Simultaneous hyperspectral quantitative analysis of amylose and amylopectin in foxtail millet using a heterogeneous stacking ensemble with a soft constraint on component error complementarity

The eating quality and processing characteristics of foxtail millet are primarily determined by the content and ratio of amylose and amylopectin, both of which directly influence gelatinization properties, texture, and digestibility. Traditional chemical analysis methods are tedious, time-consuming, labor-intensive, and destructive, making it difficult to meet the demands of large-scale germplasm screening and rapid quality evaluation. Hyperspectral imaging (HSI) technology has emerged as a vital tool for cereal quality analysis owing to its rapid, non-destructive, and multi-component synchronous detection capabilities. However, existing single-model approaches exhibit limited accuracy when handling complex spectral data and generally overlook the reciprocal complementary relationship between amylose and amylopectin, leading to poor prediction self-consistency and weak chemical interpretability. To address these issues, this work proposes a heterogeneous stacking ensemble modeling strategy that incorporates a soft constraint on component error complementarity. The strategy first employs three complementary base learners - partial least squares regression (PLSR), support vector regression (SVR), and extreme learning machine (ELM) - to independently optimize feature wavelengths via a hybrid variable selection algorithm combing competitive adaptive reweighted sampling (CARS) and iteratively retains informative variables (IRIV), thereby generating diverse meta-features. Subsequently, these meta-features are fed into a Ridge regression meta-learner embedded with a soft constraint term, which penalizes same-sign prediction errors and encourages opposite-sign errors between amylose and amylopectin, guiding the model to capture the inherent complementary structure of the two components. Experimental results show that the proposed constrained stacking model achieves a ratio of performance to deviation (RPD) of 2.75 for amylose and 2.45 for amylopectin, significantly outperforming the best single model (ELM: RPD of 2.31 and 2.13) and the unconstrained stacking model (RPD of 2.36 and 2.15). Concurrently, the mean absolute deviation of the sum of the two components' prediction errors drops from 0.37 g/100 g for the unconstrained model to 0.09 g/100 g, indicating a marked improvement in prediction self-consistency. The proposed method effectively balances prediction accuracy with chemical interpretability, offering a novel approach for the simultaneous multi-component quantitative analysis of cereals.