simulated data, and on a real data set derived from sleep EEG signal. [1] L. Larsen, E. Ruspini, J. McDew, D. Walter, and W. Adey, "A test of sleep staging system in the unrestrained chimpanzee,"Brain Res., vol. 40, pp. 319-343, 1972.[2] J. C. Bezdek, "Feature selection for binary data: Medical diagnosis with fuzzy sets," inProc. 25th Nat. Computer Conf., 1976, pp. 1057- 1068.[3] J. C. Bezdek and W. A. Fordon, "Analysis of hypertensive patients by the use of fuzzy ISODATA algorithm," inProc. JACC, vol. 3, 1978, pp. 349-356.[4] I. Gath and E. Bar-On, "Computerized method for scoring of polygraphic sleep recordings,"Comput. Progr. Biomed., vol. 11, pp. 217-223, 1980.[5] J. C. Bezdek, "Fuzzy mathematics in pattern classification," Ph.D. dissertation, Cornell Univ., Ithaca, NY, 1973.[6] J. C. Bezdek, "A convergence theorem for the fuzzy ISODATA clustering algorithms,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI- 2, no. 1, pp. 1-8, 1980.[7] J. C. Bezdek and J. C. Dunn, "Optimal fuzzy partition: A heuristic for estimating the parameters in a mixture of normal distributions,"IEEE Trans. Comput., vol. C-24, pp. 835-838, 1975.[8] J. C. Bezdek, C. Coray, R. Gunderson, and J. Watson, "Detection and characterization of cluster substructure. I. Linear structure: Fuzzy c-lines,"SIAM J. Appl. Math., vol. 40, pp. 339-357, 1981.[9] J. J. C. Bezdek, C. Coray, R. Gunderson, and J. Watson, "Detection and characterization of cluster substructure. II. Fuzzy c-varieties and convex combinations thereof,"SIAM J. Appl. Math., vol. 40, pp. 358-372, 1981.[10] E. E. Gustafson and W. C. Kessel, "Fuzzy clustering with a fuzzy covariance matrix," inProc. IEEE CDC, San Diego, CA, 1979, pp. 761-766.[11] J. C. Bezdek,Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum, New York, 1981.[12] A. S. Gevins, "Pattern recognition of human brain electrical potentials,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-2, no. 5, pp. 383-404, 1980.[13] B. H. Jansen and W. K. Cheng, "Classification of sleep patterns by means of markov modeling and correspondence analysis,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-9, no. 5, pp. 707- 710, 1987.[14] I. Gath and E. Bar-On, "Classical sleep stages and the spectral content of the EEG signal,"Int. J. Neurosci., vol. 22, pp. 147-155, 1983.[15] N. E. Day, "Estimating the components of a mixture of normal distributions,"Biometrika, vol. 56, pp. 463-474, 1969.[16] E. Backer and A. K. Jain, "A clustering performance measure based on fuzzy set decomposition,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-3, no. 1, pp. 66-74, 1981.[17] E. Anderson, "The irises of the Gaspe peninsula,"Bull. Amer. Iris Soc., vol. 59, pp. 2-5, 1935,[18] R. A. Fisher, "The use of multiple measurements in taxonomic problems,"Ann. Eugenics, vol. 7, pp. 179-188, 1936.[19] K. Leszczynski, P. Penczek, and W. Grochulski, "Sugeno's fuzzy measure and fuzzy clustering,"Fuzzy Sets Syst., vol. 15, pp. 147- 158, 1985.[20] R. L. Cannon, J. V. Dave, and J. C. Bezdek, "Efficient implementation of the fuzzy c-means clustering algorithms,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, no. 2, pp. 248-255, 1986.[21] M. P. Windham, "Cluster validity for the fuzzy c-means clustering algorithm,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI- 4, no. 4, pp. 357-363, 1982.[22] I. Gath and E. Bar-On, "Sequential fuzzy clustering of sleep EEG recordings," inMethods of Sleep Research, S. Kubicki and W. Herrmann, Eds. Jena, Germany: Gustav Fischer, 1985, pp. 55-64.[23] J. C. Bezdek, "Numerical taxonomy with fuzzy sets,"J. Math. Biol., vol. 1-1, pp. 57-71, 1974.[24] M. P. Windham, "Cluster validity for fuzzy clustering algorithms,"Fuzzy Sets Syst., vol. 3, pp. 1-9, 1980.[25] T. Gou and B. Dubuisson, "A loose-pattern process approach to clustering fuzzy data sets,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-7, no. 3, pp. 366-372, 1985.[26] C. T. Zahn, "Graph-theoretical methods for detecting and describing gestalt clusters,"IEEE Trans. Comput., vol. C-20, no. 1, pp. 68- 86, 1971.[27] R. Dubes and A. K. Jain, "Validity studies in clustering methodologies,"Pattern Recognition, vol. 11, pp. 235-254, 1979.[28] P. H. A. Sneath and R. Sokal,Numerical Taxonomy. San Francisco, CA: Freeman, 1973.[29] D. L. Davis and D. W. Bouldin, "A cluster separation measure,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-1, no. 2, pp. 224-227, 1979.[30] A. K. Jain and J. V. Moreau, "Bootstrap technique in cluster analysis,"Patt. Recog., vol. 20, no. 5, pp. 547-568, 1987.
Index Terms:
pattern recognition; fuzzy set theory; unsupervised optimal fuzzy clustering; fuzzy classification; cluster validity; fuzzy K-means algorithm; fuzzy maximum-likelihood estimation; unsupervised fuzzy partition-optimal number of classes algorithm; sleep EEG signal; electroencephalography; fuzzy set theory; pattern recognition
Citation:
I. Gath, A.B. Geva, "Unsupervised Optimal Fuzzy Clustering," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 11, no. 7, pp. 773-780, July 1989, doi:10.1109/34.192473
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