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Eng."],"published-print":{"date-parts":[[2026,6]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Industrial processes often involve the generation\u2014and the analysis\u2014of multivariate time series data, which poses several challenges from the anomaly detection perspective. In addition to the need to detect previously unseen anomalies, the high dimensionality of industrial datasets introduces the complexity of simultaneously analyzing multiple features and their interactions. Finally, industrial datasets are typically highly imbalanced, with minimal information on anomalous processes. To address these issues, we propose a novel anomaly detection framework that introduces two embedding models, based on Time2Vec and Discrete Wavelet Transforms, leveraging their capabilities to represent multivariate time series as vectors while capturing and preserving temporal dependencies and combining them with several classifiers to enhance the overall performance of anomaly detection. We tested our solution using a publicly available benchmark dataset and a real industrial use case, particularly data collected from a Bonfiglioli gear manufacturing plant. The results demonstrate that, unlike traditional reconstruction-based autoencoders, which often struggle with sporadic noise, our embedding-based solutions maintain high performance across various noise conditions.<\/jats:p>","DOI":"10.1007\/s41019-025-00295-w","type":"journal-article","created":{"date-parts":[[2025,6,24]],"date-time":"2025-06-24T04:47:49Z","timestamp":1750740469000},"page":"378-394","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Embedding Models for Multivariate Time Series Anomaly Detection in Industry 5.0"],"prefix":"10.1007","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-9681-9842","authenticated-orcid":false,"given":"Lorenzo","family":"Colombi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-4350-8151","authenticated-orcid":false,"given":"Michela","family":"Vespa","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-6053-433X","authenticated-orcid":false,"given":"Nicolas","family":"Belletti","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-2363-8509","authenticated-orcid":false,"given":"Matteo","family":"Brina","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7335-9773","authenticated-orcid":false,"given":"Simon","family":"Dahdal","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-9661-394X","authenticated-orcid":false,"given":"Filippo","family":"Tabanelli","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-9900-717X","authenticated-orcid":false,"given":"Francesco","family":"Resca","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3717-3779","authenticated-orcid":false,"given":"Elena","family":"Bellodi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7417-4455","authenticated-orcid":false,"given":"Mauro","family":"Tortonesi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4617-1836","authenticated-orcid":false,"given":"Cesare","family":"Stefanelli","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Massimiliano","family":"Vignoli","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,6,24]]},"reference":[{"issue":"4","key":"295_CR1","doi-asserted-by":"publisher","first-page":"540","DOI":"10.1109\/TSUSC.2023.3293269","volume":"8","author":"M Anisetti","year":"2023","unstructured":"Anisetti M, Ardagna CA, Balestrucci A, Bena N, Damiani E, Yeun CY (2023) On the robustness of random forest against untargeted data poisoning: an ensemble-based approach. 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