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High-dimensional compositional data are commonplace in the modern omicssciences amongst others. Analysis of compositional data requires a properchoice of orthonormal coordinate representation as their relative nature is notcompatible with the direct use of standard statistical methods. Principalbalances, a specific class of log-ratio coordinates, are well suited to thiscontext since they are constructed in such a way that the first few coordinatescapture most of the variability in the original data. Focusing on regressionand classification problems in high dimensions, we propose a novel PartialLeast Squares (PLS) based procedure to construct principal balances thatmaximize explained variability of the response variable and notably facilitatesinterpretability when compared to the ordinary PLS formulation. The proposedPLS principal balance approach can be understood as a generalized version ofcommon logcontrast models, since multiple orthonormal (instead of one)logcontrasts are estimated simultaneously. We demonstrate the performance ofthe method using both simulated and real data sets.

Principal Balances of Compositional Data for Regression and Classification using Partial Least Squares