## 3 Results
### Accuracy Assessment of Spatial Decomposition Results Using Twelve Regression Models  
The accuracy of the decomposition results derived from the various algorithms was evaluated using metrics such as RMSE, MAPE, and so on. The accuracy assessment of the spatial decomposition results derived from the twelve algorithms is shown in Table 7.  
We can see immediately from Table 7 that the decomposition accuracy of the OLS model was the worst as the RMSE value of the OLS model exceeded 200 and the R\({}^{2}\) value was only 0.19. Hence, an obvious inference is that the OLS model has an overfitting problem in our study case. Compared with the OLS model, the decomposition accuracies of the BSR model, the RANSAC model and the LARS model were significantly improved. The comparison results demonstrated that subsetting is an effective method to correct the overfitting problem. However, among the three subsetting regression models, the accuracy of the LARS model was the best, followed by the RANSAC model and the BSR model. This ranking implies that the solution to searching for the optimal subset combination through loop traversal may not necessarily lead to a better model. The decomposition results of four regularization models, Lasso, Ridge, Elastic Net, and B-Ridge, showed that regularization is also one of the general solutions to alleviate overfitting. In both the OLS model and the four regularization models, the decomposition accuracy was significantly improved. Among the three regularized regression models, the ridge regression model demonstrated the best prediction accuracy. Therefore, we can speculate that L2 regularization was the optimal regularization scheme in our study. Compared with the OLS model, the decomposition accuracies of the PCR model and the PLS model were also significantly improved, indicating that the feature reduction method is also useful in alleviating overfitting. The prediction accuracies of the PCR model and the PLS model were very close; they can be considered as almost equivalent models in this case. Based on the accuracy evaluation results of the above nine linear regression models, it can be considered that in addition to the OLS regression model, the remaining linear regression models are also suitable for our study. Among the linear regression models, the ridge regression model was preferred as it demonstrated the best decomposition accuracy. It is obvious that the prediction accuracies of three nonlinear regression models presented in Table 4 were significantly better than in the OLS model. The decomposition accuracies of the three nonlinear regression models, in ascending order, were the SVR \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithms** & **R\({}^{2}\)** & **RMSE** & **MABE** & **MAPE (\%)** \\ \hline OLS & 0.924 & 6471.913 & 48.063 & 4733.677 \\ BSR & 0.977 & 3547.13 & 34.667 & 2282.022 \\ RANSAC & 0.899 & 7421.336 & 59.307 & 5125.861 \\ LARS & 0.888 & 7838.545 & 69.02 & 5759.284 \\ PCR & 0.914 & 6868.028 & 102.96 & 6133.461 \\ PLS & 0.922 & 6535.272 & 89.433 & 5666.922 \\ Lasso & 0.924 & 6459.609 & 51.043 & 4819.67 \\ Ridge & 0.907 & 7128.09 & 76.27 & 5874.865 \\ Elastic Net & 0.915 & 6828.741 & 81.983 & 5814.385 \\ SVR & 0.876 & 8157.352 & 71.263 & 5924.128 \\ KNN & 0.925 & 6424.436 & 50.105 & 4711.419 \\ RF & 0.977 & 3606.155 & 21.562 & 2429.656 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Evaluation of decomposition results. model, the RF model, and the KNN model. Among them, the R\({}^{2}\) values of the RF model and the KNN model both exceeded 0.7, indicating that they both offer good decomposition effects. Therefore, the KNN model and the RF model were both suitable for this study. Because the decomposition accuracy of the RF model was slightly worse than that of the KNN model, the KNN model was the preferred nonlinear model in this study. The experiment demonstrated again that there is no universal model for machine learning regression.