Interpretable Classification of Time Series Using Euler Characteristic Surfaces

Interpretable Classification of Time Series Using Euler Characteristic Surfaces | 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 Article Interpretable Classification of Time Series Using Euler Characteristic Surfaces Buddha Nath Sharma, Vishal Mandal, Salam Rabindrajit Luwang, Md. Nurujjaman, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9295091/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 10 You are reading this latest preprint version Abstract Persistent homology (PH)—the conventional method in topological data analysis—is computationally expensive, requires further vectorization of its signatures before machine learning (ML) can be applied, and captures information along only the spatial axis. For time series data, we propose Euler Characteristic Surfaces (ECS) as an alternative topological signature based on the Euler characteristic (χ)—a fundamental topological invariant. The ECS provides a computationally efficient, spatiotemporal, and inherently discretized feature representation that can serve as direct input to ML models. We prove a stability theorem guaranteeing that the ECS remains stable under small perturbations of the input time series. We first demonstrate that ECS effectively captures nontrivial topological differences between the limit cycle and the strange attractor in the Rossler system. We then develop an ECS-based classification framework and apply it to five benchmark biomedical datasets (four ECG, one EEG) from the UCR/UEA archive. On ECG5000, our single-feature ECS classifier achieves 98% accuracy with O(n+R・ T) complexity, compared to 62% reported by a recent PH-based method. An AdaBoost extension raises accuracy to 98.6%, matching the best deep learning results while retaining full interpretability. Strong results are also obtained on TwoLeadECG (94.1%) and Epilepsy2 (92.6%). Biological sciences/Computational biology and bioinformatics Physical sciences/Engineering Physical sciences/Mathematics and computing Full Text Additional Declarations No competing interests reported. Supplementary Files TemplateforsubmissionstoScientificReports1.pdf Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 17 May, 2026 Reviewers agreed at journal 11 May, 2026 Reviews received at journal 06 May, 2026 Reviewers agreed at journal 05 May, 2026 Reviewers agreed at journal 16 Apr, 2026 Reviewers invited by journal 14 Apr, 2026 Editor assigned by journal 14 Apr, 2026 Editor invited by journal 14 Apr, 2026 Submission checks completed at journal 10 Apr, 2026 First submitted to journal 10 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. 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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-9295091","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":626676520,"identity":"1304a306-ead9-4972-bbe3-325e0ac26ac0","order_by":0,"name":"Buddha Nath Sharma","email":"","orcid":"","institution":"National Institute of Technology Sikkim","correspondingAuthor":false,"prefix":"","firstName":"Buddha","middleName":"Nath","lastName":"Sharma","suffix":""},{"id":626676521,"identity":"cd837144-2fef-4cb7-9d64-deaf1c49ee51","order_by":1,"name":"Vishal Mandal","email":"","orcid":"","institution":"National Institute of Technology Sikkim","correspondingAuthor":false,"prefix":"","firstName":"Vishal","middleName":"","lastName":"Mandal","suffix":""},{"id":626676522,"identity":"c1f767d0-5e44-48aa-876b-0e4250181d6c","order_by":2,"name":"Salam Rabindrajit Luwang","email":"","orcid":"","institution":"National Institute of Technology Sikkim","correspondingAuthor":false,"prefix":"","firstName":"Salam","middleName":"Rabindrajit","lastName":"Luwang","suffix":""},{"id":626676523,"identity":"b00b5a0b-54c2-48b2-9a68-c68f620837cc","order_by":3,"name":"Md. 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An AdaBoost extension raises accuracy to 98.6%, matching the best deep learning results while retaining full interpretability. 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