Parameter Free Clustering with Cluster Catch Digraphs (Technical Report)

Abstract: We propose clustering algorithms based on a recently developed geometric digraph family called cluster catch digraphs (CCDs). These digraphs are used to devise clustering methods that are hybrids of density-based and graph-based clustering methods. CCDs are appealing digraphs for clustering, since they estimate the number of clusters; however, CCDs (and density-based methods in general) require some information on a parameter representing the \emph{intensity} of assumed clusters in the data set. We propose algorithms that are parameter free versions of the CCD algorithm and does not require a specification of the intensity parameter whose choice is often critical in finding an optimal partitioning of the data set. We estimate the number of convex clusters by borrowing a tool from spatial data analysis, namely Ripley's $K$ function. We call our new digraphs utilizing the $K$ function as RK-CCDs. We show that the minimum dominating sets of RK-CCDs estimate and distinguish the clusters from noise clusters in a data set, and hence allow the estimation of the correct number of clusters. Our robust clustering algorithms are comprised of methods that estimate both the number of clusters and the intensity parameter, making them completely parameter free. We conduct Monte Carlo simulations and use real life data sets to compare RK-CCDs with some commonly used density-based and prototype-based clustering methods.