Hypergraph regularized nonnegative triple decomposition for multiway data analysis

Hypergraph regularized nonnegative triple decomposition for multiway data analysis | 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 Hypergraph regularized nonnegative triple decomposition for multiway data analysis Qingshui Liao, Qilong Liu, Fatimah Abdul Razak This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3847135/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 20 Apr, 2024 Read the published version in Scientific Reports → Version 1 posted 9 You are reading this latest preprint version Abstract Tucker decomposition is widely used for image representation, data reconstruction , and machine learning tasks, but the calculation cost for updating the Tucker core is high. Bilevel form of triple decomposition (TriD) overcomes this issue by decomposing the Tucker core into three low-dimensional third-order factor tensors and plays an important role in the dimension reduction of data representation. TriD, on the other hand, is incapable of precisely encoding similarity relationships for tensor data with a complex manifold structure. To address this shortcoming, we take advantage of hypergraph learning and propose a novel hypergraph regu-larized nonnegative triple decomposition for multiway data analysis that employs the hypergraph to model the complex relationships among the raw data. Furthermore , we develop a multiplicative update algorithm to solve our optimization problem and theoretically prove its convergence. Finally, we perform extensive numerical tests on six real-world datasets, and the results show that our proposed algorithm outperforms some state-of-the-art methods. Physical sciences/Mathematics and computing/Computational science Physical sciences/Mathematics and computing/Applied mathematics Nonnegative tensor decomposition Triple decomposition Hypergraph regularization Data anaylsis Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 20 Apr, 2024 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 04 Mar, 2024 Reviews received at journal 10 Feb, 2024 Reviewers agreed at journal 29 Jan, 2024 Reviewers agreed at journal 29 Jan, 2024 Reviewers invited by journal 29 Jan, 2024 Editor assigned by journal 22 Jan, 2024 Editor invited by journal 14 Jan, 2024 Submission checks completed at journal 14 Jan, 2024 First submitted to journal 08 Jan, 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. 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-3847135","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":267193587,"identity":"033c2285-a3e3-462d-9b64-f40190c2b2e3","order_by":0,"name":"Qingshui Liao","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABBklEQVRIiWNgGAWjYBACA2YwCcQSDAwHPhjY8PAzMx9+QLSWgzMq0mQk29nSDPBqgbOAWph5zhy2MTjPoyCBVws788MHbwru2M2f3WN4gLeNmcf4MA/QoBqbaNwOYzM2nGPwLHnDnTMGByTb2HjMDvMeeMBwLC23AbdfzKR5DA4nG0jkGBwwbOMBauFLMGBsOIxHC/s3sBb5GUAtiW0SPMbNPAYS+LXwgG2xY7gB1HLgjAEPUISglmKgXw4nGNxIKzjYUJHAI3EYGMgJePxi339844M3fw7by89I3vz5j8F/e/7+w4cffKixwakFDHgYGBJRFSTgUw7VYk9IzSgYBaNgFIxgAAB9algct6B/6gAAAABJRU5ErkJggg==","orcid":"","institution":"Universiti Kebangsaan Malaysia","correspondingAuthor":true,"prefix":"","firstName":"Qingshui","middleName":"","lastName":"Liao","suffix":""},{"id":267193588,"identity":"45877e44-7d6c-4d10-bf54-af5aa32af35b","order_by":1,"name":"Qilong Liu","email":"","orcid":"","institution":"Guizhou Normal University","correspondingAuthor":false,"prefix":"","firstName":"Qilong","middleName":"","lastName":"Liu","suffix":""},{"id":267193589,"identity":"ec11b3e0-83d6-404d-936a-e9933ee60381","order_by":2,"name":"Fatimah Abdul Razak","email":"","orcid":"","institution":"Universiti Kebangsaan Malaysia","correspondingAuthor":false,"prefix":"","firstName":"Fatimah","middleName":"Abdul","lastName":"Razak","suffix":""}],"badges":[],"createdAt":"2024-01-09 03:52:31","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3847135/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3847135/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-024-59300-3","type":"published","date":"2024-04-20T22:40:27+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":55690562,"identity":"4982d550-c59d-40e3-85d2-662a43d19710","added_by":"auto","created_at":"2024-05-01 22:40:41","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":499521,"visible":true,"origin":"","legend":"","description":"","filename":"HNTriD20240109NEW.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3847135/v1_covered_0bb784e8-bfdb-480d-ad32-ac7a88b7da35.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Hypergraph regularized nonnegative triple decomposition for multiway data analysis","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Nonnegative tensor decomposition, Triple decomposition, Hypergraph regularization, Data anaylsis","lastPublishedDoi":"10.21203/rs.3.rs-3847135/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3847135/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Tucker decomposition is widely used for image representation, data reconstruction , and machine learning tasks, but the calculation cost for updating the Tucker core is high. 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