Formulation of Fuzzy c-Means Clustering Using Calculus of Variations and Twofold Membership Clusters
*Department of Risk Engineering, School of Systems and Information Engineering, University of Tsukuba
Ibaraki 305-8573, Japan
A membership matrix of fuzzy c-means clustering is associated with corresponding fuzzy classification rules as membership functions defined on the whole data space. We directly derive such functions in fuzzy c-means and possibilistic clustering using the calculus of variations, generalizing ordinary fuzzy c-means and deriving new twofold membership clustering using this framework.
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