A General Framework for Divergence Approximation on Gaussian Mixture Models

A General Framework for Divergence Approximation on Gaussian Mixture Models | 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 A General Framework for Divergence Approximation on Gaussian Mixture Models Amit Vishwakarma, K.S. Subrahamanian Moosath This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8341940/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 Widely used divergences like Kullback–Leibler (KL) divergence, Bhattacharyya divergence and Cauchy-Schwarz divergence have no closed form expression in the case of Gaussian Mixture Models (GMMs). This led to computationally expensive methods like numerical approximations, componentwise methods which fails to capture the mixture structure. In this paper, we develop a divergence approximation through the embedding of GMMs into the manifold of symmetric positive definite (SPD) matrices. The main result is that for regular divergences on compact set of non-degenerate GMM parameters, uniform equivalence is obtained for the divergence between two GMMs and computationally tractable corresponding divergence between their centered multivariate normal distribution representations in the SPD manifold. This is an extension of the work presented in GSI'25 conference. We further prove a stability theorem showing that the uniform equivalence degrades only linearly under spectral perturbations of the Hessian, ensuring robustness in numerical implementation. Experiments on the UIUC and KTH-TIPS texture recognition benchmarks evaluate three divergence measures computed via the SPD embedding: symmetric KL divergence, Bhattacharyya divergence and Cauchy-Schwarz divergence. Gaussian Mixture Models Symmetric Positive Definite Matrices Divergence Texture Recognition Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 28 Feb, 2026 Reviews received at journal 20 Feb, 2026 Reviewers agreed at journal 06 Feb, 2026 Reviewers invited by journal 06 Feb, 2026 Editor assigned by journal 13 Dec, 2025 Submission checks completed at journal 13 Dec, 2025 First submitted to journal 12 Dec, 2025 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-8341940","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":587005568,"identity":"04c536a2-22b3-4e32-b07b-d075e41e62da","order_by":0,"name":"Amit Vishwakarma","email":"","orcid":"","institution":"Indian Institute of Space Science and Technology (IIST)","correspondingAuthor":false,"prefix":"","firstName":"Amit","middleName":"","lastName":"Vishwakarma","suffix":""},{"id":587005570,"identity":"a341d4e6-eae0-43b1-ba6e-025bc5beb9f7","order_by":1,"name":"K.S. 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