Application of fractional-order derivative in the quantitative estimation of soil organic matter content through visible and near-infrared spectroscopy

The spectral preprocessing method has become an integral component of soil analysis through visible and near-infrared (Vis-NIR) spectroscopy. Various spectral pretreatment techniques are applied to improve model accuracy by removing undesired side effects, such as spectral noise, baseline shift, and light scattering, and by accentuating spectral features. Conventional integer-order derivatives (i.e., first and second derivatives), which represent specific cases of fractional-order derivatives (FODs), may neglect some detailed spectral information related to target variables. The objective of this study was to compare the performance of FOD in the estimation of soil organic matter (SOM) with that of conventional first and second derivatives. A total of 258 soil samples (180 for calibration and 78 for validation) were collected from Jianghan Plain, Central China. The reflectance spectra and SOM concentrations of the samples were obtained in the laboratory. Two regression techniques, namely, partial least squares (PLS) and PLS-support vector machine (PLS-SVM), and eight FOD transformation processes for spectral data were combined and compared. Results indicated that as the derivative order increased, the details of the FOD spectra changed and the spectral resolution of reflectance curves improved; the intensity of the spectral signals, however, weakened. The correlation between SOM and FOD spectra was enhanced at some specific wavelengths (e.g., the absolute value of the best one-dimensional correlation coefficient of the 1.25-order derivative spectra could reach 0.65 but that of the original reflectance spectra was only 0.47). In most cases, the PLS-SVM models performed better in SOM estimation than the PIS models. The PLS-SVM model with the 1.25-order derivative spectra exhibited the best model performance and provided the validation R-2 and ratio of performance to an interquartile range of 0.79 and 3.03, respectively. FOD offers greater advantages in balancing the spectral resolution and the magnitude of spectral strength than traditional integer-order derivatives. Furthermore, the FOD algorithm has strong application potential in soil Vis-NIR spectroscopy and other types of spectroscopy.