Article: A novel validity index in fuzzy clustering algorithm Journal: International Journal of Wireless and Mobile Computing (IJWMC) 2016 Vol.10 No.2 pp.183 - 190 Abstract: Fuzzy clustering algorithms, especially the fuzzy c-means (FCM) algorithm, need the number of clusters specified manually in advance, which, to some extent, limits the application of FCM algorithm. To solve this problem of fuzzy clustering algorithm not being able to predict the number of clusters, this paper proposes a new cluster validity index. This algorithm produces membership matrix and cluster centroid by implementing the FCM algorithm iteratively, figuring out the corresponding inter-class degree of separation, intra-class compactness and inter-class degree of overlap. A new cluster validity index v<SUB align="right"><SMALL>oscar</SMALL></SUB> is defined by using the three indices. This new index solves the problem that FCM algorithm needs to preset a number of clusters, as well as avoiding the low accuracy of fuzzy degree introduced in the calculation of distance due to uneven distribution of data, particularly in the presence of intra-class overlap. The experiments conducted on artificial data sets and the actual data sets show that the proposed index can make correct evaluations of the fuzzy clustering results, and can automatically obtain the optimal number of clusters so as to improve the effect of clustering. Meanwhile it also shows that this index possesses excellent reliability for different fuzzy factors. Inderscience Publishers - linking academia, business and industry through research

Title: A novel validity index in fuzzy clustering algorithm

Authors: Zheng Feng; Jian-Cong Fan

Addresses: Provincial Key Lab for Information Technology of Wisdom Mining of Shandong Province, Qingdao 266590, China; College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao 266590, China ' Provincial Key Lab for Information Technology of Wisdom Mining of Shandong Province, Qingdao 266590, China; College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao 266590, China

Abstract: Fuzzy clustering algorithms, especially the fuzzy c-means (FCM) algorithm, need the number of clusters specified manually in advance, which, to some extent, limits the application of FCM algorithm. To solve this problem of fuzzy clustering algorithm not being able to predict the number of clusters, this paper proposes a new cluster validity index. This algorithm produces membership matrix and cluster centroid by implementing the FCM algorithm iteratively, figuring out the corresponding inter-class degree of separation, intra-class compactness and inter-class degree of overlap. A new cluster validity index v_oscar is defined by using the three indices. This new index solves the problem that FCM algorithm needs to preset a number of clusters, as well as avoiding the low accuracy of fuzzy degree introduced in the calculation of distance due to uneven distribution of data, particularly in the presence of intra-class overlap. The experiments conducted on artificial data sets and the actual data sets show that the proposed index can make correct evaluations of the fuzzy clustering results, and can automatically obtain the optimal number of clusters so as to improve the effect of clustering. Meanwhile it also shows that this index possesses excellent reliability for different fuzzy factors.

Keywords: fuzzy clustering; fuzzy c-means clustering; FCM; cluster validity index; optimal number of clusters; membership matrix; cluster centroid.

DOI: 10.1504/IJWMC.2016.076153

International Journal of Wireless and Mobile Computing, 2016 Vol.10 No.2, pp.183 - 190

Received: 20 Jul 2015
Accepted: 26 Nov 2015
Published online: 27 Apr 2016 *

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Title: A novel validity index in fuzzy clustering algorithm

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