## 2 Materials and Methods
### Data Sets and Data Processing
#### 2.1.2 Data Preprocessing  
For data preprocessing, this study employed piecewise pooling averaging (PPA), also known as the bin-averaging method. PPA is a dimensionality-reduction technique that applies local mean pooling to high-dimensional spectral data: the spectrum is partitioned into fixed intervals, and the mean of each interval is computed to generate a compressed feature set. This procedure preserves global trend information while effectively suppressing random noise and lowering computational cost. Given that Vis-NIR spectra typically comprise thousands of bands, PPA was used to condense the original 4200-dimensional \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Element** & **Set** & **Size** & **Mean** & **Std** & **Median** & **Mode** & **Kurtosis** & **Iqr** \\ \hline \multirow{3}{*}{Clay (\%)} & Complete & 17,939 & 18.88 & 13.00 & 17.00 & 4.00 & 0.69 & 18.50 \\  & Test & 5980 & 18.88 & 13.01 & 17.00 & 4.00 & 0.69 & 18.25 \\  & Train & 11,959 & 18.89 & 13.00 & 17.00 & 4.00 & 0.69 & 18.50 \\ \hline \multirow{3}{*}{Silt (\%)} & Complete & 17,939 & 38.23 & 18.30 & 37.00 & 32.00 & \(-\)0.54 & 26.00 \\  & Test & 5980 & 38.23 & 18.30 & 37.00 & 32.00 & \(-\)0.54 & 26.00 \\  & Train & 11,959 & 38.23 & 18.30 & 37.00 & 32.00 & \(-\)0.54 & 26.00 \\ \hline \multirow{3}{*}{Sand (\%)} & Complete & 17,939 & 42.88 & 26.11 & 42.00 & 5.00 & \(-\)1.10 & 45.00 \\  & Test & 5980 & 42.87 & 26.11 & 42.00 & 5.00 & \(-\)1.10 & 45.00 \\  & Train & 11,959 & 42.89 & 26.11 & 42.00 & 5.00 & \(-\)1.10 & 45.00 \\ \hline \multirow{3}{*}{PH in CaCl\({}_{2}\)} & Complete & 19,031 & 5.59 & 1.43 & 5.64 & 7.36 & \(-\)1.30 & 2.68 \\  & Test & 6344 & 5.60 & 1.43 & 5.64 & 7.36 & \(-\)1.29 & 2.68 \\  & Train & 12,687 & 5.59 & 1.43 & 5.65 & 7.36 & \(-\)1.30 & 2.68 \\ \hline \multirow{3}{*}{PH in H\({}_{2}\)O} & Complete & 19,031 & 6.20 & 1.35 & 6.21 & 7.76 & \(-\)1.24 & 2.45 \\  & Test & 6344 & 6.20 & 1.35 & 6.21 & 7.76 & \(-\)1.24 & 2.45 \\  & Train & 12,687 & 6.20 & 1.35 & 6.21 & 7.76 & \(-\)1.24 & 2.45 \\ \hline \multirow{3}{*}{OC (g/kg)} & Complete & 19,031 & 49.92 & 91.19 & 20.80 & 11.40 & 13.53 & 27.00 \\  & Test & 6344 & 49.34 & 90.40 & 20.60 & 11.40 & 13.95 & 26.70 \\  & Train & 12,687 & 50.22 & 91.58 & 20.80 & 11.40 & 13.32 & 27.10 \\ \hline \multirow{3}{*}{CaCO\({}_{3}\) (g/kg)} & Complete & 19,031 & 51.61 & 125.33 & 1.00 & 0.00 & 9.07 & 12.00 \\  & Test & 6344 & 51.71 & 125.59 & 1.00 & 0.00 & 9.00 & 12.00 \\  & Train & 12,687 & 51.56 & 125.21 & 1.00 & 0.00 & 9.10 & 12.00 \\ \hline \multirow{3}{*}{N (g/kg)} & Complete & 19,031 & 2.92 & 3.75 & 1.70 & 1.20 & 16.85 & 1.70 \\  & Test & 6344 & 2.91 & 3.73 & 1.70 & 1.20 & 16.31 & 1.70 \\  & Train & 12,687 & 2.92 & 3.76 & 1.70 & 1.20 & 17.11 & 1.70 \\ \hline \multirow{3}{*}{P (mg/kg)} & Complete & 19,031 & 30.05 & 32.81 & 22.30 & 0.00 & 173.50 & 32.00 \\  & Test & 6344 & 29.98 & 32.66 & 22.20 & 0.00 & 71.46 & 31.90 \\  & Train & 12,687 & 30.09 & 32.88 & 22.40 & 0.00 & 223.09 & 32.00 \\ \hline \multirow{3}{*}{K (mg/kg)} & Complete & 19,030 & 196.99 & 229.29 & 136.40 & 0.00 & 166.43 & 176.80 \\  & Test & 6343 & 195.13 & 229.66 & 135.50 & 0.00 & 185.74 & 174.40 \\ \cline{1-1}  & Train & 12,687 & 197.92 & 229.11 & 137.00 & 0.00 & 156.71 & 177.95 \\ \hline \multirow{3}{*}{CEC (mol(+)/kg)} & Complete & 19,031 & 15.75 & 14.48 & 12.40 & 0.00 & 34.08 & 13.30 \\ \cline{1-1}  & Test & 6344 & 15.73 & 14.55 & 12.40 & 0.00 & 37.99 & 13.30 \\ \cline{1-1}  & Train & 12,687 & 15.76 & 14.45 & 12.40 & 0.00 & 32.07 & 13.30 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Dataset statistics table. spectral vectors to 128 dimensions, substantially improving both computational efficiency and training speed without sacrificing predictive accuracy. Let the original spectral matrix be \(\text{A}_{\text{x}}\in R^{m\times n}\), where m is the sample and n is the feature dimension.