Atwood-weighted Normalized Mutual Information (ANMI): a physics-inspired metric for image classification evaluation

Abstract

Normalized Mutual Information (NMI) is a widely used metric for evaluating image classification and clustering. However, standard NMI often yields over-optimistic results when there is a significant discrepancy in cluster density, such as in over-clustering scenarios. In this paper, we propose a novel evaluation metric, Atwood-weighted Normalized Mutual Information (ANMI), inspired by the Atwood number in fluid dynamics. By defining an Information Atwood Number (AI\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A_I$$\end{document}) based on the entropy difference between ground truth and predicted distributions, we introduce a complexity-aware penalty term. Our experimental results demonstrate that ANMI provides a more robust and conservative assessment than standard NMI, particularly penalizing models that fail to match the intrinsic information density of the data.