title: Regularized Partial Least Squares with an Application to NMR Spectroscopy.
abstract: 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 adoption 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.
authors: Department of Statistics, Rice University, Houston, TX, USA ; Department of Pediatrics-Neurology, Baylor College of Medicine, Houston, TX, USA ; Jan and Dan Duncan Neurological Research Institute, Texas Children's Hospital, Houston, TX, USA.
authors: Genevera I
authors: GI
authors: Allen
authors: Department of Statistics, Rice University, Houston, TX, USA.
authors: Christine
authors: C
authors: Peterson
authors: Department of Statistics, Rice University, Houston, TX, USA.
authors: Marina
authors: M
authors: Vannucci
authors: Department of Pediatrics-Neurology, Baylor College of Medicine, Houston, TX, USA ; Jan and Dan Duncan Neurological Research Institute, Texas Children's Hospital, Houston, TX, USA.
authors: Mirjana
authors: M
authors: Maletić-Savatić
keywords: NMR spectroscopy; generalized PCA; generalized PLS; non-negative PLS; sparse PCA; sparse PLS