## 3 Results and Discussion
### The Best Regression Models of Visible Near-Infrared (VIS-NIR)  
This manuscript demonstrates the performance of all the best models that not only contain PLS, SVR, and boosting but also ElasticNet, Lasso, and Ridge [27; 28] because these three methods are also used frequently. Table 6 shows that PLS, SVR, and boosting algorithms are the best because the RPD levels of ElasticNet, Lasso, and Ridge are only level B or level C. The best model for the PLS algorithm is PLS_RBF, which has LV and Gamma parameters of 27 and 0.1, respectively. The LVs of PLS_linear and PLS_sigmoid are 14 and 16, respectively. The best model for the SVR algorithm is SVR_RBF, which has C and Gamma parameters of 150,000 and 0.1, respectively. The kernel function of RBF is shown to be better than the linear and sigmoid functions. The C values of SVR_linear and SVR_sigmoid are 40,000 and 1,270,000, respectively. The number of estimators is 3100 and 100, respectively, for GBRT and AdaBoost. Considering the \(R^{2}\) of these best models, PLS_linear, PLS_RBF, SVR_RBF, GBRT, and AdaBoost are over 0.9 with the testing dataset, and the RPD level of only PLS_linear is B. The best pretreatment methods for PLS_RBF, SVR_RBF, GBRT, and AdaBoost are DT, SG + DT, FD, SG + LG + FD, respectively. Therefore, different regression algorithms correspond to different pretreatment datasets to achieve optimal performance.  
Figure 6: Ratio of performance to interquartile distance (RPIQ) value of regression models with different pretreatment methods.  
Figure 7 shows the RPIQ values of the best models from the discrete levels of the RPD value. The values of SVR_RBF, PLS_RBF, GBRT, and AdaBoost are more important than those of the other methods, and GBRT and AdaBoost are preferable to PLS_RBF and SVR_RBF.  
Figure 8 shows the comparison diagram of SVR_RBF, PLS_RBF, GBRT, and AdaBoost with the testing dataset. The details of the evaluation metrics show that the RPD value of GBRT is higher than that of AdaBoost, but AdaBoost has better accuracy and stability than GBRT from the comparison of RPIQ values. Meanwhile, the \(R^{2}\) and RMSE values of AdaBoost are also preferable to those of GBRT. Through the above analysis, the AdaBoost algorithm was determined to exhibit the best performance in predicting the soil-available potassium content by VIS-NIR.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Regression** & \multicolumn{2}{c}{**Training Dataset**} & \multicolumn{2}{c}{**Testing Dataset**} & \multicolumn{2}{c}{**RPD**} & \multicolumn{2}{c}{**Pretreatment**} & \multicolumn{1}{c}{**Parameters**} \\ \cline{2-7}
**Model** & \(\mathbf{R^{2}}\) & **RMSE** & \(\mathbf{R^{2}}\) & **RMSE** & **Level** & **Methods** & **Parameters** \\ \hline PLS\_linear & 0.90 & 44.3 & 0.903 & 39.8 & B & SG + LG & LVs = 14 \\ \hline PLS\_sigmoid & 0.90 & 42.4 & 0.887 & 42.9 & B & SG + MC & LVs = 16, Gamma = 0.005 \\ \hline PLS\_RBF & 0.97 & 23.3 & 0.928 & 34.3 & A & DT & LVs = 27, Gamma = 0.1 \\ \hline SVR\_linear & 0.90 & 42.5 & 0.876 & 45.0 & B & SG + LG & C = 40,000 \\ \hline SVR\_sigmoid & 0.88 & 47.1 & 0.842 & 49.8 & B & SG + DT & C = 1,270,000, Gamma = 0.005 \\ \hline SVR\_RBF & 0.95 & 28.9 & 0.923 & 35.5 & A & SG + DT & C = 150,000, Gamma = 0.1 \\ \hline GBRT & 0.99 & 5.53 & 0.939 & 31.5 & A & FD & Estimators = 3100 \\ \hline AdaBoost & 0.99 & 13.7 & 0.941 & 31.2 & A & SG + LG + FD & Estimators = 100 \\ \hline ElasticNet & 0.84 & 53.2 & 0.818 & 54.6 & C & SG + FD & L1 = 0.3, Alpha = \(2\times 10^{-6}\) \\ \hline Lasso & 0.83 & 56.3 & 0.843 & 50.7 & B & SG & Alpha = 0.02 \\ \hline Ridge & 0.9 & 41.9 & 0.853 & 49.0 & B & SG + LG + FD & Alpha = 0.0001 \\ \hline \hline \end{tabular}
\end{table}
Table 6: The performance and parameters of the best regression models.  
Figure 7: RPIQ and accuracy of the best regression models.