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Anomaly detection: A functional analysis perspective

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  • Castrillón-Candás, Julio E.
  • Kon, Mark

Abstract

We develop a new approach for detecting anomalies in the behavior of stochastic processes and random fields. The approach uses tensor product representations, in particular the multivariate Karhunen–Loève (KL) expansion on complex domains. From the associated eigenspaces of the covariance operator a series of nested function spaces are constructed, allowing detection of signals lying in orthogonal subspaces. In particular this can succeed even if the stochastic behavior of the signal changes either in a global or local sense. A mathematical approach is developed to locate and measure sizes of extraneous components based on construction of multilevel nested subspaces. We show examples in R and on a spherical domain S2. However, the method is flexible, allowing the detection of orthogonal signals on general topologies, including spatio-temporal domains.

Suggested Citation

  • Castrillón-Candás, Julio E. & Kon, Mark, 2022. "Anomaly detection: A functional analysis perspective," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    • Handle: RePEc:eee:jmvana:v:189:y:2022:i:c:s0047259x21001639
    DOI: 10.1016/j.jmva.2021.104885
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    References listed on IDEAS

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