Anomaly detection: A functional analysis perspective

Julio E. Castrillón-Candás and Mark Kon

Journal of Multivariate Analysis, 2022, vol. 189, issue C

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.

Keywords: Functional data analysis; Karhunen–Loève expansions; Stochastic processes; Random fields; Multilevel spaces; Computational applied mathematics (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.jmva.2021.104885

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