Linear optimal transport subspaces for point set classification

Linear optimal transport subspaces for point set classification | 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 Linear optimal transport subspaces for point set classification Mohammad Shifat-E-Rabbi, Naqib Sad Pathan, Shiying Li, Yan Zhuang, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4106387/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 15 Jul, 2025 Read the published version in Journal of Mathematical Imaging and Vision → Version 1 posted 9 You are reading this latest preprint version Abstract Learning from point sets is an essential component in many computer vision and machine learning applications. Native, unordered, and permutation invariant set structure space is challenging to model, particularly for point set classification under spatial deformations. Here we propose a framework for classifying point sets experiencing certain types of spatial deformations, with a particular emphasis on datasets featuring affine deformations. Our approach employs the Linear Optimal Transport (LOT) transform to obtain a linear embedding of set-structured data. Utilizing the mathematical properties of the LOT transform, we demonstrate its capacity to accommodate variations in point sets by constructing a convex data space, effectively simplifying point set classification problems. Our method, which employs a nearest-subspace algorithm in the LOT space, demonstrates label efficiency, non-iterative behavior, and requires no hyper-parameter tuning. It achieves competitive accuracies compared to state-of-the-art methods across various point set classification tasks. Furthermore, our approach exhibits robustness in out-of-distribution scenarios where training and test distributions vary in terms of deformation magnitudes. particle-LOT subspace modeling point set classification optimal transport Full Text Additional Declarations Competing interest reported. We would request to exclude Gabriel Peyré, Marco Cuturi, and Justin Solomon from the review process. Cite Share Download PDF Status: Published Journal Publication published 15 Jul, 2025 Read the published version in Journal of Mathematical Imaging and Vision → Version 1 posted Editorial decision: Revision requested 21 Jan, 2025 Reviews received at journal 21 Jan, 2025 Reviewers agreed at journal 16 May, 2024 Reviews received at journal 08 May, 2024 Reviewers agreed at journal 01 May, 2024 Reviewers invited by journal 26 Mar, 2024 Editor assigned by journal 25 Mar, 2024 Submission checks completed at journal 20 Mar, 2024 First submitted to journal 15 Mar, 2024 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. 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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-4106387","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":281875441,"identity":"b3c62ebd-a44c-4f1c-8cca-475a38c76af5","order_by":0,"name":"Mohammad Shifat-E-Rabbi","email":"data:image/png;base64,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","orcid":"","institution":"North South University","correspondingAuthor":true,"prefix":"","firstName":"Mohammad","middleName":"","lastName":"Shifat-E-Rabbi","suffix":""},{"id":281875443,"identity":"04881a96-10b6-4c85-916f-f8bfc6cd5fbe","order_by":1,"name":"Naqib Sad Pathan","email":"","orcid":"","institution":"University of Virginia","correspondingAuthor":false,"prefix":"","firstName":"Naqib","middleName":"Sad","lastName":"Pathan","suffix":""},{"id":281875444,"identity":"25b5c4b3-6c94-41fd-9e0c-bd731182b579","order_by":2,"name":"Shiying Li","email":"","orcid":"","institution":"University of North Carolina at Chapel Hill","correspondingAuthor":false,"prefix":"","firstName":"Shiying","middleName":"","lastName":"Li","suffix":""},{"id":281875446,"identity":"b663d41c-7fa9-4ce7-8431-ae64a3cd22af","order_by":3,"name":"Yan Zhuang","email":"","orcid":"","institution":"National Institutes of Health Clinical Center","correspondingAuthor":false,"prefix":"","firstName":"Yan","middleName":"","lastName":"Zhuang","suffix":""},{"id":281875448,"identity":"610856b0-6e52-4220-a705-44d73fa8680c","order_by":4,"name":"Abu Hasnat Mohammad Rubaiyat","email":"","orcid":"","institution":"University of Virginia","correspondingAuthor":false,"prefix":"","firstName":"Abu","middleName":"Hasnat Mohammad","lastName":"Rubaiyat","suffix":""},{"id":281875450,"identity":"3a18255b-aadb-4e44-9496-12b142da13c8","order_by":5,"name":"Gustavo K Rohde","email":"","orcid":"","institution":"University of Virginia","correspondingAuthor":false,"prefix":"","firstName":"Gustavo","middleName":"K","lastName":"Rohde","suffix":""}],"badges":[],"createdAt":"2024-03-15 08:56:56","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4106387/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4106387/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s10851-025-01261-x","type":"published","date":"2025-07-15T16:05:30+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":87220305,"identity":"4d48f338-5b70-47e3-b3ed-7cd9f82982ce","added_by":"auto","created_at":"2025-07-21 16:11:38","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":517974,"visible":true,"origin":"","legend":"","description":"","filename":"POINTCLOUDJMIV.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4106387/v1_covered_c19c5cf8-ee17-47e0-b2e0-4c536c97e642.pdf"}],"financialInterests":"Competing interest reported. 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Native, unordered, and permutation invariant set structure space is challenging to model, particularly for point set classification under spatial deformations. Here we propose a framework for classifying point sets experiencing certain types of spatial deformations, with a particular emphasis on datasets featuring affine deformations. Our approach employs the Linear Optimal Transport (LOT) transform to obtain a linear embedding of set-structured data. Utilizing the mathematical properties of the LOT transform, we demonstrate its capacity to accommodate variations in point sets by constructing a convex data space, effectively simplifying point set classification problems. Our method, which employs a nearest-subspace algorithm in the LOT space, demonstrates label efficiency, non-iterative behavior, and requires no hyper-parameter tuning. It achieves competitive accuracies compared to state-of-the-art methods across various point set classification tasks. 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