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


  • Alashwali, Fatimah
  • Kent, John T.


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

    1. 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.
    2. 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).
    3. 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.
    4. 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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