ABSTRACT
Most of the methods in mixOmics employ variants of the Projection to Latent Structures (PLS) method that projects data onto components to reduce their dimensions. These methods define the components differently according to the optimisation of a specific statistical criterion, such as maximising the variance, covariance, or correlation. This chapter begins by describing how PCA can be solved through different techniques, including matrix factorisation and data projection, Singular Value Decomposition (SVD) and the iterative PLS algorithm with Non-linear Iterative Partial Least Squares (NIPALS) to obtain components and loading vectors. The chapter introduces the key concepts of local regressions and deflation, and how missing values are managed during the process. Understanding SVD and NIPALS will enable readers to gain a deeper insight into the algorithms that underpin the methods employed in mixOmics.
