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The use of a common location measure in the invariant coordinate selection and projection pursuit

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  • Alashwali, Fatimah
  • Kent, John T.

Abstract

Invariant coordinate selection (ICS) and projection pursuit (PP) are two methods that can be used to detect clustering directions in multivariate data by optimizing criteria sensitive to non-normality. In particular, ICS finds clustering directions using a relative eigen-decomposition of two scatter matrices with different levels of robustness; PP is a one-dimensional variant of ICS. Each of the two scatter matrices includes an implicit or explicit choice of location. However, when different measures of location are used, ICS and PP can behave counter-intuitively. In this paper we explore this behavior in a variety of examples and propose a simple and natural solution: use the same measure of location for both scatter matrices.

Suggested Citation

  • Alashwali, Fatimah & Kent, John T., 2016. "The use of a common location measure in the invariant coordinate selection and projection pursuit," Journal of Multivariate Analysis, Elsevier, vol. 152(C), pages 145-161.
    • Handle: RePEc:eee:jmvana:v:152:y:2016:i:c:p:145-161
    DOI: 10.1016/j.jmva.2016.08.007
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    References listed on IDEAS

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    1. David E. Tyler & Frank Critchley & Lutz Dümbgen & Hannu Oja, 2009. "Invariant co‐ordinate selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 549-592, June.
    2. Pena D. & Prieto F.J., 2001. "Cluster Identification Using Projections," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1433-1445, December.
    3. Peña, Daniel & Prieto, Francisco J. & Viladomat, Júlia, 2010. "Eigenvectors of a kurtosis matrix as interesting directions to reveal cluster structure," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 1995-2007, October.
    4. Nordhausen, Klaus & Oja, Hannu & Tyler, David E., 2008. "Tools for Exploring Multivariate Data: The Package ICS," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 28(i06).
    5. Todorov, Valentin & Filzmoser, Peter, 2009. "An Object-Oriented Framework for Robust Multivariate Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i03).
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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. Ortiz, Santiago & Laniado, Henry & Peña, Daniel & Prieto, Francisco J., 2026. "Dimension reduction for outlier detection in high-dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 211(C).
    3. Nordhausen, Klaus & Ruiz-Gazen, Anne, 2022. "On the usage of joint diagonalization in multivariate statistics," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    4. Becquart, Colombe & Archimbaud, Aurore & Ruiz-Gazen, Anne & Prilé, Luka & Nordhausen, Klaus, 2024. "Invariant Coordinate Selection and Fisher Discriminant Subspace Beyond The Case of Two Groups," TSE Working Papers 24-1579, Toulouse School of Economics (TSE).
    5. 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.
    6. Becquart, Colombe & Archimbaud, Aurore & Ruiz-Gazen, Anne & Prilć, Luka & Nordhausen, Klaus, 2026. "Invariant Coordinate Selection and Fisher discriminant subspace beyond the case of two groups," Journal of Multivariate Analysis, Elsevier, vol. 211(C).
    7. Nicola Loperfido, 2023. "Kurtosis removal for data pre-processing," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(1), pages 239-267, March.

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