# Improved mutual information measure for classification and community detection

arXiv: https://arxiv.org/abs/1907.12581 · HTML: https://mlsanity.com/paper/1907.12581/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jul 2019.

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

- [Normalized mutual information is a biased measure for classification and community detection](https://mlsanity.com/paper/2307.01282/) (2023)
- [Characterizing and comparing external measures for the assessment of cluster analysis and community detection](https://mlsanity.com/paper/2102.00708/) (2021)
- [Bayan Algorithm: Detecting Communities in Networks Through Exact and Approximate Optimization of Modularity](https://mlsanity.com/paper/2209.04562/) (2022)
- [Analyzing Modularity Maximization in Approximation, Heuristic, and Graph Neural Network Algorithms for Community Detection](https://mlsanity.com/paper/2310.10898/) (2023)
- [Exact and rapid linear clustering of networks with dynamic programming](https://mlsanity.com/paper/2301.10403/) (2023)
- [Unifying Information-Theoretic and Pair-Counting Clustering Similarity](https://mlsanity.com/paper/2511.03000/) (2025)

## Abstract (arXiv)

The information theoretic quantity known as mutual information finds wide use in classification and community detection analyses to compare two classifications of the same set of objects into groups. In the context of classification algorithms, for instance, it is often used to compare discovered classes to known ground truth and hence to quantify algorithm performance. Here we argue that the standard mutual information, as commonly defined, omits a crucial term which can become large under real-world conditions, producing results that can be substantially in error. We demonstrate how to correct this error and define a mutual information that works in all cases. We discuss practical implementation of the new measure and give some example applications.