Formulation of Fuzzy c-Means Clustering Using Calculus of Variations

Authors:
Sadaaki Miyamoto
Affiliations:
Department of Risk Engineering, Faculty of Systems and Information Engineering, University of Tsukuba, Ibaraki 305-8573, Japan
Venue:
MDAI '07 Proceedings of the 4th international conference on Modeling Decisions for Artificial Intelligence
Year:
2007

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Abstract

A membership matrix of fuzzy c-mans clustering is associated with the corresponding fuzzy classification rules as membership functions defined on the whole space. In this paper such functions in fuzzy c-means and possibilistic clustering are directly derived using the calculus of variations. Consequently, the present formulation generalizes the ordinary fuzzy c-means and moreover related methods can be discussed within this framework.