Abstract
One of the main techniques embodied in many pattern recognition systems is cluster analysis — the identification of substructure in unlabeled data sets. The fuzzy c-means algorithms (FCM) have often been used to solve certain types of clustering problems. During the last two years several new local results concerning both numerical and stochastic convergence of FCM have been found. Numerical results describe how the algorithms behave when evaluated as optimization algorithms for finding minima of the corresponding family of fuzzy c-means functionals. Stochastic properties refer to the accuracy of minima of FCM functionals as approximations to parameters of statistical populations which are sometimes assumed to be associated with the data. The purpose of this paper is to collect the main global and local, numerical and stochastic, convergence results for FCM in a brief and unified way.
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Hathaway, R.J., Bezdek, J.C. Recent convergence results for the fuzzy c-means clustering algorithms. Journal of Classification 5, 237–247 (1988). https://doi.org/10.1007/BF01897166
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DOI: https://doi.org/10.1007/BF01897166