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

arXiv: https://arxiv.org/abs/2310.12806 · HTML: https://mlsanity.com/paper/2310.12806/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Oct 2023.

## Built on by (most cited first, 5 of 5)

- [Beyond Labels: Advancing Cluster Analysis with the Entropy of Distance Distribution (EDD)](https://mlsanity.com/paper/2311.16621/) (2023)
- [MNIST-Nd: a set of naturalistic datasets to benchmark clustering across dimensions](https://mlsanity.com/paper/2410.16124/) (2024)
- [Internal Evaluation of Density-Based Clusterings with Noise](https://mlsanity.com/paper/2503.00127/) (2025)
- [SHADE: Deep Density-based Clustering](https://mlsanity.com/paper/2410.06265/) (2024)
- [An unsupervised clustering analysis of breast cancer data derived from electronic health records enhanced through UMAP dimensionality reduction](https://mlsanity.com/paper/2607.19089/) (2026)

## Abstract (arXiv)

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.