## 4 Results
### Case Study of PLS-MARS Method
#### 4.2.3 Comparison of the PLS-MARS Model with Typical Prediction Models  
The MLR, PLS, SVM, and PLS-GWR methods were utilized to construct the SOM prediction model based on the VNIR spectra in the research region to verify the availability of the PLS-MARS method. The precision of the prediction method was substantially correlated with the selected calibration set. Hence, the C, KS, Rank-KS, and MVARC-R-KS methods were introduced to obtain the representative calibration sets. The performance of the models was evaluated using fitness assessment indices (e.g., AICc, \(R_{c}^{2}\), RMSEV, \(R_{p}^{2}\), RMSEP, and RPD) (Table 4). Two conclusions could be drawn. One was that the performance of the prediction models highly relied on the selected calibration sets; such performance was achieved for the following reasons. The results imply that the accuracies of the models based on different calibration sets fluctuated heavily. For example, the prediction models calibrated using the calibration sets selected by the C and KS methods had poor prediction capabilities. The Rank-KS method selected the calibration \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Prediction Model**} & \multirow{2}{*}{**Selection Method**} & \multicolumn{2}{c}{**Corrected Akaike**} & \multirow{2}{*}{\(R_{c}^{2}\)} & \multirow{2}{*}{\(R_{p}^{2}\)} & \multirow{2}{*}{\(R_{p}^{2}\)} & \multirow{2}{*}{**RMSEP**} \\  & & **Information Criterion (AICc)** & & & & & **(g kg\({}^{-1}\))** \\ \hline \multirow{4}{*}{MLR} & C & 1005.54 & 0.54 & 8.9 & 0.11 & 28.0 & 0.44 \\  & KS & 973.4 & 0.62 & 8.19 & 0.11 & 26.0 & 0.47 \\  & Rank–KS & 948.65 & 0.50 & 9.04 & 0.22 & 23.1 & 0.52 \\  & MVARC-R-KS & 937.79 & 0.54 & 8.9 & 0.09 & 30.8 & 0.39 \\ \hline \multirow{4}{*}{PLS} & C & 877.64 & 0.73 & 6.39 & 0.53 & 8.21 & 1.48 \\  & KS & 844.87 & 0.78 & 5.87 & 0.50 & 8.82 & 1.38 \\  & Rank–KS & 829.80 & 0.71 & 6.51 & 0.56 & 8.48 & 1.51 \\  & MVARC-R-KS & 785.50 & 0.79 & 5.83 & 0.70 & 6.98 & 1.61 \\ \hline \multirow{4}{*}{SVM} & C & 996.75 & 0.54 & 8.70 & 0.50 & 8.78 & 1.38 \\  & KS & 972.02 & 0.58 & 8.16 & 0.39 & 9.47 & 1.29 \\  & Rank–KS & 912.02 & 0.55 & 8.17 & 0.46 & 9.34 & 1.38 \\  & MVARC-R-KS & 935.36 & 0.50 & 8.84 & 0.55 & 8.11 & 1.56 \\ \hline \multirow{4}{*}{PLS-GWR} & C & 1187.90 & 0.75 & 5.80 & 0.54 & 8.18 & 1.49 \\  & KS & 1227.43 & 0.79 & 5.19 & 0.50 & 8.76 & 1.42 \\  & Rank–KS & 1190.26 & 0.76 & 5.55 & 0.60 & 8.02 & 1.60 \\  & MVARC-R-KS & 1213.80 & 0.74 & 6.12 & 0.66 & 6.83 & 1.78 \\ \hline \multirow{4}{*}{PLS-MARS} & C & 1156.61 & 0.80 & 5.45 & 0.53 & 8.20 & 1.48 \\  & KS & 1213.20 & 0.83 & 5.12 & 0.55 & 8.13 & 1.50 \\ \cline{1-1}  & Rank–KS & 1166.12 & 0.79 & 5.50 & 0.62 & 7.88 & 1.63 \\ \cline{1-1}  & MVARC-R-KS & 1135.50 & 0.84 & 5.14 & 0.71 & 6.52 & 1.94 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Evaluation results of prediction models calibrated by different calibration set selection methods. Figure 6: Root-mean-square error (RMSEV) of the prediction model constructed using the latent variables (i.e., principal components (PCs)). set for building prediction models with relatively higher accuracies than those of the C and KS methods. The prediction models calibrated by the samples obtained utilizing the MVARC-R-KS method had the highest prediction accuracies. These results sufficiently verified the dependency of the performance of the prediction models on the selected calibration sets. Because the PLS-GWR model was a local prediction model, the calibration sets had less effect on the prediction results. Another conclusion was that the PLS-MARS method outperformed the typical prediction models for estimating VNIR-spectrum-based SOM content in the study area. The following results support this conclusion. The results in Table 4 show that the MLR model had poor prediction accuracies and thus could not be used to predict SOM content in the study area. The possible reason is due to the inapplicability of these methods for complex high-dimension data sets.