Use of symmetry and stability for data clustering

摘要

An important consideration in clustering is the determination of an algorithm appropriate for partitioning a given data set. Thereafter identification of the correct model order and determining the corresponding partition ing need to be performed. In this paper, at first the effec tiveness of the recently developed symmetry based cluster validity index named Sym-index which provides a measure of "symmetricity" of the different partitionings of a data set is shown to address all the above mentioned issues, viz., identifying the appropriate clustering algorithm, deter mining the proper model order and evolving the proper partitioning as long as the clusters possess the property of symmetry. Results demonstrating the superiority of the proposed cluster validity measure in appropriately deter mining the proper clustering technique as well as appro priate model order as compared to five other recently proposed measures, namely PS-index, I-index, CS-index, well-known XB-index, and stability based index, are pro vided for several clustering methods viz., two recently developed genetic algorithm based clustering techniques, the average linkage clustering algorithm, self organizing map and the expectation maximization clustering algo rithm. Five artificial data sets and three real life data sets, are considered for this purpose. In the second part of the rnpaper, a new measure of stability of clustering solutions over different bootstrap samples of a data set is proposed. Thereafter a multiobjective optimization based clustering technique is developed which optimizes both Sym-index and the measure of stability simultaneously to automati cally determine the appropriate number of clusters and the appropriate partitioning of the data sets having symmetrical shaped clusters. Results on five artificial and five real-life data sets show that the proposed technique is well-suited to detect the number of clusters from data sets having point symmetric clusters.