Use of line based symmetry for developing cluster validity indices

Abstract

From a dataset automatically identifying possible count of clusters is an important task of unsupervised classification. To address this issue, in the current paper, we have focused on the symmetry property of any cluster. Point and line symmetry are two important attributes of data partitions. Here we have proposed line symmetry versions of eight well-known validity indices: XB, PBM, FCM, PS, FS, K, SV, and DB indices to make them capable of identifying the accurate count of partitions from data sets containing clusters having line symmetric property. The global optimality of two of these newly developed indices is established mathematically. Eight artificially generated data sets of varying dimensions containing clusters of different convexities and shapes and three real-life data sets are used for the purpose of experiment. Initially, to obtain different partitions an existing genetic clustering technique which uses line symmetry property (GALS clustering) is applied on data sets varying the count of clusters. queryPlease check and confirm the edit in the following sentence: We have also provided a comparative study of our proposed line-symmetry-based cluster validity indices with their point-symmetry-based versions and original versions based on Euclidean distance. We have also provided a comparative study of our proposed line-symmetry-based cluster validity indices with their point-symmetry-based versions and original versions based on Euclidean distance. From the experimental results it is revealed that most of the line-symmetry-distance-based cluster validity indices perform better than their point symmetry and Euclidean-distance-based versions.