Evaluating accuracy of community detection using the relative normalized mutual information

TL;DR

This paper identifies limitations of the normalized mutual information (NMI) in evaluating community detection accuracy due to finite-size effects, and proposes a new metric, rNMI, that accounts for statistical significance to improve evaluation reliability.

Contribution

The paper introduces the relative NMI (rNMI), a new metric that corrects for finite-size biases in NMI by comparing observed values to random partition expectations.

Findings

NMI is significantly affected by finite network size.

rNMI effectively reduces finite-size bias in community detection evaluation.

Numerical tests confirm rNMI's robustness over traditional NMI.

Abstract

The Normalized Mutual Information (NMI) has been widely used to evaluate the accuracy of community detection algorithms. However in this article we show that the NMI is seriously affected by systematic errors due to finite size of networks, and may give a wrong estimate of performance of algorithms in some cases. We give a simple theory to the finite-size effect of NMI and test our theory numerically. Then we propose a new metric for the accuracy of community detection, namely the relative Normalized Mutual Information (rNMI), which considers statistical significance of the NMI by comparing it with the expected NMI of random partitions. Our numerical experiments show that the rNMI overcomes the finite-size effect of the NMI.