## 4 Results
### Case Study of PLS-MARS Method
#### 4.2.1 Calibration Set Selected Using MVARC-R-KS Method  
The procedure of selecting the calibration set using the MVARC-R-KS method comprised two phases [3]. Phase 1 consisted of obtaining clustering zones with similar influences of the environment on SOM content. Phase 2 utilized the Rank-KS method to select representative samples from the clustering zones. The selected samples were eventually merged as the calibration set (Figure 4). Typical methods, such as C, KS, and Rank-KS methods, were used for comparison to verify the representation of the calibration set. If the calibration set was representative, then the distribution characteristics of the calibration set would be similar to the entire samples. The statistical values of SOM content and the spectral reflectance information of the calibration sets selected by the aforementioned methods were calculated and are shown in Figure 5 and Table 3. The results showed that the mean and median values of the SOM content in the calibration set selected by the KS method were lower than those in the entire samples. In contrast to the KS method, the C, Rank-KS, and MVARC-R-KS methods obtained calibration sets having a considerably similar distribution to the entire samples for SOM content. Compared with the calibration sets selected by the KS, Rank-KS, and MVARC-R-KS methods, the calibration set selected by the C method had less similar spectral reflectance information to that of the entire samples. Compared with the C, KS, and Rank-KS methods, the MVARC-R-KS method further took into consideration the spatial variation and impacts of the environmental variables [3].  
Figure 4: Calibration and validation samples selected utilizing the regional multi-variable associate rule mining and Rank–Kennard-Stone (MVARC-R-KS) method.  
In summary, the calibration set selected by the MVARC-R-KS method was the SOM content, spectrum representative, and environment representative [3]. Hence, the MVARC-R-KS method seemed to be reasonable to select a representative calibration set.  
2.2 Performance of the PLS-MARS Model Calibrated by the Calibration Set Selected Utilizing the MVARC-R-KS Method  
The PLS-MARS method was used to build the SOM prediction model based on the VNIR spectra in accordance with the selected calibration set (Figure 4). PCs were first calculated and selected. The count of PCs was set at 10, with the highest precision (i.e., RMSE) of the constructed regression model (Figure 6) based on the PC selection procedure described in Phase 1 of Section 3.2. Thereafter, the PLS-MARS model was constructed based on the PCs and SOM content. The PLS-MARS model was eventually evaluated. Table 4 shows the fit assessments of the prediction model. The result indicated that the PLS-MARS model calibrated by the samples selected utilizing the MVARC-R-KS method [3] could estimate SOM content with high stability and prediction precision.  
Figure 5: Statistics of the soil organic matter (SOM) content in the following samples: (1) all samples; (2) samples selected utilizing the concentration gradient (C) method; (3) samples selected utilizing the Rank–Kennard-Stone (Rank–KS) method; (4) samples selected using the Rank method; (5) samples selected utilizing the MVARC-R-KS method.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Statistic Values**} & \multirow{2}{*}{**All Samples**} & \multicolumn{4}{c}{**Samples Selected by Typical Methods**} \\ \cline{3-6}  & & **C** & **Rank–KS** & **KS** & **MVARC-R-KS** \\ \hline Mean & 0.3542 & 0.3495 & 0.3563 & 0.3561 & 0.3541 \\ Variation & 0.0369 & 0.0360 & 0.0404 & 0.0401 & 0.0405 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Statistical values of the spectral reflectance information in the samples.