Validating Spectral Quality Measures as Proxies for Task Performance: A Controlled-Perturbation Framework for Raman Spectroscopy

Abstract

Raman preprocessing and enhancement methods are often assessed by comparing their output with a clean reference spectrum using measures such as mean squared error (MSE). Whether these spectral quality measures reflect downstream analytical performance is rarely tested. We propose a controlled-perturbation framework for this test. Five perturbation types (baseline distortion, independent noise, correlated noise, global wavenumber shift, and nonlinear axis warping) at eight strengths produce paired changes in a quality measure (metric harm) and in downstream performance (task harm). The alignment gap (AG) quantifies how much a single monotone metric-to-task relationship, fitted by isotonic regression, improves when each perturbation type receives its own relationship. Ordering concordance (OC), a clustered Kendall-type index, measures how often a measure ranks conditions of different perturbation types in the same order as their task harm. Cluster-bootstrap intervals and Holm-adjusted sign-flip tests compare twelve candidate measures with MSE. Three public datasets are used: bacterial classification by principal component analysis and logistic regression, sugar-mixture quantification by partial least squares regression, and mineral identification by cosine library matching. Models are fitted to unperturbed or to correspondingly perturbed training spectra. For bacterial classifiers fitted to unperturbed spectra, Wasserstein distance improved both statistics relative to MSE (Holm-adjusted p < 0.05), also after axis perturbations were removed or spectra were compared on a common grid; refitting to perturbed spectra reversed this advantage. Peak-based measures and a structure-to-noise ratio improved both statistics only for refitted sugar calibrations, and no candidate did so for mineral identification. Open code supports testing new measures.