# Pairwise Adjusted Mutual Information

arXiv: https://arxiv.org/abs/2103.12641 · HTML: https://mlsanity.com/paper/2103.12641/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 14 references that are in the map.
- First posted on arXiv 23 Mar 2021.

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

- [Adjusting for Chance Clustering Comparison Measures](https://mlsanity.com/paper/1512.01286/) (2015)
- [A Comparative Analysis of Community Detection Algorithms on Artificial Networks](https://mlsanity.com/paper/1608.00763/) (2016)

## Built on by (most cited first, 3 of 3)

- [Do Large Language Models Understand Morality Across Cultures?](https://mlsanity.com/paper/2507.21319/) (2025)
- [LLMs as mirrors of societal moral standards: reflection of cultural divergence and agreement across ethical topics](https://mlsanity.com/paper/2412.00962/) (2024)
- [FastAMI -- a Monte Carlo Approach to the Adjustment for Chance in Clustering Comparison Metrics](https://mlsanity.com/paper/2305.03022/) (2023)

## Abstract (arXiv)

A well-known metric for quantifying the similarity between two clusterings is the adjusted mutual information. Compared to mutual information, a corrective term based on random permutations of the labels is introduced, preventing two clusterings being similar by chance. Unfortunately, this adjustment makes the metric computationally expensive. In this paper, we propose a novel adjustment based on {pairwise} label permutations instead of full label permutations. Specifically, we consider permutations where only two samples, selected uniformly at random, exchange their labels. We show that the corresponding adjusted metric, which can be expressed explicitly, behaves similarly to the standard adjusted mutual information for assessing the quality of a clustering, while having a much lower time complexity. Both metrics are compared in terms of quality and performance on experiments based on synthetic and real data.