# Spatio-Temporal Heterogeneous Ensemble Learning Method for Predicting Land Subsidence
## 3 Experiments
### Results
#### 3.5.2 Spatio-Temporal Prediction Results
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **Metric** & **Cluster 1** & **Cluster 2** & **Cluster 3** \\ \hline \multirow{3}{*}{Seq2 Seq} & RMSE & 3.5680 & 4.6509 & 6.9436 \\  & MAE & 2.8608 & 3.7389 & 5.1175 \\  & \(R^{2}\) & 0.9520 & 0.9591 & 0.9676 \\ \hline \multirow{3}{*}{GCN-Seq2 Seq} & RMSE & 2.8094 & 4.7664 & 7.3231 \\  & MAE & 2.1040 & 3.6568 & 6.2494 \\  & \(R^{2}\) & 0.9742 & 0.9570 & 0.9640 \\ \hline \multirow{3}{*}{DCRNN} & RMSE & 2.9939 & 4.5349 & 5.7840 \\  & MAE & 2.1669 & 3.3007 & 3.6702 \\  & \(R^{2}\) & 0.9662 & 0.9610 & 0.9775 \\ \hline \multirow{3}{*}{GMAN} & RMSE & 3.1274 & 4.2175 & 4.6243 \\  & MAE & 2.4888 & 3.3909 & 3.8729 \\  & \(R^{2}\) & 0.9627 & 0.9662 & 0.9857 \\ \hline \multirow{3}{*}{Ensemble} & RMSE & 1.3988 & 1.4696 & 0.9597 \\  & MAE & 1.0355 & 1.2248 & 0.6788 \\ \cline{1-1}  & \(R^{2}\) & 0.9925 & 0.9959 & 0.9994 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Prediction accuracy of ensemble model and base models. Figure 10: _Cont_. Figure 9: Comparison of average time series prediction results for each site in cluster 1, obtained by the ensemble model and the base model: (**a**) Seq2 Seq; (**b**) GCN-Seq2 Seq; (**c**) DCRNN; (**d**) GMAN; (**e**) Ensemble model. Figure 11: _Cont._  
Figure 10: Comparison of average time series prediction results for each site in cluster 2, obtained by the ensemble model and the base model: (**a**) Seq2 Seq; (**b**) GCN-Seq2 Seq; (**c**) DCRNN; (**d**) GMAN; (**e**) Ensemble model. Figure 11: Comparison of average time series prediction results for each site in cluster 3, obtained by the ensemble model and the base model: (**a**) Seq2 Seq; (**b**) GCN-Seq2 Seq; (**c**) DCRNN; (**d**) GMAN; (**e**) Ensemble model. This study further utilized a paired t-test to evaluate whether the prediction accuracy of the ensemble model is statistically significantly improved compared to the base model [43]. This test helps assess whether the observed differences in prediction performance are statistically significant or likely due to random variation. For each model \(M_{i}\), the error sequence is calculated:  
\[E_{i}=\left\{\left|y_{A}^{1}-\hat{y}_{A}^{1}\right|_{i}\left|y_{A}^{2}-\hat{y}_{ A}^{2}\right|,\ldots,\left|y_{A}^{t}-\hat{y}_{A}^{t}\right|\ldots\left|y_{A}^{N_{E} }-\hat{y}_{A}^{N_{E}}\right|\right\} \tag{19}\]  
where \(y_{  
in Table 10, the performance of the ensemble model at peak monitoring points is also better than that of the base model; the prediction accuracy of models considering spatio-temporal dependence is generally better than that of models considering only time dependence. This study also conducted a paired t-test on the prediction results of peak monitoring point data to determine whether the prediction accuracy of ensemble model at these points is statistically better than that of the basic model. As shown in Tables 11-13, compared to the basic model, the ensemble model achieves statistically significant improvement at extreme monitoring points. Figure 12: The peak monitoring points of the average time series of each cluster: (**a**) peak monitoring points of cluster 1; (**b**) peak monitoring points of cluster 2; (**c**) peak monitoring points of cluster 3.