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Discriminant analysis for compositional data and robust parameter estimation

Author

Listed:
  • Peter Filzmoser

    ()

  • Karel Hron

    ()

  • Matthias Templ

    ()

Abstract

Compositional data, i.e. data including only relative information, need to be transformed prior to applying the standard discriminant analysis methods that are designed for the Euclidean space. Here it is investigated for linear, quadratic, and Fisher discriminant analysis, which of the transformations lead to invariance of the resulting discriminant rules. Moreover, it is shown that for robust parameter estimation not only an appropriate transformation, but also affine equivariant estimators of location and covariance are needed. An example and simulated data demonstrate the effects of working in an inappropriate space for discriminant analysis. Copyright Springer-Verlag 2012

Suggested Citation

  • Peter Filzmoser & Karel Hron & Matthias Templ, 2012. "Discriminant analysis for compositional data and robust parameter estimation," Computational Statistics, Springer, vol. 27(4), pages 585-604, December.
  • Handle: RePEc:spr:compst:v:27:y:2012:i:4:p:585-604
    DOI: 10.1007/s00180-011-0279-8
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    References listed on IDEAS

    as
    1. He, Xuming & Fung, Wing K., 2000. "High Breakdown Estimation for Multiple Populations with Applications to Discriminant Analysis," Journal of Multivariate Analysis, Elsevier, vol. 72(2), pages 151-162, February.
    2. Hron, K. & Templ, M. & Filzmoser, P., 2010. "Imputation of missing values for compositional data using classical and robust methods," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3095-3107, December.
    3. John Aitchison & Michael Greenacre, 2002. "Biplots of compositional data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 51(4), pages 375-392.
    4. Hubert, Mia & Van Driessen, Katrien, 2004. "Fast and robust discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 301-320, March.
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