Metabolomics is the systematic study of the small-molecule profiles of biological samples produced by specific cellular processes. The high-throughput technologies used in metabolomic investigations generate datasets where variables are strongly correlated and redundancy is present in the data. Discovering the hidden information is a challenge, and suitable approaches for data analysis must be employed. Projection to latent structures regression (PLS) has successfully solved a large number of problems, from multivariate calibration to classification, becoming a basic tool of metabolomics. PLS2 is the most used implementation of PLS. Despite its success, PLS2 showed some limitations when the so called 'structured noise' affects the data. Suitable methods have been recently introduced to patch up these limitations. In this study, a comprehensive and up-to-date presentation of PLS2 focused on metabolomics is provided. After a brief discussion of the mathematical framework of PLS2, the post-transformation procedure is introduced as a basic tool for model interpretation. Orthogonally-constrained PLS2 is presented as strategy to include constraints in the model according to the experimental design. Two experimental datasets are investigated to show how PLS2 and its improvements work in practice.
Keywords: PLS-DA; orthogonally-constrained PLS2; post-transformation of PLS2; projection to latent structures regression.