  To evaluate clustering results is a significant part of cluster analysis.
Since there are no true class labels for clustering in typical unsupervised
learning, many internal cluster validity indices (CVIs), which use predicted
labels and data, have been created. Without true labels, to design an effective
CVI is as difficult as to create a clustering method. And it is crucial to have
more CVIs because there are no universal CVIs that can be used to measure all
datasets and no specific methods of selecting a proper CVI for clusters without
true labels. Therefore, to apply a variety of CVIs to evaluate clustering
results is necessary. In this paper, we propose a novel internal CVI -- the
Distance-based Separability Index (DSI), based on a data separability measure.
We compared the DSI with eight internal CVIs including studies from early Dunn
(1974) to most recent CVDD (2019) and an external CVI as ground truth, by using
clustering results of five clustering algorithms on 12 real and 97 synthetic
datasets. Results show DSI is an effective, unique, and competitive CVI to
other compared CVIs. We also summarized the general process to evaluate CVIs
and created the rank-difference metric for comparison of CVIs' results.
