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Whether class labels in a given data set correspond to meaningful clusters iscrucial for the evaluation of clustering algorithms using real-world data sets.This property can be quantified by separability measures. A review of theexisting literature shows that neither classification-based complexity measuresnor cluster validity indices (CVIs) adequately incorporate the central aspectsof separability for density-based clustering: between-class separation andwithin-class connectedness. A newly developed measure (density clusterseparability index, DCSI) aims to quantify these two characteristics and canalso be used as a CVI. Extensive experiments on synthetic data indicate thatDCSI correlates strongly with the performance of DBSCAN measured via theadjusted rand index (ARI) but lacks robustness when it comes to multi-classdata sets with overlapping classes that are ill-suited for density-based hardclustering. Detailed evaluation on frequently used real-world data sets showsthat DCSI can correctly identify touching or overlapping classes that do notform meaningful clusters.

DCSI -- An improved measure of cluster separability based on separation and connectedness