# Random Models for Fuzzy Clustering Similarity Measures

arXiv: https://arxiv.org/abs/2312.10270 · HTML: https://mlsanity.com/paper/2312.10270/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 29 references that are in the map.
- First posted on arXiv 16 Dec 2023.

## Builds on (most cited first, 3 of 3)

- [The Impact of Random Models on Clustering Similarity](https://mlsanity.com/paper/1701.06508/) (2017)
- [Ground Truth Bias in External Cluster Validity Indices](https://mlsanity.com/paper/1606.05596/) (2016)
- [Adjusting the adjusted Rand Index -- A multinomial story](https://mlsanity.com/paper/2011.08708/) (2020)

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

- [A Pragmatic Method for Comparing Clusterings with Overlaps and Outliers](https://mlsanity.com/paper/2602.14855/) (2026)
- [Adjusted Similarity Measures and a Violation of Expectations](https://mlsanity.com/paper/2601.10641/) (2026)

## Abstract (arXiv)

The Adjusted Rand Index (ARI) is a widely used method for comparing hard clusterings, but requires a choice of random model that is often left implicit. Several recent works have extended the Rand Index to fuzzy clusterings, but the assumptions of the most common random model is difficult to justify in fuzzy settings. We propose a single framework for computing the ARI with three random models that are intuitive and explainable for both hard and fuzzy clusterings, along with the benefit of lower computational complexity. The theory and assumptions of the proposed models are contrasted with the existing permutation model. Computations on synthetic and benchmark data show that each model has distinct behaviour, meaning that accurate model selection is important for the reliability of results.