# Normalised clustering accuracy: An asymmetric external cluster validity measure

arXiv: https://arxiv.org/abs/2209.02935 · HTML: https://mlsanity.com/paper/2209.02935/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 77 references that are in the map.
- First posted on arXiv 7 Sep 2022.

## Builds on (most cited first, 8 of 8)

- [The Impact of Random Models on Clustering Similarity](https://mlsanity.com/paper/1701.06508/) (2017)
- [Element-centric clustering comparison unifies overlaps and hierarchy](https://mlsanity.com/paper/1706.06136/) (2017)
- [Are Cluster Validity Measures (In)valid?](https://mlsanity.com/paper/2208.01261/) (2022)
- [Minimum adjusted Rand index for two clusterings of a given size](https://mlsanity.com/paper/2002.03677/) (2020)
- [Validation of cluster analysis results on validation data: A systematic framework](https://mlsanity.com/paper/2103.01281/) (2021)
- [Ground Truth Bias in External Cluster Validity Indices](https://mlsanity.com/paper/1606.05596/) (2016)
- [Characterizing and comparing external measures for the assessment of cluster analysis and community detection](https://mlsanity.com/paper/2102.00708/) (2021)
- [A close-up comparison of the misclassification error distance and the adjusted Rand index for external clustering evaluation](https://mlsanity.com/paper/1907.11505/) (2019)

## Built on by (most cited first, 2 of 2)

- [A framework for benchmarking clustering algorithms](https://mlsanity.com/paper/2209.09493/) (2022)
- [MMM and MMMSynth: Clustering of heterogeneous tabular data, and synthetic data generation](https://mlsanity.com/paper/2310.19454/) (2023)

## Abstract (arXiv)

There is no, nor will there ever be, single best clustering algorithm. Nevertheless, we would still like to be able to distinguish between methods that work well on certain task types and those that systematically underperform. Clustering algorithms are traditionally evaluated using either internal or external validity measures. Internal measures quantify different aspects of the obtained partitions, e.g., the average degree of cluster compactness or point separability. However, their validity is questionable because the clusterings they endorse can sometimes be meaningless. External measures, on the other hand, compare the algorithms' outputs to fixed ground truth groupings provided by experts. In this paper, we argue that the commonly used classical partition similarity scores, such as the normalised mutual information, Fowlkes-Mallows, or adjusted Rand index, miss some desirable properties. In particular, they do not identify worst-case scenarios correctly, nor are they easily interpretable. As a consequence, the evaluation of clustering algorithms on diverse benchmark datasets can be difficult. To remedy these issues, we propose and analyse a new measure: a version of the optimal set-matching accuracy, which is normalised, monotonic with respect to some similarity relation, scale-invariant, and corrected for the imbalancedness of cluster sizes (but neither symmetric nor adjusted for chance).