Robust Constrained Partial Least Squares: A Robust Integrated Algorithm for Multivariate Regression in the Presence of Outliers, Interfering Analytes, and Structured External Influences

ABSTRACT Partial least squares (PLS) regression is widely used for multivariate calibration in high‐dimensional and collinear settings. However, classical PLS relies on least squares optimization and is therefore sensitive to anomalous observations, leverage points, and structured spectral interferences. Robust PLS variants mitigate the influence of outliers via alternative estimators or iterative reweighting, whereas orthogonalization strategies such as external parameter orthogonalization (EPO) aim to remove structured external variation. These approaches are typically applied independently, despite the frequent coexistence of outliers and structured external variation in real spectroscopic data. We propose robust constrained partial least squares (RC‐PLS), a unified algorithm that integrates iterative reweighting within each LV extraction step with constrained orthogonalization of loading vectors against predefined structured external variation. The proposed algorithm retains the computational structure of classical PLS while improving robustness and interpretability. Evaluation on NIR and Raman datasets demonstrates enhanced prediction stability and reduced sensitivity to both anomalous samples and structured external variation compared with standard PLS. RC‐PLS provides a coherent framework for constrained and robust latent variables regression in real‐world chemometric applications.