A relaxation approach to the fuzzy clustering problem

Mohamed S. Kamel; Shokri Z. Selim

doi:10.1016/0165-0114(94)90232-1

A relaxation approach to the fuzzy clustering problem

Mohamed S. Kamel^*, Shokri Z. Selim

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

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

39 Scopus citations

Abstract

In this paper a new algorithm for fuzzy clustering is presented. The proposed algorithm utilizes the idea of relaxation. Convergence of the proposed algorithm is proved and limits on the relaxation parameter are derived. Stopping criteria and resulting convergence behaviour of the algorithms are discussed. The performance of the new algorithm is compared to the fuzzy c-means algorithm by testing both on three published data sets. Theoretical and empirical results reported in this paper show that the new algorithm is more efficient and leads to significant computational savings.

Original language	English
Pages (from-to)	177-188
Number of pages	12
Journal	Fuzzy Sets and Systems
Volume	61
Issue number	2
DOIs	https://doi.org/10.1016/0165-0114(94)90232-1
State	Published - 24 Jan 1994

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 first author. The second author acknowledges the support of King Fahd University of Petroleum and Minerals. The Relaxation Algorithm was coded by Mr. Heru T. Natalisa and the computational results of Section 6 were obtained by him. Earlier discussion on the use of relaxation with Dr. M. A. Ismail is acknowledged.

Keywords

Fuzzy c-means algorithm
cluster analysis
fuzzy clustering
pattern recognition
relaxation techniques

ASJC Scopus subject areas

Logic
Artificial Intelligence

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10.1016/0165-0114(94)90232-1

Cite this

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title = "A relaxation approach to the fuzzy clustering problem",

abstract = "In this paper a new algorithm for fuzzy clustering is presented. The proposed algorithm utilizes the idea of relaxation. Convergence of the proposed algorithm is proved and limits on the relaxation parameter are derived. Stopping criteria and resulting convergence behaviour of the algorithms are discussed. The performance of the new algorithm is compared to the fuzzy c-means algorithm by testing both on three published data sets. Theoretical and empirical results reported in this paper show that the new algorithm is more efficient and leads to significant computational savings.",

keywords = "Fuzzy c-means algorithm, cluster analysis, fuzzy clustering, pattern recognition, relaxation techniques",

author = "Kamel, \{Mohamed S.\} and Selim, \{Shokri Z.\}",

note = "Funding Information: This work was partially supported by the Natural Science and Engineering Research Council of Canada through a research grant to the first author. The second author acknowledges the support of King Fahd University of Petroleum and Minerals. The Relaxation Algorithm was coded by Mr. Heru T. Natalisa and the computational results of Section 6 were obtained by him. Earlier discussion on the use of relaxation with Dr. M. A. Ismail is acknowledged.",

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AU - Selim, Shokri Z.

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PY - 1994/1/24

Y1 - 1994/1/24

N2 - In this paper a new algorithm for fuzzy clustering is presented. The proposed algorithm utilizes the idea of relaxation. Convergence of the proposed algorithm is proved and limits on the relaxation parameter are derived. Stopping criteria and resulting convergence behaviour of the algorithms are discussed. The performance of the new algorithm is compared to the fuzzy c-means algorithm by testing both on three published data sets. Theoretical and empirical results reported in this paper show that the new algorithm is more efficient and leads to significant computational savings.

AB - In this paper a new algorithm for fuzzy clustering is presented. The proposed algorithm utilizes the idea of relaxation. Convergence of the proposed algorithm is proved and limits on the relaxation parameter are derived. Stopping criteria and resulting convergence behaviour of the algorithms are discussed. The performance of the new algorithm is compared to the fuzzy c-means algorithm by testing both on three published data sets. Theoretical and empirical results reported in this paper show that the new algorithm is more efficient and leads to significant computational savings.

KW - Fuzzy c-means algorithm

KW - cluster analysis

KW - fuzzy clustering

KW - pattern recognition

KW - relaxation techniques

UR - https://www.scopus.com/pages/publications/38149147494

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M3 - Article

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SN - 0165-0114

VL - 61

SP - 177

EP - 188

JO - Fuzzy Sets and Systems

JF - Fuzzy Sets and Systems

IS - 2

ER -

A relaxation approach to the fuzzy clustering problem

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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