  Whether class labels in a given data set correspond to meaningful clusters is
crucial for the evaluation of clustering algorithms using real-world data sets.
This property can be quantified by separability measures. The central aspects
of separability for density-based clustering are between-class separation and
within-class connectedness, and neither classification-based complexity
measures nor cluster validity indices (CVIs) adequately incorporate them. A
newly developed measure (density cluster separability index, DCSI) aims to
quantify these two characteristics and can also be used as a CVI. Extensive
experiments on synthetic data indicate that DCSI correlates strongly with the
performance of DBSCAN measured via the adjusted Rand index (ARI) but lacks
robustness when it comes to multi-class data sets with overlapping classes that
are ill-suited for density-based hard clustering. Detailed evaluation on
frequently used real-world data sets shows that DCSI can correctly identify
touching or overlapping classes that do not correspond to meaningful
density-based clusters.
