# Improved mutual information measure for classification and community detection

## TL;DR

This paper introduces a corrected mutual information measure for classification and community detection that addresses limitations of the standard version, ensuring accurate comparisons across all scenarios.

## Contribution

The authors propose a new mutual information measure that includes a crucial omitted term, improving accuracy in real-world classification and community detection tasks.

## Key findings

- Corrected mutual information performs reliably across diverse cases.
- The new measure reduces errors in performance evaluation.
- Practical implementation guidelines are provided.

## Abstract

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.