Development of Some Line Symmetry Based Cluster Validity Indices

Most of the existing literatures use Euclidean distance based cluster validity measures in order to identify correct number of clusters for different datasets. It is a very important consideration for clustering. Symmetry can be considered as an important attribute for data clustering. It can be of two types, point symmetry and line symmetry. In this paper we have introduced a newly developed line symmetry based distance in the definitions of four well known cluster validity indices, namely Xie Beni(XB) index, PBM index, FCM index and PS index to identify proper partitioning and accurate number of clusters from five artificially generated datasets. Initially in order to obtain different partitions an existing genetic clustering technique which uses line symmetry property (GALS clustering) is applied on datasets varying the number of clusters. We have also provided a comparative study of our proposed line symmetry based cluster validity indices with their original versions which follow euclidean distance based computation. From the experimental results, it is revealed that most of the validity indices which follow Line symmetry based distances, perform better than euclidean distance based original validity indices.