## 2 Materials and Methods
### Spectral Data Feature Band Selection  
It is vital to perform feature band selection on the preprocessed soil hyperspectral data in order to draw out the most pertinent and important information from the vast array of spectral bands and lessen data redundancy and noise. In order to concentrate on certain spectral areas of interest and record the spectrum responses of target substances or characteristics, this selection process seeks to find the bands that are closely connected to the study objectives. This makes it easier to analyze the target components or traits quantitatively or qualitatively. The selection of feature bands not only lowers the cost of storing and processing data, but also increases the effectiveness and precision of model training. The link between spectral data and geophysical features is better understood since it makes it simpler for the model to learn and create correlations with the target. Common methods for feature band selection, as mentioned in [17], include successive projections algorithm (SPA), principal component analysis (PCA), Competitive Adaptive Reweighted Sampling (CARS), and SCARS. Among these methods, SCARS demonstrates significant advantages in dealing with high-dimensional data and complex problems. It effectively captures the intrinsic structure and relationships between features during the feature selection and sample resampling processes. It not only automatically adjusts the weights of  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Differential** & \multicolumn{3}{c}{**Differential**} \\
**Transformation** & **Theoretical Formula** & **Transformation** & **Theoretical Formula** \\
**Method** & & **Method** & \\ \hline FD & \(\widetilde{\mathrm{x}}^{\prime}\) & SD & \(\widetilde{\mathrm{x}}^{\prime}\) \\ LFD & \((\log\widetilde{\mathrm{x}})^{\prime}\) & LSD & \((\log\widetilde{\mathrm{x}})^{\prime}\) \\ RFD & \((1/\widetilde{\mathrm{x}})^{\prime}\) & RSD & \((1/\widetilde{\mathrm{x}})^{\prime}\) \\ LRFD & \((1/\log(\widetilde{\mathrm{x}}))^{\prime}\) & LRSD & \((1/\log(\widetilde{\mathrm{x}}))^{\prime}\) \\ RLFD & \((\log(1/\widetilde{\mathrm{x}}))^{\prime}\) & RLSD & \((\log(1/\widetilde{\mathrm{x}}))^{\prime}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Differential transformation methods and their theoretical formulas.  
samples based on their distribution, effectively handling imbalanced or noisy datasets, but also quickly converges to the global optimal solution. Moreover, it retains the maximum amount of information from the original data while keeping a smaller sample size, thereby improving the predictive performance and generalization ability of the model [18].  
The computational process of using SCARS to find the optimal subset of variables in spectral data consists of N cyclic processes. In each iteration, SCARS first calculates the stability of each wavelength variable. Variables with larger stable values are then screened as a new subset of variables via Adaptive Reweighted Sampling and Exponentially Decreasing Function. After multiple iterations of selection, the final subset of variables is obtained. The Partial Least Squares Regression model is then applied to this final subset to calculate the root mean square error of cross-validation (RMSECV). Finally, the subset with the smallest RMSECV value is chosen as the optimal subset of variables, representing the optimal feature bands.