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Outlier Detection for Compositional Data Using Robust Methods

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Abstract

Outlier detection based on the Mahalanobis distance (MD) requires an appropriate transformation in case of compositional data. For the family of logratio transformations (additive, centered and isometric logratio transformation) it is shown that the MDs based on classical estimates are invariant to these transformations, and that the MDs based on affine equivariant estimators of location and covariance are the same for additive and isometric logratio transformation. Moreover, for 3-dimensional compositions the data structure can be visualized by contour lines. In higher dimension the MDs of closed and opened data give an impression of the multivariate data behavior.

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Authors and Affiliations

  1. Dept. of Statistics and Probability Theory, Vienna University of Technology, Wiedner Hauptstr. 8-10, 1040, Vienna, Austria

    Peter Filzmoser

  2. Dept. of Mathematical Analysis and Applications of Mathematics, Palacký University Olomouc, Tomkova 40, 77100, Olomouc, Czech Republic

    Karel Hron

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  1. Peter Filzmoser
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  2. Karel Hron
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Correspondence to Peter Filzmoser.

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Filzmoser, P., Hron, K. Outlier Detection for Compositional Data Using Robust Methods. Math Geosci 40, 233–248 (2008). https://doi.org/10.1007/s11004-007-9141-5

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  • DOI: https://doi.org/10.1007/s11004-007-9141-5

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