Interpretation of multivariate outliers for compositional data

Authors:
Peter Filzmoser;Karel Hron;Clemens Reimann
Affiliations:
Department of Statistics and Probability Theory, Vienna University of Technology, Wiedner Hauptstraíe 8-10, A-1040 Vienna, Austria;Department of Mathematical Analysis and Applications of Mathematics, Palacký University, Faculty of Science, 17. listopadu 12, CZ-77146 Olomouc, Czech Republic;Geological Survey of Norway (NGU), P.O.Box 6315 Sluppen, N-7491 Trondheim, Norway
Venue:
Computers & Geosciences
Year:
2012

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Abstract

Compositional data-and most data in geochemistry are of this type-carry relative rather than absolute information. For multivariate outlier detection methods this implies that not the given data but appropriately transformed data need to be used. We use the isometric logratio (ilr) transformation, which seems to be generally the most proper one for theoretical and practical reasons. In this space it is difficult to interpret the outliers, because the reason for outlyingness can be complex. Therefore we introduce tools that support the interpretation of outliers by representing multivariate information in biplots, maps, and univariate scatterplots.