A Validity Measure for Fuzzy Clustering
IEEE Transactions on Pattern Analysis and Machine Intelligence
Performance Evaluation of Some Clustering Algorithms and Validity Indices
IEEE Transactions on Pattern Analysis and Machine Intelligence
GAPS: A clustering method using a new point symmetry-based distance measure
Pattern Recognition
Cluster Analysis
A survey of evolutionary algorithms for clustering
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
Clustering by integrating multi-objective optimization with weighted k-means and validity analysis
IDEAL'06 Proceedings of the 7th international conference on Intelligent Data Engineering and Automated Learning
Nonparametric genetic clustering: comparison of validity indices
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
Evolution-Based Tabu Search Approach to Automatic Clustering
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
A New Nonbinary Matrix Clustering Algorithm for Development of System Architectures
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
Hierarchical Pattern Discovery in Graphs
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
Some new indexes of cluster validity
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
An extensive comparative study of cluster validity indices
Pattern Recognition
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Identification of the correct number of clusters is an important consideration in clustering where several cluster validity indexes, primarily utilizing the Euclidean distance, have been used in the literature. The property of symmetry is observed in most clustering solutions. In this paper, the symmetry versions of nine cluster validity indexes, namely, Davies-Bouldin index, Dunn index, generalized Dunn index, point symmetry (PS) index, I index, Xie-Beni index, FS index, K index, and SV index, are proposed. It is empirically established that incorporation of the property of symmetry significantly improves the capabilities of these indexes in identifying the appropriate number of clusters. A recently developed PS-based genetic clustering technique, GAPS clustering, is used as the underlying partitioning algorithm. Results on six artificially generated and five real-life datasets show that symmetry-distance-based I index performs the best as compared to all the other eight indexes.