A New Point Symmetry Based Distance and its Application to Clustering

In this paper, an evolutionary clustering technique is described that uses a point symmetry based distance measure. The algorithm is therefore able to detect both convex and non-convex clusters. Kd-tree based nearest neighbor search is used to reduce the complexity of finding the closest symmetric point. The proposed GA with point symmetry distance based (GAPS) clustering technique is compared with existing symmetry based clustering technique SBKM, its modified version, and the well-known K-means algorithm. Several data sets are used to demonstrate its superiority. For real-life data sets of dimension more than 3, MANOVA statistical analysis is performed to compare the actual clusters and the clusters obtained by different algorithms. An important approach for image segmentation is clustering the pixels based on their spectral properties. The proposed point symmetry distance is used to define a new cluster validity index named S-index (Symmetry distance based index) which can provide a measure of goodness of clustering on different partitions of a data set. We have used two genetic clustering algorithms for partitioning the data set. Results demonstrating the superiority of the S-index in appropriately determining the number of clusters as compared to two other recently proposed measures, namely the PS index and PBM index, are first provided for two artificial data sets. The effectiveness of the proposed validity index is then demonstrated for automatically classifying different landcover regions in remote sensing imagery.