DCSI -- An improved measure of cluster separability based on separation
  and connectedness
Jana Gauss Fabian Scheipl Moritz Herrmann
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. A review of the
existing literature shows that neither classification-based complexity measures
nor cluster validity indices (CVIs) adequately incorporate the central aspects
of separability for density-based clustering: between-class separation and
within-class connectedness. 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
form meaningful clusters.