  Compositional data represent a specific family of multivariate data, where
the information of interest is contained in the ratios between parts rather
than in absolute values of single parts. The analysis of such specific data is
challenging as the application of standard multivariate analysis tools on the
raw observations can lead to spurious results. Hence, it is appropriate to
apply certain transformations prior further analysis. One popular multivariate
data analysis tool is independent component analysis. Independent component
analysis aims to find statistically independent components in the data and as
such might be seen as an extension to principal component analysis. In this
paper we examine an approach of how to apply independent component analysis on
compositional data by respecting the nature of the former and demonstrate the
usefulness of this procedure on a metabolomic data set.
