A Distance-based Separability Measure for Internal Cluster Validation

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.