Formulation of Fuzzy <i>c</i>-Means Clustering Using Calculus of Variations and Twofold Membership Clusters

Sadaaki Miyamoto

doi:10.20965/jaciii.2008.p0454

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JACIII Vol.12 No.5 pp. 454-460

doi: 10.20965/jaciii.2008.p0454

(2008)

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Formulation of Fuzzy c-Means Clustering Using Calculus of Variations and Twofold Membership Clusters

Sadaaki Miyamoto^*

^*Department of Risk Engineering, School of Systems and Information Engineering, University of Tsukuba
Ibaraki 305-8573, Japan

Received:

October 10, 2007

Accepted:

February 15, 2008

Published:

September 20, 2008

Keywords:

fuzzy c-means clustering, calculus of variations, twofold memberships

Abstract

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.

Cite this article as:

S. Miyamoto, “Formulation of Fuzzy c-Means Clustering Using Calculus of Variations and Twofold Membership Clusters,” J. Adv. Comput. Intell. Intell. Inform., Vol.12 No.5, pp. 454-460, 2008.

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This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

Formulation of Fuzzy c-Means Clustering Using Calculus of Variations and Twofold Membership Clusters

Sadaaki Miyamoto*

Sadaaki Miyamoto^*