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<p>Multivariate calibration techniques such as Partial Least Squares (PLS) and Principal Component Regression (PCR) are widely used for quantitative analysis of complex spectral data. However, the structural interpretation of the resulting regression vector and its relationship with analyte selectivity and non-analyte spectral variation remains underexplored. In this work, we introduce a geometrical framework for calibration that explicitly constructs the model vector based on subspace projection and a duality-based description of PCR. This approach provides a transparent interpretation of the calibration vector beyond algorithmic computation. The proposed methodology is evaluated using a noise-free simulated multicomponent dataset and experimentally using a well-characterized corn near-infrared (NIR) dataset with multiple analytes. Under ideal simulated conditions, the descriptive model vector, standard PCR, and PLS all recover the same analyte direction with negligible calibration and prediction errors, confirming theoretical consistency. In the experimental case, regression vectors obtained from descriptive and duality-based PCR are compared with conventional PCR and PLS for four analytes, demonstrating comparable predictive performance and structural consistency across methods. By focusing on the geometry and explicit construction of regression vectors, this study provides a comprehensive perspective on multivariate calibration, laying a conceptual foundation for future calibration updating and model transfer strategies.</p>

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A descriptive formulation of the model vector in multivariate calibration

  • 期刊论文

  • 发表日期：

    2026年5月11日

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  • Somaye Vali Zade

摘要

Multivariate calibration techniques such as Partial Least Squares (PLS) and Principal Component Regression (PCR) are widely used for quantitative analysis of complex spectral data. However, the structural interpretation of the resulting regression vector and its relationship with analyte selectivity and non-analyte spectral variation remains underexplored. In this work, we introduce a geometrical framework for calibration that explicitly constructs the model vector based on subspace projection and a duality-based description of PCR. This approach provides a transparent interpretation of the calibration vector beyond algorithmic computation. The proposed methodology is evaluated using a noise-free simulated multicomponent dataset and experimentally using a well-characterized corn near-infrared (NIR) dataset with multiple analytes. Under ideal simulated conditions, the descriptive model vector, standard PCR, and PLS all recover the same analyte direction with negligible calibration and prediction errors, confirming theoretical consistency. In the experimental case, regression vectors obtained from descriptive and duality-based PCR are compared with conventional PCR and PLS for four analytes, demonstrating comparable predictive performance and structural consistency across methods. By focusing on the geometry and explicit construction of regression vectors, this study provides a comprehensive perspective on multivariate calibration, laying a conceptual foundation for future calibration updating and model transfer strategies.