Density-based clustering validation

Density-Based Clustering Validation (DBCV) is a metric designed to assess the quality of clustering solutions, particularly for density-based clustering algorithms like DBSCAN, Mean shift, and OPTICS. This metric is particularly suited for identifying concave and nested clusters, where traditional metrics such as the Silhouette coefficient, Davies–Bouldin index, or Calinski–Harabasz index often struggle to provide meaningful evaluations.

In each graph, an increasing level of noise is introduced to the initial data, which consist of two well-defined semicircles. As the noise increases and thus the overlap between the two groups, the value of the DBCV index progressively decreases. Image released under MIT license.^[1]

Unlike traditional validation measures, which often rely on compact and well-separated clusters, DBCV index evaluates how well clusters are defined in terms of local density variations and structural coherence.

This metric was introduced in 2014 by David Moulavi and colleagues in their work.^[2] It utilizes density connectivity principles to quantify clustering structures, making it especially effective at detecting arbitrarily shaped clusters in concave datasets, where traditional metrics may be less reliable.

The DBCV index has been employed for clustering analysis in bioinformatics,^[3] ecology,^[4] techno-economy,^[5] and health informatics^{[6] [7]}, as well as in numerous other fields.^{[8] [9]}

Definition

DBCV index evaluates clustering structures by analyzing the relationships between data points within and across clusters. Given a dataset ${\displaystyle X={x_{1},x_{2},...,x_{n}}}$ , a density-based algorithm partitions it into K clusters ${\displaystyle {C_{1},C_{2},...,C_{n}}}$ . Each point belongs to a specific cluster, denoted as ${\displaystyle Cluster(X_{i})}$ 

A key concept in DBCV index is the notion of density-connected paths.^[10] Two points within the same cluster are considered density-connected if there exists a sequence of intermediate points linking them, where each consecutive pair meets a predefined density criterion. The density-based distance between two points is determined by identifying the optimal path that minimizes the maximum local reachability distance along its trajectory.

DBCV index extends the Silhouette coefficient by redefining cluster cohesion and separation using density-based distances:

• Within-cluster density distance measures how closely a point is related to other members of its cluster:

${\displaystyle a_{i}={\frac {1}{|C_{cluster(x_{i})}|-1}}\sum _{x_{j}\in C_{cluster(x_{i})},y\neq x}d_{density}(x_{j},x_{i})}$ 

• Nearest-cluster density distance quantifies how far a point is from the closest external cluster:

${\displaystyle b_{i}=\min _{C\neq C_{{\text{cluster}}(x_{i})} \atop C\in \{C_{1},\dots ,C_{k}\}}\left({\frac {1}{|C|}}\sum _{x_{j}\in C}d_{\text{density}}(x_{i},x_{j})\right).}$ 

Using these measures, the DBCV index is computed as:

${\displaystyle DBCV={\frac {1}{n}}\sum _{i=1}^{n}{\frac {b_{i}-a_{i}}{\max(a_{i},b_{i})}}}$ 

Explanation

DBCV index values range between −1 and +1:

• +1: Strongly cohesive and well-separated clusters.
• 0: Ambiguous clustering structure.
• −1: Poorly formed clusters or incorrect assignments.

By leveraging density-based distances instead of traditional Euclidean measures, DBCV index provides a more robust evaluation of clustering performance in datasets with irregular or non-spherical distributions.^[2]

References

• Moulavi, David; Jaskowiak, Pablo A.; Campello, Ricardo J. G. B.; Zimek, Arthur; Sander, Jörg (2014), "Density-based clustering validation", Proceedings of the 2014 SIAM International Conference on Data Mining (PDF), SIAM, pp. 839–847, doi:10.1137/1.9781611973440.96, ISBN 978-1-61197-344-0

• Chicco, Davide; Sabino, Giuseppe; Oneto, Luca; Jurman, Giuseppe (2025), "The DBCV index is more informative than DCSI, CDbw, and VIASCKDE indices for unsupervised clustering internal assessment of concave-shaped and density-based clusters", PeerJ Computer Science, PeerJ Inc., pp. 1–37, doi:10.7717/peerj-cs.3095

Implementations

• Python DBCV Implementation by Felipe Alves Siqueira
• R DBCV Implementation by Pablo Andretta Jaskowiak

See also

• Cluster analysis
• DBSCAN
• Silhouette coefficient
• Dunn index
• Calinski-Harabasz index
• Davies–Bouldin index

References

1. GitHub. FelSiq/DBCV Fast Density-Based Clustering Validation (DBCV) Python package -- https://github.com/FelSiq/DBCV
2. Moulavi, David; Jaskowiak, Pablo A.; Campello, Ricardo J. G. B.; Zimek, Arthur; Sander, Jörg (2014), "Density-Based Clustering Validation", Proceedings of the 2014 SIAM International Conference on Data Mining (PDF), SIAM, pp. 839–847, doi:10.1137/1.9781611973440.96, ISBN 978-1-61197-344-0
3. Di Giovanni, Daniele (2023), "Using machine learning to explore shared genetic pathways and possible endophenotypes in autism spectrum disorder", Genes, 14 (2): 313, doi:10.3390/genes14020313, PMC 9956345, PMID 36833240
4. Poutaraud, Joachim (2024), "Meta-Embedded Clustering (MEC): A new method for improving clustering quality in unlabeled bird sound datasets", Ecological Informatics, 82, Elsevier: 102687, doi:10.1016/j.ecoinf.2024.102687
5. Shim, Jaehyun (2022), "Techno-economic analysis of micro-grid system design through climate region clustering", Energy Conversion and Management, 274, Elsevier: 116411, Bibcode:2022ECM...27416411S, doi:10.1016/j.enconman.2022.116411
6. Martínez, Rubén Yáñez (2023), "Spanish Corpora of tweets about COVID-19 vaccination for automatic stance detection", Information Processing & Management, 60 (3), Elsevier: 103294, doi:10.1016/j.ipm.2023.103294
7. Chicco D.; Oneto L.; Cangelosi D. (2025). "DBSCAN and DBCV application to open medical records heterogeneous data for identifying clinically significant clusters of patients with neuroblastoma". BioData Mining. 18 (40): 1-17. doi:10.1186/s13040-025-00455-8. PMC 12164137.
8. Beer, Anna (2025), "DISCO: Internal Evaluation of Density-Based Clustering", arXiv:2503.00127 [cs.LG]
9. Veigel, Nadja (2025), "Content analysis of multi-annual time series of flood-related Twitter (X) data", Natural Hazards and Earth System Sciences, 25 (2), Copernicus Publications Gottingen, Germany: 879–891, Bibcode:2025NHESS..25..879V, doi:10.5194/nhess-25-879-2025
10. Ester, M. (2009), Liu, L.; Özsu, M.T. (eds.), "Density-based Clustering", Encyclopedia of Database Systems, Boston, MA: Springer: 795–799, doi:10.1007/978-0-387-39940-9_605, ISBN 978-0-387-35544-3