# Spatio-Temporal Heterogeneous Ensemble Learning Method for Predicting Land Subsidence
## 3 Experiments
### Results
#### 3.5.2 Spatio-Temporal Prediction Results  
(i) Comparison of overall prediction accuracy  
The overall prediction accuracy of the ensemble model and the four base models when predicting subsidence values for cluster 1, cluster 2, and cluster 3 is displayed in Table 6. The experimental results demonstrate that the ensemble prediction model developed in this study exhibits the best prediction performance among the five models across various subsidence clusters. It is evident that the prediction accuracy of subsidence values significantly improves after the Blending ensemble is implemented in the model. Compared with the Seq2 Seq model, the ensemble model reduces the RMSE by up to 86.2% and the MAE by up to 86.7% for cluster 3; compared with the GCN-Seq2 Seq model, the RMSE is reduced by up to 86.9% and the MAE by up to 89.1% for cluster 3; compared with the DCRNN model, the RMSE is reduced by up to 83.4% and the MAE by up to 81.2% for cluster 3; and compared with the GMAN model, the RMSE is reduced by up to 79.2% and the MAE by up to 82.5% for cluster 3. Methods based on spatio-temporal graph neural networks (such as GCN-Seq2 Seq, DCRNN, and GMAN) generally outperform Seq2 Seq on the three clusters because these models consider the spatio-temporal correlation between different monitoring points. Among the methods based on spatio-temporal graph neural networks, GCN-Seq2 Seq has the best prediction performance for cluster 1 (slight subsidence area), while GMAN performs best for cluster 2 (moderate subsidence area) and cluster 3 (severe subsidence area). Compared to the basic models, the prediction accuracy of the ensemble model is significantly improved for cluster 3, as the basic models achieve their best performance on cluster 3, leading to optimal ensembling results. To intuitively compare the prediction effects of different models, this study visualized the prediction results of the five models across clusters. Given the short time series of the data, the time series in the prediction results are averaged, and the prediction results for each monitoring point are visualized, as shown in Figures 9-11. The results indicate that the prediction outcomes of the ensemble model are highly consistent with the actual subsidence values and significantly outperform the other base prediction models. \begin{table}
\begin{tabular}{c c c} \hline
**Time Pattern** & **Trend** & **Proportion** \\ \hline Time pattern 1 & Stable slight uplift & 33.78\% \\ Time pattern 2 & Stable slight subsidence & 21.40\% \\ Time pattern 3 & Stable slight subsidence–uplift & 22.69\% \\ Time pattern 4 & Slight subsidence–moderate subsidence & 15.03\% \\ Time pattern 5 & Slight subsidence–moderate subsidence–severe subsidence & 2.61\% \\ Time pattern 6 & Moderate subsidence–severe subsidence & 4.46\% \\ \hline \end{tabular}
\end{table} 
Table 4: The proportion of each time pattern in the study area. \begin{table}
\begin{tabular}{c c c c c} \hline
**Cluster ID** & **Pattern** & **Mean** & **Timestamp Range** & **Data Matrix Size** \\ \hline
1 & Slight subsidence & \(-21\) & Z27–Z55 & 26,508 \(\times\) 29 \\
2 & Moderate subsidence & \(-64\) & Z27–Z55 & 6499 \(\times\) 29 \\
3 & Moderate subsidence & \(-144\) & Z56–Z79 & 1602 \(\times\) 24 \\ \hline \end{tabular}
\end{table} 
Table 5: Spatio-temporal cluster information of three representative types of subsidence patterns. Figure 9: _Cont._