Performance Evaluation of Some Symmetry-Based Cluster Validity Indexes

Abstract

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 xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</i> index, Xie-Beni index, FS index, <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> 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 xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</i> index performs the best as compared to all the other eight indexes.