# Comparing clusterings and numbers of clusters by aggregation of calibrated clustering validity indexes

arXiv: https://arxiv.org/abs/2002.01822 · HTML: https://mlsanity.com/paper/2002.01822/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Feb 2020.

## Built on by (most cited first, 6 of 6)

- [HAWKS: Evolving Challenging Benchmark Sets for Cluster Analysis](https://mlsanity.com/paper/2102.06940/) (2021)
- [A Bayesian cluster validity index](https://mlsanity.com/paper/2402.02162/) (2024)
- [Moving Past Single Metrics: Exploring Short-Text Clustering Across Multiple Resolutions](https://mlsanity.com/paper/2502.17020/) (2025)
- [Selecting the number of clusters, clustering models, and algorithms. A unifying approach based on the quadratic discriminant score](https://mlsanity.com/paper/2111.02302/) (2021)
- [A new approach for evaluating internal cluster validation indices](https://mlsanity.com/paper/2308.03894/) (2023)
- [Longitudinal Learner Participation Profiling in Online Learning: Heterogeneous Consensus Clustering under Unequal Observation Windows](https://mlsanity.com/paper/2610.17494/) (2026)

## Abstract (arXiv)

A key issue in cluster analysis is the choice of an appropriate clustering method and the determination of the best number of clusters. Different clusterings are optimal on the same data set according to different criteria, and the choice of such criteria depends on the context and aim of clustering. Therefore, researchers need to consider what data analytic characteristics the clusters they are aiming at are supposed to have, among others within-cluster homogeneity, between-clusters separation, and stability. Here, a set of internal clustering validity indexes measuring different aspects of clustering quality is proposed, including some indexes from the literature. Users can choose the indexes that are relevant in the application at hand. In order to measure the overall quality of a clustering (for comparing clusterings from different methods and/or different numbers of clusters), the index values are calibrated for aggregation. Calibration is relative to a set of random clusterings on the same data. Two specific aggregated indexes are proposed and compared with existing indexes on simulated and real data.