[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82123-en":3,"doc-seo-82123-105":29,"detail-sidebar-cat-0-en-105":90},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},82123,1099514067415,"Rowan","https://ap-avatar.wpscdn.com/avatar/100002539d78ffe74a7?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779092875211072502",8,"Research & Report","Federated Low-Rank Koopman Learning for Multivariate Time-Series Anomaly Detection in IoT Systems","Distributed IoT systems produce multivariate time-series streams for monitoring physical assets, servers, and embedded sensors, where identifying abnormal temporal evolution is vital for fault diagnosis, predictive maintenance, and security. Conventional IoT anomaly detection is constrained by non-IID decentralized data, limited bandwidth, and restricted edge compute and memory. FedKAD proposes a resource-efficient federated Koopman framework using lightweight sliding-window representations and low-rank consensus to exchange compact subspace variables only, enabling local residual-based inference and improved accuracy with major reductions in training, communication, and latency.","Federated Low-Rank Koopman Learning for Multivariate Time-Series Anomaly Detection in IoT  \nSystems  \nTung-Anh Nguyen, Van-Phuc Bui, Anh Tuyen Le, Kim Hue Ta,  \nMinh Thuy Le, J.Andrew Zhang, and Xiaojing Huang  \narXiv :2607 .08978v 1 [ cs .LG] 9 Jul 2026  \nAbstract—Distributed IoT systems generate multivariate timeseries streams for monitoring physical assets, servers, and embedded sensing platforms. Detecting abnormal temporal behavior is critical for fault diagnosis, predictive maintenance, and security. However, practical IoT anomaly detection is hindered by decentralized and non-IID data, limited bandwidth, and the constrained computation and memory of edge devices. This paper proposes FedKAD, a resource-efficient federated Koopman anomaly detection framework for distributed IoT multivariate time series. Unlike deep-learning-based anomaly detectors that require training and communicating large neural models, FedKAD learns normal temporal dynamics through lightweight sliding-window Koopman representations. Federated training is formulated as a low-rank consensus problem, where raw sensor streams and local reduced dynamics remain on device while only compact subspace variables are exchanged with the server. To optimize the shared representation under orthonormality constraints, we develop a federated Stiefel-ADMM algorithm and provide convergence and stationarity analysis under partial client participation. During inference, each client detects anomalies locally by measuring the prediction residual between observed future trajectories and the learned Koopman dynamics. Experiments on four widely used multivariate time-series anomaly detection benchmarks show that FedKAD maintains or improves detection performance compared with federated deep-learning baselines. More importantly for IoT deployment, FedKAD provides up to 2 . 1×103 faster training, 80× lower communication, and 79 × lower inference latency than neural baselines, confirming its suitability for resource-constrained edge devices.  \nIndex Terms—Internet of Things, Federated Learning, Anomaly Detection, Multivariate Time Series, Koopman Operator, Stiefel Manifold, Edge Intelligence.  \nI. INTRODUCTION  \nDistributed Internet-of-Things (IoT) systems generate multivariate time-series (MVTS) streams for monitoring physical assets, industrial processes, servers, spacecraft subsystems, and embedded sensing platforms. Detecting abnormal temporal behavior in these streams is essential for fault diagnosis, predictive maintenance, and security monitoring [1],[2] . Unlike conventional offline anomaly detection, IoT anomaly detection must often operate continuously at the network edge, where  \nT.-A Nguyen, A. T. Le, J. A. Zhang, and X. Huang are with Faculty of Engineering and IT, University of Technology Sydney, Ultimo, NSW, 2007, Australia (emails: [tunganh.nguyen@uts.edu.au](tunganh.nguyen@uts.edu.au), [anhtuyen.le@uts.edu.au](anhtuyen.le@uts.edu.au),  \n[andrew.zhang@uts.edu.au](andrew.zhang@uts.edu.au), [xiaojing.huang@uts.edu.au](xiaojing.huang@uts.edu.au)). V.-P Bui is with the Faculty of Information Technology, FPT University, Vietnam (email: [phucbv5@fe.edu.vn](phucbv5@fe.edu.vn)). Kim Hue Ta and Minh Thuy Le are with School of Electrical and Electronic Engineering, Hanoi University of Science and Technology, Vietnam (email: [hue.tathikim@hust.edu.vn](hue.tathikim@hust.edu.vn), [minhthuy.le@hust.edu.vn](minhthuy.le@hust.edu.vn)).  \nsensor streams are produced by geographically distributed devices with limited communication, computation, memory, and energy resources. These constraints make it difficult to rely on centralized data collection or computationally expensive models, especially when raw sensor measurements are privacysensitive or operationally restricted.  \nA fundamental challenge in IoT MVTS anomaly detection is that abnormal behavior is rarely limited to an isolated point outlier. In many practical systems, faults, cyberattacks, and degradation patterns appear a","cbCaioLduRiHvqct","https://ap.wps.com/l/cbCaioLduRiHvqct","pdf",686070,1,14,"English","en",105,"# Introduction\n## Challenges in IoT Multivariate Time-Series Anomaly Detection\n## Related Work: Classical and Deep-Learning Methods","[{\"question\":\"Why is anomaly detection in IoT multivariate time-series difficult in practice?\",\"answer\":\"It must run continuously at the network edge under decentralized, non-IID data and tight limits on bandwidth, computation, memory, and energy, making centralized learning or heavy models impractical.\"},{\"question\":\"What does FedKAD change compared with deep-learning-based federated anomaly detectors?\",\"answer\":\"FedKAD avoids training and communicating large neural models by learning normal temporal dynamics via lightweight sliding-window Koopman representations and exchanging only compact subspace variables through federated low-rank consensus.\"},{\"question\":\"How are anomalies detected during inference in FedKAD?\",\"answer\":\"Each client flags anomalies locally by measuring the prediction residual between observed future trajectories and the learned Koopman dynamics.\"}]",1784178330,35,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":27},"federated-low-rank-koopman-learning-for-multivariate-time-series-anomaly-detection-in-iot-systems","",{"@graph":35,"@context":84},[36,53,67],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/federated-low-rank-koopman-learning-for-multivariate-time-series-anomaly-detection-in-iot-systems/82123/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":61,"encodingFormat":60,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-16",true,{"@type":64,"interactionType":65,"userInteractionCount":4},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"Why is anomaly detection in IoT multivariate time-series difficult in practice?","Question",{"text":74,"@type":75},"It must run continuously at the network edge under decentralized, non-IID data and tight limits on bandwidth, computation, memory, and energy, making centralized learning or heavy models impractical.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"What does FedKAD change compared with deep-learning-based federated anomaly detectors?",{"text":79,"@type":75},"FedKAD avoids training and communicating large neural models by learning normal temporal dynamics via lightweight sliding-window Koopman representations and exchanging only compact subspace variables through federated low-rank consensus.",{"name":81,"@type":72,"acceptedAnswer":82},"How are anomalies detected during inference in FedKAD?",{"text":83,"@type":75},"Each client flags anomalies locally by measuring the prediction residual between observed future trajectories and the learned Koopman 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