{
  "abstract": "The multivariate time series collected from numerous sensors exhibit complex interwoven relationships, arising from both the coupling among different components and the temporal dependencies of fluctuations within each component. Disentangling these relationships remains a persistent challenge for the time series community. Existing reconstruction-based methods attempt to unravel the intertwined relationships through sequence decomposition and multi-scale modeling. However, the decomposed components remain mixtures of complex latent factors. Moreover, most methods overlook anomalies present in the training set, which inadvertently causes the model to develop a certain affinity toward anomalous patterns. To address these limitations, we propose TFCdetector. Motivated by the intrinsic properties of anomalies, TFCdetector leverages time-frequency domain analysis to explicitly suppress the model’s representation learning of anomalies across diverse granularities and components. To further constrain the model’s learning of anomalies, we propose an energy-correlation constraint loss that operates on both segment-level energy and sequence-level correlation. Notably, the adaptively updated memory storage block enhances the expression of normal patterns by leveraging the affinity between normal patterns in the input sequence and the memory storage block. Furthermore, the meticulously designed twin frequency attention enables the model to dynamically select local or global frequency information beneficial for the task. Extensive experiments on 1 synthetic dataset and 7 real-world datasets show that TFCdetector achieves competitive results in multivariate time series detection tasks.The implementation code is available at https://github.com/FanJY3/TFCdetector.",
  "abstract_shown": true,
  "affiliations": [
    "College of Physics and Electronic Information Engineering, Qinghai Normal University, Xining, China.",
    "College of Computer Technology and Application, Qinghai University, Xining, China.",
    "College of Computer Science and Technology, Xinjiang University, Urumqi, China."
  ],
  "article_type": "Research Article",
  "arxiv": null,
  "author_total": 4,
  "authors": [
    {
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        0
      ],
      "name": "Jinyu Fan"
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    {
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        0
      ],
      "name": "Jianfei Zhao"
    },
    {
      "affs": [
        0,
        1
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      "name": "Jun Ma",
      "orcid": "0009-0007-3495-8160"
    },
    {
      "affs": [
        2
      ],
      "name": "Yuxi Cai"
    }
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  "doi": "10.1371/journal.pone.0361145",
  "fulltext_url": "https://europepmc.org/articles/PMC13716231",
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  "published": "2026-10-28",
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  "subjects": [
    {
      "field": "biology",
      "origin": "heading:Developmental Biology",
      "subfield": "developmental-biology"
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  "title": "TFCdetector: Multivariable time series anomaly detection with time-frequency constraints",
  "title_text": "TFCdetector: Multivariable time series anomaly detection with time-frequency constraints",
  "type": "peer-reviewed",
  "updated_at": "2026-11-01T12:23:16Z",
  "url": "https://research.draconitic.com/paper/94wdnbn196v4c",
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