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A New Convergence Proof of Fuzzy c-Means.
- Source :
- IEEE Transactions on Fuzzy Systems; Oct2005, Vol. 13 Issue 5, p717-720, 4p
- Publication Year :
- 2005
-
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]
Details
- Language :
- English
- ISSN :
- 10636706
- Volume :
- 13
- Issue :
- 5
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Fuzzy Systems
- Publication Type :
- Academic Journal
- Accession number :
- 18699884
- Full Text :
- https://doi.org/10.1109/TFUZZ.2005.856560