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

Aurore Archimbaud, Fériel Boulfani, Xavier Gendre, Klaus Nordhausen, Anne Ruiz-Gazen () and Joni Virta
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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

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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.

Keywords: Affine invariance; Functional outlier map; Global ICS; Outliers; Point-wise ICS; Scatter matrices (search for similar items in EconPapers)
Date: 2025-01
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Published in Econometrics and Statistics , 2025, 33, pp.282-303. ⟨10.1016/j.ecosta.2022.03.003⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-04908598

DOI: 10.1016/j.ecosta.2022.03.003

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