An Internal Cluster Validity Index Using a Distance-based Separability Measure
This work addresses the need for more CVIs in unsupervised learning, as there is no universal index, but it is incremental in proposing a new method within an established framework.
The authors tackled the problem of evaluating clustering results without true labels by proposing a new internal cluster validity index (CVI) called Distance-based Separability Index (DSI), which showed effectiveness and competitiveness compared to eight other CVIs on 12 real and 97 synthetic datasets.
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.