# Are Cluster Validity Measures (In)valid?

arXiv: https://arxiv.org/abs/2208.01261 · HTML: https://mlsanity.com/paper/2208.01261/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 61 references that are in the map.
- First posted on arXiv 2 Aug 2022.

## Builds on (most cited first, 2 of 2)

- [A Literature Survey of Benchmark Functions For Global Optimization Problems](https://mlsanity.com/paper/1308.4008/) (2013)
- [The Impact of Random Models on Clustering Similarity](https://mlsanity.com/paper/1701.06508/) (2017)

## Built on by (most cited first, 16 of 16)

- [A framework for benchmarking clustering algorithms](https://mlsanity.com/paper/2209.09493/) (2022)
- [Clustering with minimum spanning trees: How good can it be?](https://mlsanity.com/paper/2303.05679/) (2023)
- [HAD-Gen: Human-like and Diverse Driving Behavior Modeling for Controllable Scenario Generation](https://mlsanity.com/paper/2503.15049/) (2025)
- [Normalised clustering accuracy: An asymmetric external cluster validity measure](https://mlsanity.com/paper/2209.02935/) (2022)
- [On the Use of Relative Validity Indices for Comparing Clustering Approaches](https://mlsanity.com/paper/2404.10351/) (2024)
- [TopER: Topological Embeddings in Graph Representation Learning](https://mlsanity.com/paper/2410.01778/) (2024)
- [Hierarchical clustering with maximum density paths and mixture models](https://mlsanity.com/paper/2503.15582/) (2025)
- [Benchmarking of Clustering Validity Measures Revisited](https://mlsanity.com/paper/2511.05983/) (2025)
- [Cluster Analysis with Resampling for Validation and Exploration (CARVE)](https://mlsanity.com/paper/2606.00327/) (2026)
- [A new approach for evaluating internal cluster validation indices](https://mlsanity.com/paper/2308.03894/) (2023)
- [An upper bound on the silhouette evaluation metric for clustering](https://mlsanity.com/paper/2509.08625/) (2025)
- [Absolute indices for determining compactness, separability and number of clusters](https://mlsanity.com/paper/2510.13065/) (2025)
- [Visual Model Selection using Feature Importance Clusters in Fairness-Performance Similarity Optimized Space](https://mlsanity.com/paper/2510.22209/) (2025)
- [Multi-view diffusion geometry using intertwined diffusion trajectories](https://mlsanity.com/paper/2512.01484/) (2025)
- [CROCS: A Two-Stage Clustering Framework for Behaviour-Centric Consumer Segmentation with Smart Meter Data](https://mlsanity.com/paper/2601.10494/) (2026)
- [Explaining AutoClustering: Uncovering Meta-Feature Contribution in AutoML for Clustering](https://mlsanity.com/paper/2602.18348/) (2026)

## Abstract (arXiv)

Internal cluster validity measures (such as the Calinski-Harabasz, Dunn, or Davies-Bouldin indices) are frequently used for selecting the appropriate number of partitions a dataset should be split into. In this paper we consider what happens if we treat such indices as objective functions in unsupervised learning activities. Is the optimal grouping with regards to, say, the Silhouette index really meaningful? It turns out that many cluster (in)validity indices promote clusterings that match expert knowledge quite poorly. We also introduce a new, well-performing variant of the Dunn index that is built upon OWA operators and the near-neighbour graph so that subspaces of higher density, regardless of their shapes, can be separated from each other better.