PFCE2: A versatile parameter-free calibration enhancement framework for near-infrared spectroscopy.

Near-infrared (NIR) spectroscopy is a widely used technique for chemical analysis, but it has faced challenges of calibration transfer, maintenance, and enhancement among different instruments and conditions. The parameter-free calibration enhancement (PFCE) framework was developed to address these challenges with non-supervised (NS), semi-supervised (SS), and full-supervised (FS) methods. This study presented PFCE2, an updated version of the PFCE framework that incorporates two new constraints and a new method to improve the robustness and efficiency of calibration enhancement. First, normalized L2 and L1 constraints were introduced to replace the correlation coefficient (Corr) constraint used in the original PFCE. These constraints preserve the parameter-free feature of PFCE and impose smoothness or sparsity on the model coefficients. Second, multitask PFCE (MT-PFCE) was proposed within the framework to address the calibration enhancement among multiple instruments, enabling the framework to be versatile for all possible calibration transfer situations. Demonstrations conducted on three NIR datasets of tablets, plant leaves, and corn showed that the PFCE methods with the new L2 and L1 constraints can result in more accurate and robust predictions than the Corr constraint, especially when the standard sample size is small. Moreover, MT-PFCE could refine all models in the involved scenarios at once, leading to significant enhancement in model performance, compared to the original PFCE method with the same data requirements. Finally, the applicable situations of the PFCE framework and other analogous calibration transfer methods were summarized, facilitating users to choose suitable methods for their application. The source codes written in both MATLAB and Python are available at https://github.com/JinZhangLab/PFCE and https://pypi.org/project/pynir/, respectively.