Interpretation of multivariate outliers for compositional data

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.