1.8. Cross decomposition

The cross decomposition module contains two main families of algorithms: thepartial least squares (PLS) and the canonical correlation analysis (CCA).

These families of algorithms are useful to find linear relations between twomultivariate datasets: the X and Y arguments of the fit methodare 2D arrays.

Cross decomposition algorithms find the fundamental relations between twomatrices (X and Y). They are latent variable approaches to modeling thecovariance structures in these two spaces. They will try to find themultidimensional direction in the X space that explains the maximummultidimensional variance direction in the Y space. PLS-regression isparticularly suited when the matrix of predictors has more variables thanobservations, and when there is multicollinearity among X values. By contrast,standard regression will fail in these cases.

Classes included in this module are PLSRegressionPLSCanonical, CCA and PLSSVD

Reference:

• JA WegelinA survey of Partial Least Squares (PLS) methods, with emphasis on the two-block case

Examples:

• Compare cross decomposition methods