Hyperspectral Soil Metal Estimation Using Fractional-Order Derivatives and LSTM–KAN Modeling

Hyperspectral estimation of soil heavy metals is challenging because their spectral responses are weak, indirect, and strongly affected by the soil matrix. In this study, 167 surface soil samples collected from a karst open-pit coal mining area in Guizhou, China, were analyzed for As, Cr, Cu, and Hg. Spectra were processed using fractional-order derivative (FOD) preprocessing over orders of 0.0–2.0 and reorganized into wavelength-ordered sequences for a long short-term memory network coupled with a Kolmogorov–Arnold network regression head (LSTM–KAN). Random forest (RF), partial least-squares regression (PLSR), and LSTM with a fully connected regression head (LSTM–FC) were used for comparison. Using the same 117/50 sample-level holdout split across all models and elements, LSTM–KAN achieved the best overall validation performance, with a mean R2 of 0.9692 across the four metals. The holdout-selected FOD orders were 1.2 for As and Hg, 1.8 for Cr, and 1.4 for Cu. 10-fold cross-validation further supported the internal consistency of LSTM–KAN, yielding overall R2 values of 0.9148–0.9879. Spectral regions showing strong metal–reflectance correlations were mainly concentrated around 2200–2300 nm, while the FOD orders maximizing spectral correlation differed from those producing the best predictive performance. These results demonstrate that combining FOD preprocessing with wavelength-ordered sequence modeling can improve quantitative estimation of soil heavy metals within the Jinsha study area data set.