A Hybrid Statistical–Transformer Autoencoder Framework for Point and Contextual Anomaly Detection in Multivariate Operational Time-Series Data

A Hybrid Statistical–Transformer Autoencoder Framework for Point and Contextual Anomaly Detection in Multivariate Operational Time-Series Data | 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 A Hybrid Statistical–Transformer Autoencoder Framework for Point and Contextual Anomaly Detection in Multivariate Operational Time-Series Data Naeem Akhtar, Anurag Rana This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9133369/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Anomaly detection in a multivariate operational time series data is a critical requirement for intelligent information systems to support reliable monitoring and decision making in the modern cloud and data center environments. However, current statistical methods are prone to overlook contextual oddities, whereas the deep learning reconstruction models may be threshold-instable and have false alarm problems. To overcome these drawbacks, in this work, the hybrid approach to the detection of anomalies based on the processing of statistical deviations (Z-score and interquartile range) and the Transformer Autoencoder for the reconstruction of the context of the sequence is proposed. The proposed approach combines statistical evidence of anomaly and contextual reconstruction error in deep by weighted fusion approach in detection of point anomalies and contextual anomalies effectively. Experiments were performed on the Server Machine Dataset (SMD) which is a collection of telemetry data from 28 heterogeneous server machines with 38 operating features each. The results show that the hybrid model is better than statistical-only model and Transformer-only model with Mean Precision = 0.295581, Recall = 0.456487, F1-score = 0.289387 and ROC-AUC = 0.882706. These results confirm the advantages of combining the power of statistical reasoning with Transformer-based contextual modelling in order to improve the robustness of anomaly detection and increase the decision reliability in operational monitoring systems. Physical sciences/Engineering Physical sciences/Mathematics and computing Multivariate time series Anomaly detection Transformer autoencoder Statistical deviation Intelligent information systems Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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. 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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-9133369","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":611906186,"identity":"8d33273d-06e4-4df3-9470-e39bbd609d93","order_by":0,"name":"Naeem Akhtar","email":"data:image/png;base64,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","orcid":"","institution":"Shoolini University","correspondingAuthor":true,"prefix":"","firstName":"Naeem","middleName":"","lastName":"Akhtar","suffix":""},{"id":611906187,"identity":"26f2a5d8-4864-461a-9f32-a09a0606bb0f","order_by":1,"name":"Anurag Rana","email":"","orcid":"","institution":"Shoolini University","correspondingAuthor":false,"prefix":"","firstName":"Anurag","middleName":"","lastName":"Rana","suffix":""}],"badges":[],"createdAt":"2026-03-16 05:40:11","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9133369/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9133369/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":108627444,"identity":"643f6f62-e863-4b4b-853c-d642c2c2d70e","added_by":"auto","created_at":"2026-05-06 15:56:29","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":585849,"visible":true,"origin":"","legend":"","description":"","filename":"JIIS.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9133369/v1_covered_fe51d471-8e4d-48d8-86e5-9e36b9cb2efa.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A Hybrid Statistical–Transformer Autoencoder Framework for Point and Contextual Anomaly Detection in Multivariate Operational Time-Series Data","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Multivariate time series, Anomaly detection, Transformer autoencoder, Statistical deviation, Intelligent information systems","lastPublishedDoi":"10.21203/rs.3.rs-9133369/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9133369/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eAnomaly detection in a multivariate operational time series data is a critical requirement for intelligent information systems to support reliable monitoring and decision making in the modern cloud and data center environments. However, current statistical methods are prone to overlook contextual oddities, whereas the deep learning reconstruction models may be threshold-instable and have false alarm problems. To overcome these drawbacks, in this work, the hybrid approach to the detection of anomalies based on the processing of statistical deviations (Z-score and interquartile range) and the Transformer Autoencoder for the reconstruction of the context of the sequence is proposed. The proposed approach combines statistical evidence of anomaly and contextual reconstruction error in deep by weighted fusion approach in detection of point anomalies and contextual anomalies effectively. Experiments were performed on the Server Machine Dataset (SMD) which is a collection of telemetry data from 28 heterogeneous server machines with 38 operating features each. The results show that the hybrid model is better than statistical-only model and Transformer-only model with Mean Precision\u0026thinsp;=\u0026thinsp;0.295581, Recall\u0026thinsp;=\u0026thinsp;0.456487, F1-score\u0026thinsp;=\u0026thinsp;0.289387 and ROC-AUC\u0026thinsp;=\u0026thinsp;0.882706. These results confirm the advantages of combining the power of statistical reasoning with Transformer-based contextual modelling in order to improve the robustness of anomaly detection and increase the decision reliability in operational monitoring systems.\u003c/p\u003e","manuscriptTitle":"A Hybrid Statistical–Transformer Autoencoder Framework for Point and Contextual Anomaly Detection in Multivariate Operational Time-Series Data","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-27 20:28:06","doi":"10.21203/rs.3.rs-9133369/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"58e2ebef-5387-43bc-b2f9-9f31a806d87c","owner":[],"postedDate":"March 27th, 2026","published":true,"recentEditorialEvents":[{"type":"decision","content":"Rejected","date":"2026-05-06T15:51:14+00:00","index":"","fulltext":""},{"type":"reviewerAgreed","content":"178085525399789618431682030049758947173","date":"2026-04-29T19:19:33+00:00","index":48,"fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":65103943,"name":"Physical sciences/Engineering"},{"id":65103944,"name":"Physical sciences/Mathematics and computing"}],"tags":[],"updatedAt":"2026-05-06T15:55:49+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-27 20:28:06","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9133369","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9133369","identity":"rs-9133369","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}