DCSI -- An improved measure of cluster separability based on separation and connectedness

TL;DR

The paper introduces DCSI, a new measure for evaluating cluster separability based on separation and connectedness, improving clustering assessment especially for density-based methods.

Contribution

It proposes DCSI, a novel separability measure that captures separation and connectedness, filling gaps in existing cluster validity indices for density-based clustering evaluation.

Findings

DCSI correlates strongly with clustering performance measured by ARI.

DCSI effectively identifies touching or overlapping classes in real-world data.

DCSI shows limitations with multi-class overlapping data in density-based clustering.

Abstract

Whether class labels in a given data set correspond to meaningful clusters is crucial for the evaluation of clustering algorithms using real-world data sets. This property can be quantified by separability measures. The central aspects of separability for density-based clustering are between-class separation and within-class connectedness, and neither classification-based complexity measures nor cluster validity indices (CVIs) adequately incorporate them. A newly developed measure (density cluster separability index, DCSI) aims to quantify these two characteristics and can also be used as a CVI. Extensive experiments on synthetic data indicate that DCSI correlates strongly with the performance of DBSCAN measured via the adjusted Rand index (ARI) but lacks robustness when it comes to multi-class data sets with overlapping classes that are ill-suited for density-based hard clustering. Detailed evaluation on frequently used real-world data sets shows that DCSI can correctly identify touching or overlapping classes that do not correspond to meaningful density-based clusters.