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ICS for multivariate functional anomaly detection with applications to predictive maintenance and quality control

Author

Listed:
  • Aurore Archimbaud

    (Erasmus University Rotterdam)

  • Fériel Boulfani

    (UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse)

  • Xavier Gendre

    (UT - Université de Toulouse)

  • Klaus Nordhausen

    (JYU - University of Jyväskylä)

  • Anne Ruiz-Gazen

    (TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Joni Virta

    (University of Turku)

Abstract

Invariant coordinate selection (ICS) is a multivariate data transformation and a dimension reduction method that can be useful in many different contexts. It can be used for outlier detection or cluster identification, and can be seen as an independent component or a non-Gaussian component analysis method. The usual implementation of ICS is based on a joint diagonalization of two scatter matrices, and may be numerically unstable in some ill-conditioned situations. We focus on one-step M-scatter matrices and propose a new implementation of ICS based on a pivoted QR factorization of the centered data set. This factorization avoids the direct computation of the scatter matrices and their inverse and brings numerical stability to the algorithm. Furthermore, the row and column pivoting leads to a rank revealing procedure that allows computation of ICS when the scatter matrices are not full rank. Several artificial and real data sets illustrate the interest of using the new implementation compared to the original one.

Suggested Citation

  • Aurore Archimbaud & Fériel Boulfani & Xavier Gendre & Klaus Nordhausen & Anne Ruiz-Gazen & Joni Virta, 2025. "ICS for multivariate functional anomaly detection with applications to predictive maintenance and quality control," Post-Print hal-04908598, HAL.
    • Handle: RePEc:hal:journl:hal-04908598
    DOI: 10.1016/j.ecosta.2022.03.003
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    References listed on IDEAS

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    1. Archimbaud, Aurore & Nordhausen, Klaus & Ruiz-Gazen, Anne, 2018. "ICS for multivariate outlier detection with application to quality control," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 184-199.
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    1. Thomas-Agnan, Christine & Mondon, Camille & Trinh, Thi-Huong & Ruiz-Gazen, Anne, 2024. "ICS for complex data with application to outlier detection for density data," TSE Working Papers 24-1585, Toulouse School of Economics (TSE), revised May 2025.

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