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We propose clustering algorithms based on a recently developed geometricdigraph family called cluster catch digraphs (CCDs). These digraphs are used todevise clustering methods that are hybrids of density-based and graph-basedclustering methods. CCDs are appealing digraphs for clustering, since theyestimate the number of clusters; however, CCDs (and density-based methods ingeneral) require some information on a parameter representing the\emph{intensity} of assumed clusters in the data set. We propose algorithmsthat are parameter free versions of the CCD algorithm and does not require aspecification of the intensity parameter whose choice is often critical infinding an optimal partitioning of the data set. We estimate the number ofconvex 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 distinguishthe clusters from noise clusters in a data set, and hence allow the estimationof the correct number of clusters. Our robust clustering algorithms arecomprised of methods that estimate both the number of clusters and theintensity parameter, making them completely parameter free. We conduct MonteCarlo simulations and use real life data sets to compare RK-CCDs with somecommonly used density-based and prototype-based clustering methods.

Parameter Free Clustering with Cluster Catch Digraphs (Technical Report)