Principal balances of compositional data for regression and classification using partial least squares

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