Events and Meetings of Italian Statistical Society, Advances in Latent Variables - Methods, Models and Applications

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Exploring compositional data with the robust compositional biplot
Karel Hron, Peter Filzmoser

Last modified: 2013-06-16

Abstract


Principal component analysis is a method for extracting the important information from a multivariate data set. The resulting loadings and scores, containing the information of the principal component directions and the projected data, are popularly displayed together in a planar graph, called biplot, with an intuitive interpretation. In case of compositional data, multivariate observations that carry only relative information (represented usually in proportions or percentages), principal component analysis cannot be used for the original compositions. They first need to be transformed using the centered logratio (clr) transformation. If outlying observations occur in compositional data, even the clr (compositional) biplot can lead to useless conclusions. A robust alternative can be computed by using the isometric logratio (ilr) transformation, and by robustly estimating location and covariance. The robust compositional biplot has a big potential in many applications (geology, analytical chemistry, social sciences).

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