# Spatio-Temporal Heterogeneous Ensemble Learning Method for Predicting Land Subsidence
## 3 Experiments
### Results
#### 3.5.1 Spatio-Temporal Clustering Results
As illustrated in Figure 7, six temporal patterns are identified based on the temporal and spatial patterns of spatial points in the time series: stable slight uplift (temporal pattern 1, Figure 7a), stable slight subsidence (temporal pattern 2, Figure 7b), slight subsidence-slight uplift (temporal pattern 3, Figure 7c), slight subsidence-moderate subsidence (temporal pattern 4, Figure 7d), slight subsidence-moderate subsidence-severe subsidence (temporal pattern 5, Figure 7e), and moderate subsidence-severe subsidence (temporal pattern 6, Figure 7f). The spatial distribution of each temporal pattern is presented in Figure 8, with different color markings distinguishing the spatial points of various temporal patterns. The proportion of spatial points in various temporal patterns within the spatial extent of Cangzhou area is detailed in Table 4.  
The overall temporal pattern of land subsidence in Cangzhou area falls into three categories: stable (stable slight uplift, stable slight subsidence), fluctuating (slight subsidence-slight uplift, slight subsidence-moderate subsidence, and moderate subsidence-severe subsidence), and violent fluctuation (slight subsidence-moderate subsidence-severe subsidence). Of these, the stable temporal pattern accounts for the largest proportion (more than 50%), followed by the fluctuating temporal pattern (accounting for more than 40%), while the violent fluctuation temporal pattern accounts for the lowest proportion (less than 5%). The spatial distribution of the six temporal pattern points in the Cangzhou area is illustrated in Figure 8. Slight subsidence-moderate subsidence is primarily found in the southwest part, while moderate subsidence-severe subsidence is primarily found in the westernmost part. This indicates that the land subsidence conditions in these areas have been continuously intensifying over the 80-period timeframe. Slight subsidence-moderate subsidence-severe subsidence is primarily found in the southwest part; moderate subsidence-severe subsidence is mainly distributed in the northwest part. This suggests that the land subsidence in these areas is worsening and necessitates intervention and control by relevant authorities. This study employs a two-stage hybrid spatio-temporal clustering method to conduct co-clustering on the land subsidence data of the Cangzhou area. Although each spatio-temporal cluster is roughly continuous in space, there are still a considerable number of points mixed with other clusters. To facilitate subsequent subsidence value prediction of land subsidence spatio-temporal data, the spatio-temporal clustering results were post-processed to obtain spatio-temporally continuous and homogeneous subclusters. First, KNN is employed to identify the spatio-temporal neighbors of each spatio-temporal object. Then, the spatio-temporal cluster IDs of all neighbors in its spatio-temporal neighborhood are voted on, and the cluster ID with the highest vote is assigned as the final ID of the object. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Spatial Pattern** & **Slight Uplift** & **Slight Subsidence** & **Moderate Subsidence** & **Severe Subsidence** & **Time Period** \\ \hline Spatial pattern 1 & 33.78\% & 66.10\% & 0.1\% & 0 & 27 \\ Spatial pattern 2 & 41.20\% & 37.75\% & 18.33\% & 2.72\% & 29 \\ Spatial pattern 3 & 56.47\% & 21.40\% & 15.04\% & 7.08\% & 24 \\ \hline \end{tabular}
\end{table} 
Table 3: The proportion of each type of spatio-temporal subsidence pattern and the number of time periods they occupy in each spatial pattern. Finally, the isolated points from the KNN spatio-temporal neighbor voting results are manually assigned the IDs of the surrounding points to obtain the final clustering results. For subsequent land subsidence prediction, this study selected three representative subsidence pattern clusters: the slight subsidence pattern (cluster 1), the moderate subsidence pattern (cluster 2), and the severe subsidence pattern (cluster 3).