  High-dimensional data common in genomics, proteomics, and chemometrics often
contains complicated correlation structures. Recently, partial least squares
(PLS) and Sparse PLS methods have gained attention in these areas as dimension
reduction techniques in the context of supervised data analysis. We introduce a
framework for Regularized PLS by solving a relaxation of the SIMPLS
optimization problem with penalties on the PLS loadings vectors. Our approach
enjoys many advantages including flexibility, general penalties, easy
interpretation of results, and fast computation in high-dimensional settings.
We also outline extensions of our methods leading to novel methods for
Non-negative PLS and Generalized PLS, an adaption of PLS for structured data.
We demonstrate the utility of our methods through simulations and a case study
on proton Nuclear Magnetic Resonance (NMR) spectroscopy data.
