Assessing the Quality of Fuzzy Partitions Using Relative Intersection

Dae-Won KIM  Young-il KIM  Doheon LEE  Kwang Hyung LEE 

Publication
IEICE TRANSACTIONS on Information and Systems  Vol.E88-D  No.3  pp.594-602
Publication Date: 2005/03/01
Online ISSN: 
Print ISSN: 0916-8532
Type of Manuscript: PAPER
Category: Computation and Computational Models
Keyword: 
cluster validity,  fuzzy clustering,  fuzzy c-means, 

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Summary: 
In this paper, conventional validity indexes are reviewed and the shortcomings of the fuzzy cluster validation index based on inter-cluster proximity are examined. Based on these considerations, a new cluster validity index is proposed for fuzzy partitions obtained from the fuzzy c-means algorithm. The proposed validity index is defined as the average value of the relative intersections of all possible pairs of fuzzy clusters in the system. It computes the overlap between two fuzzy clusters by considering the intersection of each data point in the overlap. The optimal number of clusters is obtained by minimizing the validity index with respect to c. Experiments in which the proposed validity index and several conventional validity indexes were applied to well known data sets highlight the superior qualities of the proposed index.