An Internal Cluster Validity Index Using a Distance-based Separability Measure

TL;DR

This paper introduces a new internal cluster validity index called Distance-based Separability Index (DSI), which effectively evaluates clustering quality without true labels, and compares it with existing indices across multiple datasets.

Contribution

The paper proposes the DSI, a novel CVI based on data separability, and provides a comprehensive comparison with existing CVIs using real and synthetic datasets.

Findings

DSI is effective and competitive among other CVIs.

DSI outperforms some existing indices in clustering evaluation.

The paper introduces a new method, rank difference, for comparing CVI results.

Abstract

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.