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

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