On the mathematical and numerical properties of the fuzzy c-means algorithm

Shokri Z. Selim; M. S. Kamel

doi:10.1016/0165-0114(92)90323-V

On the mathematical and numerical properties of the fuzzy c-means algorithm

Shokri Z. Selim, M. S. Kamel^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

The 'fuzzy clustering' problem is investigated. Interesting properties of the points generated in the course of applying the fuzzy c-means algorithm are revealed using the concept of reduced objective function. We investigate seven quantities that could be used for stopping the algorithm and prove relationships among them. Finally, we empirically show that these quantities converge linearly.

Original language	English
Pages (from-to)	181-191
Number of pages	11
Journal	Fuzzy Sets and Systems
Volume	49
Issue number	2
DOIs	https://doi.org/10.1016/0165-0114(92)90323-V
State	Published - 27 Jul 1992
Externally published	Yes

Bibliographical note

Funding Information:
This work was partially supported by the Natural Science and Engineering Research Council of Canada through a research grant to the second author.

Keywords

Fuzzy c-means algorithm
convergence of fuzzy c-means algorithm
fuzzy clustering
stopping criteria for fuzzy c-means

ASJC Scopus subject areas

Logic
Artificial Intelligence

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10.1016/0165-0114(92)90323-V

Cite this

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abstract = "The 'fuzzy clustering' problem is investigated. Interesting properties of the points generated in the course of applying the fuzzy c-means algorithm are revealed using the concept of reduced objective function. We investigate seven quantities that could be used for stopping the algorithm and prove relationships among them. Finally, we empirically show that these quantities converge linearly.",

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AU - Kamel, M. S.

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PY - 1992/7/27

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AB - The 'fuzzy clustering' problem is investigated. Interesting properties of the points generated in the course of applying the fuzzy c-means algorithm are revealed using the concept of reduced objective function. We investigate seven quantities that could be used for stopping the algorithm and prove relationships among them. Finally, we empirically show that these quantities converge linearly.

KW - Fuzzy c-means algorithm

KW - convergence of fuzzy c-means algorithm

KW - fuzzy clustering

KW - stopping criteria for fuzzy c-means

UR - https://www.scopus.com/pages/publications/38249008056

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ER -

On the mathematical and numerical properties of the fuzzy c-means algorithm

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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