# Spatio-Temporal Heterogeneous Ensemble Learning Method for Predicting Land Subsidence
## 3 Experiments
### Results  
#### 3.5.1 Spatio-Temporal Clustering Results  
Following the two-stage hybrid spatio-temporal clustering, the spatio-temporal data matrix of land subsidence was divided into four clusters. Based on the mean value of subsidence in each spatio-temporal cluster, the four homogeneous spatio-temporal clusters are defined as slight uplift, slight subsidence, moderate subsidence, and severe subsidence. According to these definitions, the spatio-temporal clustering results are shown in Figure 5. The time clusters are arranged in chronological order, and the spatial clusters are arranged by the mean value of the rows within the cluster. The clustering result matrix shows that most spatio-temporal points fall into the slight uplift and slight subsidence categories. Statistical information of the spatio-temporal clustering results is presented in Table 2. The mean values for the four subsidence patterns are as follows: slight uplift (15 mm), slight subsidence (\(-\)17 mm), moderate subsidence (\(-\)65 mm), and severe subsidence (\(-\)124 mm). Judging from the proportion of the four spatio-temporal subsidence patterns, the spatio-temporal points of land subsidence in the entire study area are mainly categorized as slight uplift and slight subsidence, accounting for 85.7%, indicating that the overall subsidence in the study area is slight. The spatio-temporal points of land subsidence with moderate and severe subsidence patterns account for a small proportion, totaling 14.3%. \begin{table}
\begin{tabular}{c c} \hline \hline
**Model** & **Hyper Parameters** \\ \hline Seq2 Seq & batch size = 64, epochs = 100, hidden units = 16, learning rate = 0.001, teacher forcing ratio = 0.2 \\ GCN-Seq2 Seq & batch size = 64, epochs = 100, hidden units = 16, learning rate = 0.001, teacher forcing ratio = 0.2 \\ DCRNN & batch size = 64, epochs = 100, learning rate = 2.0 \(\times\) 10\({}^{-6}\) \\ GMAN & batch size = 64, epochs = 100, learning rate = 0.005 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of the base models. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Cluster ID** & **Pattern** & **Mean (mm)** & **Proportion** \\ \hline
1 & slight uplift & \(15\) & \(43.28\%\) \\
2 & slight subsidence & \(-17\) & \(42.42\%\) \\
3 & moderate subsidence & \(-65\) & \(11.19\%\) \\
4 & severe subsidence & \(-124\) & \(3.11\%\) \\ \hline \hline \end{tabular} (i) Spatial distribution pattern  
The spatio-temporal distribution pattern of subsidence was initially analyzed from a spatial perspective. Columns corresponding to the same time cluster in the spatio-temporal clustering matrix were merged to derive three spatial patterns, as illustrated in Figure 6. The proportion of each type of spatio-temporal subsidence pattern points in each spatial pattern and the number of occupied time periods are presented in Table 3.  
\end{table} 
Table 2: Statistics of spatio-temporal clustering matrix of land subsidence data. Figure 5: Spatio-temporal clustering result matrix. Figure 6: Spatial distribution patterns: (**a**) spatial pattern 1; (**b**) spatial pattern 2; (**c**) spatial pattern 3. In spatial pattern 1, the slight subsidence and slight uplift patterns account for nearly all spatio-temporal points, with the slight subsidence pattern representing the largest proportion. Moderate subsidence is represented minimally, while severe subsidence is absent in spatial pattern 1. In spatial pattern 3, the slight subsidence and slight uplift patterns still account for most spatio-temporal points, with the slight uplift pattern representing the largest proportion. (ii) Temporal distribution pattern  
Additionally, the subsidence pattern was analyzed from a temporal perspective. Spatial points exhibiting the same changes in the temporal dimension in the clustering result matrix were merged and classified into six temporal patterns.