J-CORE: A Logic-Driven Joint Covariation Representation Framework for Accurate, Stable Regression Modeling with a Transparent Latent Structure Assessed with NIR Spectra.

High-dimensional analytical data pose persistent challenges for supervised multivariate regression, requiring a balance between predictive accuracy, stable performance, and transparent latent representations. However, classical latent-variable regression methods may not fully capture the predictor-response relationship when response-related information is relatively weak compared to dominant background variation, thereby limiting the extraction of informative latent representations. In contrast, flexible machine-learning algorithms can model more complex relationships but often require greater computational effort and careful hyperparameter optimization. To address these challenges, we propose J-CORE (Joint COvariation REpresentation), a calibration framework designed to capture predictor-response covariation through a joint latent-variable representation and subsequently achieve prediction by linking the predictors to the resulting latent representation through regression. Based on the standard framework, two adaptive extension strategies were further incorporated, including a k-coefficient optimization scheme for adjusting the relative variance contribution of weak signal y and a flexible Covariation Mapping Regression (CMR) step, which accommodates both linear and nonlinear regression algorithms to enhance adaptability. For example, by embedding nonlinear enhancements within a linear representation space, J-CORE effectively addresses nonlinear deviations from complex linear analytical matrices, ensuring higher precision while preserving the fundamental transparent structure. The performance of the proposed framework was evaluated on four representative near-infrared spectroscopy (NIRS) datasets, characterized by high dimensionality, severe collinearity, and weak signals. The superiority of J-CORE was comprehensively validated through theoretical derivation, comparative prediction studies against benchmarks (PCR, PLS, SVR), repeated random split experiments, and empirical validation of theoretical principles. The results demonstrate that J-CORE provides competitive predictive performance and stable behavior across different calibration scenarios, while its adaptive extensions enhance flexibility in handling weak response signals and nonlinear relationships. Overall, J-CORE provides a transparent and adaptive calibration framework that offers an effective balance between predictive performance and stability in NIRS modeling.