Regularized linear and kernel redundancy analysis

Redundancy analysis (RA) is a versatile technique used to predict multivariate criterion variables from multivariate predictor variables. The reduced-rank feature of RA captures redundant information in the criterion variables in a most parsimonious way. A ridge type of regularization was introduced in RA to deal with the multicollinearity problem among the predictor variables. The regularized linear RA was extended to nonlinear RA using a kernel method to enhance the predictability. The usefulness of the proposed procedures was demonstrated by a Monte Carlo study and through the analysis of two real data sets.