Network Reliability Analysis by means of Generalized Matrix Learning Vector Quantization

Network Reliability Analysis by means of Generalized Matrix Learning Vector Quantization | 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 Network Reliability Analysis by means of Generalized Matrix Learning Vector Quantization Klaus Dohmen, Mandy Lange-Geisler, Thomas Villmann This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7014031/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 26 Feb, 2026 Read the published version in Applied Network Science → Version 1 posted 9 You are reading this latest preprint version Abstract We present a new approach for assessing the reliability of an error-prone system or network by using a prototype-based classification method. More specifically, reliability levels for consecutive \(k\) -out-of- \(n\) success systems and failure networks are classified using Generalized Matrix Learning Vector Quantization (GMLVQ), which provides useful information about the impact of the input probabilities on the classified reliability levels. To increase the interpretability of the learned relevance matrix in GMLVQ, we propose two graph-based visualization strategies to reveal structural patterns and relevant feature interactions, which are of considerable importance for the classification of the reliability levels. Our approach is generally applicable to any coherent system and can even be adapted to estimate the probability of any union of finitely many events, based on their individual and pairwise intersection probabilities. network reliability system reliability prototype-based classification matrix learning vector quantization interpretable machine learning Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 26 Feb, 2026 Read the published version in Applied Network Science → Version 1 posted Editorial decision: Revision requested 27 Oct, 2025 Reviews received at journal 26 Oct, 2025 Reviewers agreed at journal 06 Oct, 2025 Reviews received at journal 30 Sep, 2025 Reviewers agreed at journal 03 Sep, 2025 Reviewers invited by journal 18 Aug, 2025 Editor assigned by journal 28 Jul, 2025 Submission checks completed at journal 11 Jul, 2025 First submitted to journal 30 Jun, 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-7014031","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":504598490,"identity":"e7d3beed-917b-46b8-a66a-9f173810b9e3","order_by":0,"name":"Klaus Dohmen","email":"","orcid":"","institution":"Mittweida University of\n Applied Sciences","correspondingAuthor":false,"prefix":"","firstName":"Klaus","middleName":"","lastName":"Dohmen","suffix":""},{"id":504598492,"identity":"d739dc73-d0ea-4f0d-8cae-b43b30134be8","order_by":1,"name":"Mandy Lange-Geisler","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABAUlEQVRIiWNgGAWjYDACdjApIWcAohJABDMDkM2GRwszmLQwhmhJMCBaS0XiBjCdANaJX4tuM/Ozh18qJNK38x9g3fDwx5/EfnbmjR8YymxwajE7zGZuLHNGInfnjAS2G0CHJc5sZiuWYDiXhkcLg5m0ZJtE7oYb/N9AWnI3HOYxkGBsO4xHC/s3acl/EukG5w+Abcndf5jH+Adj2388WnjMJD82SCQYHIA4LHcDM48Z0JYD+LSUSTMckzDccAOkJc24fsZhtjKLhHPJuLUcb98m+aOmTh7ksJs/bOSM+fsPb77xocwOpxYQYObBEErAq4GBgfEHAQWjYBSMglEwwgEAjoZTuAhaazoAAAAASUVORK5CYII=","orcid":"","institution":"Mittweida University of\n Applied Sciences","correspondingAuthor":true,"prefix":"","firstName":"Mandy","middleName":"","lastName":"Lange-Geisler","suffix":""},{"id":504598500,"identity":"33e0667c-c945-4865-bfd9-418a4c95a28d","order_by":2,"name":"Thomas Villmann","email":"","orcid":"","institution":"Mittweida University of\n Applied Sciences","correspondingAuthor":false,"prefix":"","firstName":"Thomas","middleName":"","lastName":"Villmann","suffix":""}],"badges":[],"createdAt":"2025-06-30 20:38:17","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7014031/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7014031/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s41109-026-00776-5","type":"published","date":"2026-02-26T15:58:37+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":103765692,"identity":"9e63dba0-2d6c-4e85-8513-c949d00b6cce","added_by":"auto","created_at":"2026-03-02 16:07:43","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":384795,"visible":true,"origin":"","legend":"","description":"","filename":"SubmissiontoAppliedNetworkScience.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7014031/v1_covered_bc593e70-d5e3-4739-96cf-ce86487bb5e5.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Network Reliability Analysis by means of Generalized Matrix Learning Vector Quantization","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":"applied-network-science","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"apns","sideBox":"Learn more about [Applied Network Science](http://appliednetsci.springeropen.com/)","snPcode":"41109","submissionUrl":"https://submission.nature.com/new-submission/41109/3","title":"Applied Network Science","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"network reliability, system reliability, prototype-based classification, matrix learning vector quantization, interpretable machine learning","lastPublishedDoi":"10.21203/rs.3.rs-7014031/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7014031/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe present a new approach for assessing the reliability of an error-prone system or network by using a prototype-based classification method. More specifically, reliability levels for consecutive \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(k\\)\u003c/span\u003e\u003c/span\u003e-out-of-\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\\)\u003c/span\u003e\u003c/span\u003e success systems and failure networks are classified using Generalized Matrix Learning Vector Quantization (GMLVQ), which provides useful information about the impact of the input probabilities on the classified reliability levels. To increase the interpretability of the learned relevance matrix in GMLVQ, we propose two graph-based visualization strategies to reveal structural patterns and relevant feature interactions, which are of considerable importance for the classification of the reliability levels. Our approach is generally applicable to any coherent system and can even be adapted to estimate the probability of any union of finitely many events, based on their individual and pairwise intersection probabilities.\u003c/p\u003e","manuscriptTitle":"Network Reliability Analysis by means of Generalized Matrix Learning Vector Quantization","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-08-26 05:49:37","doi":"10.21203/rs.3.rs-7014031/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-10-27T14:03:51+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-10-26T04:37:09+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"231582969069221334124553111622427024498","date":"2025-10-06T08:08:23+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-09-30T10:05:59+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"296915956979218806102928298361931798447","date":"2025-09-03T09:44:29+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-08-18T13:36:36+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-07-28T14:27:25+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-07-11T17:18:01+00:00","index":"","fulltext":""},{"type":"submitted","content":"Applied Network Science","date":"2025-06-30T20:36:21+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"applied-network-science","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"apns","sideBox":"Learn more about [Applied Network Science](http://appliednetsci.springeropen.com/)","snPcode":"41109","submissionUrl":"https://submission.nature.com/new-submission/41109/3","title":"Applied Network Science","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"79e3befb-bdf5-4bc1-8fd0-ece9b527f2e4","owner":[],"postedDate":"August 26th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2026-03-02T16:04:33+00:00","versionOfRecord":{"articleIdentity":"rs-7014031","link":"https://doi.org/10.1007/s41109-026-00776-5","journal":{"identity":"applied-network-science","isVorOnly":false,"title":"Applied Network Science"},"publishedOn":"2026-02-26 15:58:37","publishedOnDateReadable":"February 26th, 2026"},"versionCreatedAt":"2025-08-26 05:49:37","video":"","vorDoi":"10.1007/s41109-026-00776-5","vorDoiUrl":"https://doi.org/10.1007/s41109-026-00776-5","workflowStages":[]},"version":"v1","identity":"rs-7014031","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7014031","identity":"rs-7014031","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}