Projection to latent structures with orthogonal constraints for metabolomics data

Multivariate techniques based on projection methods such as Principal Component Analysis and Partial Least Squares (PLS) regression are widely applied in metabolomics. However, the effects of confounding factors and the presence of specific clusters in the data could force the projection to produce inefficient representations in the latent space, preventing the identification of the most relevant data variation. To overcome this issue, we introduce a general framework for projection methods, allowing an easy integration of orthogonal constraints, which help in reducing the effect of uninformative variations. In particular, the discussed algorithms address different scenarios. When known confounding factors can be explicitly encoded into a proper constraint matrix, orthogonally Constrained Principal Component Analysis (oCPCA) and orthogonally Constrained PLS2 (oCPLS2) can be used. Orthogonal PLS (OPLS) and post‐transformation of PLS2 (ptPLS2), instead, are suited to problems in which a constraint matrix cannot be defined. Finally, a data integration task is considered: Orthogonal two‐block PLS (O2PLS) and Orthogonal Wold's two‐block Mode A PLS (OPLS‐W2A) are used to identify the common variation between two data sets