Sparse methods in spectroscopy: an introduction, overview, and perspective

Multivariate calibration methods such as partial least-squares build calibration models that are not parsimonious: all variables (either wavelengths or samples) are used to define a calibration model. In high-dimensional or large sample size settings, interpretable analysis aims to reduce model complexity by finding a small subset of variables that significantly influences the model. The term "sparsity", as used here, refers to calibration models having many zero-valued regression coefficients. Only the variables associated with non-zero coefficients influence the model. In this paper, we briefly review the regression problems associated with sparse models and discuss their spectroscopic applications. We also discuss how one can re-appropriate sparse modeling algorithms that perform wavelength selection for purposes of sample selection. In particular, we highlight specific sparse modeling algorithms that are easy to use and understand for the spectroscopist, as opposed to the overly complex "black-box" algorithms that dominate much of the statistical learning literature. We apply these sparse modeling approaches to three spectroscopic data sets.