  To evaluate clustering results is a significant part of cluster analysis.
There are no true class labels for clustering in typical unsupervised learning.
Thus, a number of internal evaluations, which use predicted labels and data,
have been created. They are also named internal cluster validity indices
(CVIs). Without true labels, to design an effective CVI is not simple because
it is similar to create a clustering method. And, to have more CVIs is crucial
because there is no universal CVI that can be used to measure all datasets, and
no specific method for selecting a proper CVI for clusters without true labels.
Therefore, to apply more CVIs to evaluate clustering results is necessary. In
this paper, we propose a novel CVI - called Distance-based Separability Index
(DSI), based on a data separability measure. We applied the DSI and eight other
internal CVIs including early studies from Dunn (1974) to most recent studies
CVDD (2019) as comparison. We used an external CVI as ground truth for
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. In addition, we summarized the general process to evaluate
CVIs and created a new method - rank difference - to compare the results of
CVIs.
