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ICS for multivariate outlier detection with application to quality control

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  • Archimbaud, Aurore
  • Nordhausen, Klaus
  • Ruiz-Gazen, Anne

Abstract

In high reliability standards fields such as automotive, avionics or aerospace, the detection of anomalies is crucial. An efficient methodology for automatically detecting multivariate outliers is introduced. It takes advantage of the remarkable properties of the Invariant Coordinate Selection (ICS) method which leads to an affine invariant coordinate system in which the Euclidian distance corresponds to a Mahalanobis Distance (MD) in the original coordinates. The limitations of MD are highlighted using theoretical arguments in a context where the dimension of the data is large. Owing to the resulting dimension reduction, ICS is expected to improve the power of outlier detection rules such as MD-based criteria. The paper includes practical guidelines for using ICS in the context of a small proportion of outliers. The use of the regular covariance matrix and the so called matrix of fourth moments as the scatter pair is recommended. This choice combines the simplicity of implementation together with the possibility to derive theoretical results. The selection of relevant invariant components through parallel analysis and normality tests is addressed. A simulation study confirms the good properties of the proposal and provides a comparison with Principal Component Analysis and MD. The performance of the proposal is also evaluated on two real data sets using a user-friendly R package accompanying the paper.

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  • 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.
    • Handle: RePEc:eee:csdana:v:128:y:2018:i:c:p:184-199
    DOI: 10.1016/j.csda.2018.06.011
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    Cited by:

    1. Loperfido, Nicola, 2021. "Some theoretical properties of two kurtosis matrices, with application to invariant coordinate selection," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    2. Javed, Farrukh & Loperfido, Nicola & Mazur, Stepan, 2024. "The Method of Moments for Multivariate Random Sums," Working Papers 2024:6, Örebro University, School of Business.
    3. Ruiz-Gazen, Anne & Thomas-Agnan, Christine & Laurent, Thibault & Mondon, Camille, 2022. "Detecting outliers in compositional data using Invariant Coordinate Selection," TSE Working Papers 22-1320, Toulouse School of Economics (TSE).
    4. Nordhausen, Klaus & Ruiz-Gazen, Anne, 2022. "On the usage of joint diagonalization in multivariate statistics," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    5. Thomas-Agnan, Christine & Mondon, Camille & Trinh, Thi-Huong & Ruiz-Gazen, Anne, 2024. "ICS for complex data with application to outlier detection for density data objects," TSE Working Papers 24_1585, Toulouse School of Economics (TSE).
    6. Archimbaud, Aurore & Boulfani, Fériel & Gendre, Xavier & Nordhausen, Klaus & Ruiz-Gazen, Anne & Virta, Joni, 2021. "ICS for multivariate functional anomaly detection with applications to predictive maintenance and quality control," TSE Working Papers 21-1182, Toulouse School of Economics (TSE), revised Mar 2022.

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