## 5 Analysis of Experimental Results
### Analysis of Soil Heavy-Metal Prediction Results  
In the soil heavy-metal content prediction experiment, the dataset was divided into training and test sets to train and verify the performance of the model, respectively. The experimental dataset contained 322 sets of heavy-metal data, elevation information for each sampling point, and the coordinates of 224 enterprises that may produce pollution. The originally obtained data were normalized and preprocessed to produce the experimental dataset. The possible polluting enterprises were used as points of interest and combined with node characteristics. Ninety percent of the data in the experimental dataset were randomly selected as the training set; the remaining 10% of the data were used as the test set to predict the contents of Hg and Ni in the soil at unknown points. The model performance was verified using the test set. Figure 8: Iteration Process of SA-FOA and FOA Algorithms. Figure 7: Comparison of measured Cd value and values predicted by different models. For prediction of mercury and nickel in the soil, the RMSE, MAE, and R\({}^{2}\) at different \(\lambda\) were obtained; the calculated error indicators are presented in Table 2.  
From Table 2, the SE-GCN model predicts mercury at \(\lambda\) 0.25; the RMSE, MAE, and R\({}^{2}\) are lower than other values. The MAE decreased by 20% and R\({}^{2}\) increased by 0.016 compared to \(\lambda\) 0.75. The RMSE decreased by 7.17%, the MAE decreased by 20%, and R\({}^{2}\) increased by 0.014 in the prediction of nickel. The RMSE, MAE, and R\({}^{2}\) were lower than other values. Compared to a value of 0, the RMSE decreased by 29.32%, the MAE decreased by 29.28%, and R\({}^{2}\) increased by 0.25. Compared with a value of 0.5, the RMSE decreased by 5.38%, the MAE decreased by 6.54%, and R\({}^{2}\) increased by 0.009. Compared with a value of 0.75, the RMSE decreased by 10%, the MAE decreased by 8.32%, and R\({}^{2}\) increased by 0.019. In predicting soil heavy metals, adding spatial autocorrelation can alleviate most of the overfitting problems in the model. From Table 2, the SE-GCN model had lower RMSE, MAE, and R\({}^{2}\) values for each evaluation indicator of mercury at \(\lambda\) = 0.25 than the other models. Compared with \(\lambda\) = 0, the RMSE decreased by 21.89%, the MAE decreased by 42.86%, and R\({}^{2}\) increased by 0.055. Compared with \(\lambda\) = 0.5, the RMSE decreased by 8.41%, the MAE decreased by 20%, and R\({}^{2}\) increased by 0.016. Compared with \(\lambda\) = 0.75, the RMSE decreased by 7.17%, the MAE decreased by 20%, and R\({}^{2}\) increased by 0.014. At \(\lambda\) = 0.25, the RMSE, MAE, and R\({}^{2}\) for nickel were lower than for other metals. Compared with \(\lambda\) = 0, the RMSE decreased by 29.32%, the MAE decreased by 29.28%, and R\({}^{2}\) increased by 0.081. Compared with \(\lambda\) = 0.5, the RMSE decreased by 5.38%, the MAE decreased by 5.54%, and R\({}^{2}\) increased by 0.009. Compared with \(\lambda\) = 0.75, the RMSE decreased by 10%, the MAE decreased by 8.32%, and R\({}^{2}\) increased by 0.019. Thus, the SE-CGN model constructed in this study can alleviate most of the overfitting problems by adding spatial autocorrelation in predicting soil heavy metals. Figure 9 shows the fitting curves of the predicted and actual values of Hg for different \(\lambda\). The predicted Hg with \(\lambda\) = 0.25 fit best with the actual values. Figure 10 shows the fitting curves of the predicted and actual values of Ni predicted by SE-GCN for different \(\lambda\). The predicted Ni with \(\lambda\) = 0.25 fit best with the actual value. The prediction performance of the proposed SE-GCN model was further demonstrated through comparative experiments. The SE-GCN model (for 0.25), GCN model, DCNN, Kriging, and RBF were used to predict soil heavy-metal content, and the RMSE, MAE, and R\({}^{2}\) indices were compared. The evaluation indices for the predicted soil heavy-metal values for each model are shown in Table 3.