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K. Hron, P. Filzmoser:
"Exploring compositional data with the robust compositional biplot";
in: "Advances in Latent Variables. Part of the series Studies in Theoretical and Applied Statistics", M. Carpita, E. Brentari, E.M. Qannari (Hrg.); Springer International Publishing Switzerland, 2015, S. 219 - 226.

Loadings and scores of principal component analysis 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 analy-
sis 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 biplot 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, like in geology, analytical chemistry, or social sciences.

Compositional data . Compositional biplot . Principal component analysis . Robust statistics

http://www.springer.com/us/book/9783319029665