Regularized Partial Least Squares with an Application to NMR Spectroscopy

TL;DR

This paper introduces a flexible regularized Partial Least Squares framework that improves dimension reduction in high-dimensional structured data, demonstrated through simulations and NMR spectroscopy case studies.

Contribution

It presents a novel regularized PLS method with penalties on loadings, extending to Non-negative and Generalized PLS for structured data analysis.

Findings

Enhanced interpretability and flexibility of PLS methods.

Fast computation suitable for high-dimensional data.

Successful application to NMR spectroscopy data.

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 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.