  High-dimensional compositional data are commonplace in the modern omics
sciences amongst others. Analysis of compositional data requires a proper
choice of orthonormal coordinate representation as their relative nature is not
compatible with the direct use of standard statistical methods. Principal
balances, a specific class of log-ratio coordinates, are well suited to this
context since they are constructed in such a way that the first few coordinates
capture most of the variability in the original data. Focusing on regression
and classification problems in high dimensions, we propose a novel Partial
Least Squares (PLS) based procedure to construct principal balances that
maximize explained variability of the response variable and notably facilitates
interpretability when compared to the ordinary PLS formulation. The proposed
PLS principal balance approach can be understood as a generalized version of
common logcontrast models, since multiple orthonormal (instead of one)
logcontrasts are estimated simultaneously. We demonstrate the performance of
the method using both simulated and real data sets.
