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Numerical Considerations and a New Implementation for Invariant Coordinate Selection

Author

Listed:
  • Aurore Archimbaud

    (Erasmus University Rotterdam)

  • Zlatko Drmac

    (University of Zagreb)

  • Klaus Nordhausen

    (JYU - University of Jyväskylä)

  • Una Radojicic

    (TU Wien - Vienna University of Technology = Technische Universität Wien)

  • 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)

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 & Zlatko Drmac & Klaus Nordhausen & Una Radojicic & Anne Ruiz-Gazen, 2023. "Numerical Considerations and a New Implementation for Invariant Coordinate Selection," Post-Print hal-04038657, HAL.
    • Handle: RePEc:hal:journl:hal-04038657
    DOI: 10.1137/22M1498759
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    Cited by:

    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 objects," TSE Working Papers 24_1585, Toulouse School of Economics (TSE).

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