A note on the Gustafson-Kessel and adaptive fuzzy clustering algorithms

In this letter, we show that the Gustafson-Kessel (G-K) algorithm (1979) and the original adaptive fuzzy clustering (AFC) algorithm can be thought of as special cases of a more general algorithm. Our analysis shows that the G-K algorithm is better suited for ellipsoidal clusters of equal volume, whereas the original AFC algorithm is better suited for linear clusters. We also discuss a new variation of these algorithms, which can be used to improve the results of the G-K and AFC algorithms in some cases.

[1]  James C. Bezdek,et al.  Pattern Recognition with Fuzzy Objective Function Algorithms , 1981, Advanced Applications in Pattern Recognition.

[2]  J. Wolfe.  PATTERN CLUSTERING BY MULTIVARIATE MIXTURE ANALYSIS. , 1970, Multivariate behavioral research.

[3]  Donald Gustafson,et al.  Fuzzy clustering with a fuzzy covariance matrix , 1978, 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes.

[4]  R.N. Dave,et al.  On generating solid models of mechanical parts through fuzzy clustering , 1997, Proceedings of 6th International Fuzzy Systems Conference.

[5]  R. Krishnapuram,et al.  Fuzzy and robust formulations of maximum-likelihood-based Gaussian mixture decomposition , 1996, Proceedings of IEEE 5th International Fuzzy Systems.

[6]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[7]  Isak Gath,et al.  Unsupervised Optimal Fuzzy Clustering , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[8]  Rajesh N. Dave,et al.  Use Of The Adaptive Fuzzy Clustering Algorithm To Detect Lines In Digital Images , 1990, Other Conferences.

[9]  Yoshiteru Nakamori,et al.  Adaptive fuzzy clustering and fuzzy prediction models , 1995, Proceedings of 1995 IEEE International Conference on Fuzzy Systems..

[10]  Donald B. Rubin,et al.  Max-imum Likelihood from Incomplete Data , 1972 .

[11]  George S. Sebestyen,et al.  Decision-making processes in pattern recognition , 1962 .

[12]  R.J. Hathaway,et al.  Switching regression models and fuzzy clustering , 1993, IEEE Trans. Fuzzy Syst..

[13]  Richard O. Duda,et al.  Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.