1. A New Convergence Proof of Fuzzy c-Means.
- Author
-
Gröll, Lutz and Jäkel, Jens
- Subjects
ALGORITHMS ,FUZZY systems ,SYSTEM analysis ,STOCHASTIC convergence ,PROOF theory ,MATHEMATICAL optimization - Abstract
In this letter, we give a new, more direct derivation of the con- vergence properties of the fuzzy c-means (FCM) algorithm, using the equivalence between the original and reduced FCM criterion. From the point of view of the reduced criterion, the FCM algorithm is simply a steepest descent algorithm with variable steplength. We prove that steplength adjustment follows from the majorization principle for steplength. By applying the majorization principle we give a straightforward proof of global con- vergence. Further convergence properties follow immediately using known results of optimization theory. [ABSTRACT FROM AUTHOR]
- Published
- 2005
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