A validity index based on cluster symmetry

An important consideration in clustering is the determination of the correct number of clusters and the appropriate partitioning of a given data set. In this paper, a newly developed point symmetry distance is used to propose a new cluster validity index named Sym -index which provides a measure of "symmetricity" of the different partitionings of a data set. The index is able to address all the above mentioned issues, viz., determining the number of clusters and evolving the proper partitioning as long as the clusters possess the property of symmetry. A Kd-tree-based data structure is used to reduce the complexity of computing the symmetry distance. Results demonstrating the superiority of the Sym-index in appropriately determining the proper partitioning and the number of clusters, as compared to two other recently proposed measures, namely the PS-index and I-index, are provided for three clustering methods viz., two recently developed genetic algorithm based clustering techniques and the average linkage clustering algorithm. Four artificial data sets and two real life data sets are considered for this purpose. The effectiveness of the proposed validity index is then demonstrated for automatically classifying different landcover regions in remote sensing imagery.