Smoothed Linear Modeling for Smooth Spectral Data

Classification and prediction problems using spectral data lead to high-dimensional data sets. Spectral data are, however, different from most other high-dimensional data sets in that information usually varies smoothly with wavelength, suggesting that fitted models should also vary smoothly with wavelength. Functional data analysis, widely used in the analysis of spectral data, meets this objective by changing perspective from the raw spectra to approximations using smooth basis functions. This paper explores linear regression and linear discriminant analysis fitted directly to the spectral data, imposing penalties on the values and roughness of the fitted coefficients, and shows by example that this can lead to better fits than existing standard methodologies.