Independent Component Analysis for Compositional Data
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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.
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