Atwood-weighted Normalized Mutual Information (A-NMI): A Physics-Inspired Metric for Image Classification Evaluation

Atwood-weighted Normalized Mutual Information (A-NMI): A Physics-Inspired Metric for Image Classification Evaluation | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Atwood-weighted Normalized Mutual Information (A-NMI): A Physics-Inspired Metric for Image Classification Evaluation Grace Kim, Dongyung Kim This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9453983/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 7 You are reading this latest preprint version 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 (A-NMI), inspired by the Atwood number in fluid dynamics. By defining an Information Atwood Number (A I) based on the entropy difference between ground truth and predicted distributions, we introduce a complexity-aware penalty term. Our experimental results demonstrate that A-NMI provides a more robust and conservative assessment than standard NMI, particularly penalizing models that fail to match the intrinsic information density of the data. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 06 May, 2026 Reviewers agreed at journal 03 May, 2026 Reviewers agreed at journal 02 May, 2026 Reviewers invited by journal 30 Apr, 2026 Editor assigned by journal 29 Apr, 2026 Submission checks completed at journal 22 Apr, 2026 First submitted to journal 18 Apr, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9453983","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":635821287,"identity":"69e86246-0394-4f61-8b74-ec85447ebf37","order_by":0,"name":"Grace Kim","email":"","orcid":"","institution":"Arizona State University","correspondingAuthor":false,"prefix":"","firstName":"Grace","middleName":"","lastName":"Kim","suffix":""},{"id":635821288,"identity":"144eb9c3-b6ee-4e02-937c-2770da23d354","order_by":1,"name":"Dongyung Kim","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA6ElEQVRIiWNgGAWjYDCCA1BagpmB8QGQ5uEjRQuzAUgLG/FaGBjYJEAMglr4jvcefs3bdsduZjt3WuXXHDsZNgbmh49u4NEieeZcmjVv27Pk2cy8227LbksGOozN2DgHjxaDGzlmxrxth5PlQFoktzEDtfCwSROtpVhyWz1RWowfA7XYSQO1MH7cdpiwFskzZ8wY55w7nCDZzLtZmnHbcR42ZgJ+4TveY/zhTdlhe4nzZzd+/Lmt2p6fvfnhY3xagIBNioeBIbEByGLmAfGZ8SsHK/n4g4HBHsRi/EFY9SgYBaNgFIxAAADSGEd8E9+fWQAAAABJRU5ErkJggg==","orcid":"","institution":"Benedictine University","correspondingAuthor":true,"prefix":"","firstName":"Dongyung","middleName":"","lastName":"Kim","suffix":""}],"badges":[],"createdAt":"2026-04-18 04:23:16","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9453983/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9453983/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":108929890,"identity":"72a40c8d-e622-4dc1-928d-c6f11c68f313","added_by":"auto","created_at":"2026-05-11 01:46:13","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":187331,"visible":true,"origin":"","legend":"","description":"","filename":"JDSAANMIv2DoubleFormattedColumn.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9453983/v1_covered_d33900e3-a186-4d19-b66b-fd0ace3299ba.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Atwood-weighted Normalized Mutual Information (A-NMI): A Physics-Inspired Metric for Image Classification Evaluation","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"international-journal-of-data-science-and-analytics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jdsa","sideBox":"Learn more about [International Journal of Data Science and Analytics](http://link.springer.com/journal/41060)","snPcode":"41060","submissionUrl":"https://submission.nature.com/new-submission/41060/3","title":"International Journal of Data Science and Analytics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-9453983/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9453983/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Normalized Mutual Information (NMI) is a widely used metric for evaluating image classification and clustering. 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