Adaptive Multi-Kernel and Graph Semi-Supervised Support Vector Machine

Adaptive Multi-Kernel and Graph Semi-Supervised Support Vector Machine | 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 Adaptive Multi-Kernel and Graph Semi-Supervised Support Vector Machine WeiGuo Yi, HaiYang Ge This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7469419/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 9 You are reading this latest preprint version Abstract The performance of semi-supervised support vector machines ( \((\mathrm{S^3VMs})\) ) depends on the quality of the graph regularizer and the choice of kernel, yet most existing methods keep the graph fixed and tune a single kernel by exhaustive search. We propose AMG-S \((^3)\) VM ( Adaptive Multi-Kernel and Graph \((\mathrm{S^3VM})\) ), which embeds Laplacian refinement and kernel-weight optimization into one unified objective. During each iteration, graph edge weights are updated by a closed-form simplex projection that blends Euclidean proximity with the current margin, while kernel coefficients are adjusted through momentum-augmented mirror descent under simplex constraints. These two updates, followed by a convex \((\mathrm{S^3VM})\) subproblem, yield a block-convex procedure whose objective is proven to decrease monotonically and converge to a critical point; the overhead grows only linearly with the number of base kernels. Extensive experiments on diverse benchmark datasets show that AMG-S \((^3)\) VM consistently surpasses classical Laplacian, deep-kernel, and graph-regularized competitors, yet requires only a coarse grid for a handful of scalar hyper-parameters. The results demonstrate that graph–kernel co-adaptation provides a principled and computationally efficient route to robust semi-supervised learning. Semi-supervised support vector machine sep Adaptive Laplacian sep Multi-kernel learning sep Graph regularization sep Kernel weight optimization Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Revision requested 13 May, 2026 Reviews received at journal 19 Mar, 2026 Reviewers agreed at journal 19 Mar, 2026 Reviews received at journal 12 Oct, 2025 Reviewers agreed at journal 18 Sep, 2025 Reviewers invited by journal 18 Sep, 2025 Editor assigned by journal 31 Aug, 2025 Submission checks completed at journal 28 Aug, 2025 First submitted to journal 27 Aug, 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. 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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-7469419","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":521683586,"identity":"e07ebca2-016b-4bf9-9df6-1f18b6297764","order_by":0,"name":"WeiGuo 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Cybernetics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Semi-supervised support vector machine, sep, Adaptive Laplacian, sep, Multi-kernel learning, sep, Graph regularization, sep, Kernel weight optimization","lastPublishedDoi":"10.21203/rs.3.rs-7469419/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7469419/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe performance of semi-supervised support vector machines (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((\\mathrm{S^3VMs})\\)\u003c/span\u003e\u003c/span\u003e) depends on the quality of the graph regularizer and the choice of kernel, yet most existing methods keep the graph fixed and tune a single kernel by exhaustive search. We propose \u003cb\u003eAMG-S\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((^3)\\)\u003c/span\u003e\u003c/span\u003eVM\u003c/b\u003e (\u003cem\u003eAdaptive Multi-Kernel and Graph \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((\\mathrm{S^3VM})\\)\u003c/span\u003e\u003c/span\u003e\u003c/em\u003e), which embeds Laplacian refinement and kernel-weight optimization into one unified objective. During each iteration, graph edge weights are updated by a closed-form simplex projection that blends Euclidean proximity with the current margin, while kernel coefficients are adjusted through momentum-augmented mirror descent under simplex constraints. These two updates, followed by a convex \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((\\mathrm{S^3VM})\\)\u003c/span\u003e\u003c/span\u003e subproblem, yield a block-convex procedure whose objective is proven to decrease monotonically and converge to a critical point; the overhead grows only linearly with the number of base kernels. Extensive experiments on diverse benchmark datasets show that AMG-S\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((^3)\\)\u003c/span\u003e\u003c/span\u003eVM consistently surpasses classical Laplacian, deep-kernel, and graph-regularized competitors, yet requires only a coarse grid for a handful of scalar hyper-parameters. The results demonstrate that graph\u0026ndash;kernel co-adaptation provides a principled and computationally efficient route to robust semi-supervised learning.\u003c/p\u003e","manuscriptTitle":"Adaptive Multi-Kernel and Graph Semi-Supervised Support Vector Machine","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-09-29 06:32:36","doi":"10.21203/rs.3.rs-7469419/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-05-13T04:38:08+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-03-20T02:27:56+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"194425460199711312962387474100213359211","date":"2026-03-20T01:28:40+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-10-13T02:16:55+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"314722583469878891231492718549818384047","date":"2025-09-18T10:42:20+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-09-18T07:03:28+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-09-01T02:27:43+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-08-29T03:32:06+00:00","index":"","fulltext":""},{"type":"submitted","content":"International Journal of Machine Learning and Cybernetics","date":"2025-08-27T08:14:02+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"international-journal-of-machine-learning-and-cybernetics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jmlc","sideBox":"Learn more about [International Journal of Machine Learning and Cybernetics](http://actavetscand.biomedcentral.com/)","snPcode":"13042","submissionUrl":"https://submission.nature.com/new-submission/13042/3","title":"International Journal of Machine Learning and Cybernetics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"c62583c4-e6e9-4017-9e8f-6aacafa9050c","owner":[],"postedDate":"September 29th, 2025","published":true,"recentEditorialEvents":[{"type":"decision","content":"Revision requested","date":"2026-05-13T04:38:08+00:00","index":"","fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"in-revision","subjectAreas":[],"tags":[],"updatedAt":"2026-05-13T04:54:34+00:00","versionOfRecord":[],"versionCreatedAt":"2025-09-29 06:32:36","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7469419","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7469419","identity":"rs-7469419","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}