A gradient calibration-set reduction framework for evaluating wavelength selection robustness in small-sample near-infrared protein quantification of cereal grains

Near-infrared (NIR) spectroscopy combined with partial least squares regression (PLSR) enables rapid, nondestructive quantification of protein content in cereal grains. However, model reliability depends on the stability of the selected spectral variables, especially under small-sample conditions where independent validation samples are scarce. This work introduces a gradient calibration-set reduction (CSR) framework that systematically varies the prediction-to-calibration sample allocation ratio to map how fixed wavelength subsets respond to calibration-set size, summarized as a robustness profile (mean ± SD of R2P and RMSEP over B = 50 replicated WSPXY partitions per gradient). Four wavelength-selection algorithms—equidistant combination PLS (ECPLS), moving-window PLS (MWPLS), competitive adaptive reweighted sampling (CARS) and uninformative variable elimination (UVE)—were benchmarked against a full-spectrum baseline on two public cereal NIR datasets (corn and wheat protein) within the same CSR workflow. Across CSR gradients from 0.27 to 1.00 (corn) and 0.2 to 1.0 (wheat), the CARS subsets sustained consistently high predictive performance (R2P 0.92–0.95 for corn and 0.76–0.82 for wheat), whereas subsets retaining more non-protein variables tended to degrade more strongly as the calibration set shrank, most pronouncedly for corn. Paired statistical comparisons across the replicated partitions corroborated these rankings. The CSR-derived rankings were cross-referenced with independent external validation sets (10 corn and 108 wheat samples held out a priori). Because a single external snapshot cannot statistically resolve model rankings at these sample sizes (the sampling error of one RMSE estimate is about ±23% of its value at n = 10), the replicated prediction-set assessment served as the primary ranking basis, with external validation as a diagnostic check for overfitting or data leakage. The workflow thus complements conventional single-partition validation with a sample-efficient, statistically grounded robustness assessment for wavelength-selection stability in cereal NIR modeling.