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On the use of inclusion structure in fuzzy clustering algorithm in case of Gaussian membership functions

Nefti-Meziani, Samia; Oussalah, Mourad; Soufian, Majeed

Authors

Samia Nefti-Meziani

Mourad Oussalah

Majeed Soufian



Abstract

This article addresses the problem of incorporating an inclusion structure in the general class of fuzzy c-means algorithms. Conventionally, all the classes of fuzzy clustering algorithms involve a distance structure as the main tool to compute the interaction between the expected class prototypes and all the patterns. However, as the inclusion violates the basic metric assumptions, thereby it cannot be directly substituted for regular distance structure. The approach, advocated in this paper, consists of supporting the distance structure by a semi definite matrix A, which preserves the inclusion constraint globally for each class. Particularly, a graded inclusion index is put forward that takes into account the rational requirements underlying the definition of the inclusion of two Gaussian membership functions. Behaviour and algebraic properties of the proposed methodology are investigated. The proposed approach is then incorporated into the general fuzzy c-mean scheme, where the corresponding optimization problem is solved. Using both synthetic and real datasets, some illustrations are carried out in order to highlight the performances of the constructed algorithm and their evaluations, which are also compared to standard fuzzy c-means algorithm.

Citation

Nefti-Meziani, S., Oussalah, M., & Soufian, M. (2015). On the use of inclusion structure in fuzzy clustering algorithm in case of Gaussian membership functions. Journal of Intelligent and Fuzzy Systems, 28(4), 1477-1493. https://doi.org/10.3233/IFS-141407

Journal Article Type Article
Acceptance Date Jul 20, 2014
Publication Date 2015-07
Deposit Date May 8, 2017
Journal Journal of Intelligent and Fuzzy Systems
Print ISSN 1064-1246
Electronic ISSN 1875-8967
Publisher IOS Press
Peer Reviewed Peer Reviewed
Volume 28
Issue 4
Pages 1477-1493
DOI https://doi.org/10.3233/IFS-141407
Keywords inclusion structure, fuzzy c-means algorithms,
Public URL http://researchrepository.napier.ac.uk/Output/836220