# Spatio-Temporal Heterogeneous Ensemble Learning Method for Predicting Land Subsidence
## 3 Experiments
### Discussion  
Experimental results indicate that considering the spatio-temporal heterogeneity of land subsidence can significantly improve the prediction accuracy of the model. Additionally, the Blending ensemble model significantly outperforms individual models in terms of overall prediction accuracy and peak monitoring point prediction performance. The main reasons for this are attributed to the following two aspects: \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **Seq2 Seq** & **GCN-Seq2 Seq** & **DCRNN** & **GMAN** \\ \hline Ensemble & Yes & Yes & Yes & Yes \\ Seq2 Seq & & No & No & No \\ GCN-Seq2 Seq & & & No & No \\ DCRNN & & & No \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Statistical comparison of prediction accuracy of different models at peak monitoring points (cluster 3). \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 & 3.7265 & 4.6453 & 6.5843 \\  & MAE & 3.0159 & 3.8015 & 5.0155 \\  & \(R^{2}\) & 0.9494 & 0.9575 & 0.9659 \\ \hline \multirow{3}{*}{GCN-Seq2 Seq} & RMSE & 2.6863 & 4.776 & 7.3002 \\  & MAE & 2.0018 & 3.6522 & 6.1603 \\  & \(R^{2}\) & 0.9737 & 0.9550 & 0.9624 \\ \hline \multirow{3}{*}{DCRNN} & RMSE & 3.0955 & 4.7104 & 5.3870 \\  & MAE & 2.2744 & 3.4491 & 3.7927 \\  & \(R^{2}\) & 0.9651 & 0.9563 & 0.9796 \\ \hline \multirow{3}{*}{GMAN} & RMSE & 3.3913 & 2.7253 & 4.4028 \\  & MAE & 2.6707 & 2.1196 & 3.7022 \\  & \(R^{2}\) & 0.9581 & 0.9854 & 0.9864 \\ \hline \multirow{3}{*}{Ensemble} & RMSE & 1.5167 & 1.6109 & 1.3213 \\  & MAE & 1.1697 & 1.3289 & 0.9396 \\ \cline{1-1}  & \(R^{2}\) & 0.9916 & 0.9949 & 0.9988 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Prediction accuracy of the ensemble model and base models at peak monitoring points. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **Seq2 Seq** & **GCN-Seq2 Seq** & **DCRNN** & **GMAN** \\ \hline Ensemble & Yes & Yes & Yes & Yes \\ Seq2 Seq & & No & No & No \\ GCN-Seq2 Seq & & Yes & Yes & Yes \\ DCRNN & & & Yes & Yes \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Statistical comparison of prediction accuracy of different models at peak monitoring points (cluster 1). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **Seq2 Seq** & **GCN-Seq2 Seq** & **DCRNN** & **GMAN** \\ \hline Ensemble & Yes & Yes & Yes & Yes \\ Seq2 Seq & & No & No & No \\ GCN-Seq2 Seq & & Yes & Yes & Yes \\ DCRNN & & & Yes & Yes \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Statistical comparison of prediction accuracy of different models at peak monitoring points (cluster 2). 1. The proposed two-stage hybrid clustering method divides the large-scale land subsidence dataset into internally homogeneous spatio-temporal clusters. The heterogeneous ensemble model then shows excellent prediction performance on these clusters, demonstrating that considering the spatio-temporal heterogeneity improves the prediction performance. 2. Ensemble learning enhances prediction accuracy and reduces errors by combining the results of multiple individual models. In this study, the Blending ensemble strategy effectively combines the strengths of different individual models to achieve higher accuracy in complex subsidence prediction tasks. Although the predictions of individual model may not meet the requirements in some cases, satisfactory land subsidence prediction results are obtained after ensembling, greatly improving accuracy. The experimental results in Section 3.5 highlight the strengths and weaknesses of each individual model. For the slight subsidence pattern (Cluster 1), Seq2 Seq, which only considers temporal autocorrelation performs worse than the methods considering spatio-temporal autocorrelation. This indicates that accounting for spatial autocorrelation can improve the prediction accuracy for slight subsidence patterns with relatively uniform spatial distribution.