# Spatio-Temporal Heterogeneous Ensemble Learning Method for Predicting Land Subsidence
## 3 Experiments
### Parameter Setting  
In this study, the number of clusters in the BBAC_I algorithm and the REDCAP algorithm of the two-stage hybrid clustering needs to be manually specified. To determine the number of spatial and temporal clusters in the BBAC_I algorithm, this study tested spatial clusters ranging from 200 to 400 with an interval of 50 and temporal clusters ranging from 3 to 8 with an interval of 1. It was found that when the number of spatial clusters was 200 and the number of temporal clusters was 3, the BBAC_I algorithm could reach a convergence state, and the clustering results have the minimum mutual information loss with the original data matrix. To determine the number of clusters k in the REDCAP algorithm, the silhouette coefficient was used in this study to find the optimal clustering. As shown in Figure 4, when k is 4, the silhouette coefficient reaches an inflection point; thus, the final number of clusters is set to 4. To achieve optimal results, the BBAC_I algorithm was set with a maximum of 3000 iterations, a convergence threshold of \(1\times 10^{-5}\), and 200 repetitions. For the adjacency relationship and difference measurement method of the REDCAP algorithm, [PERSON] [30] demonstrated that using the full-order configuration for constructing the adjacency relationship and CLK for the difference measurement method achieves the best clustering performance compared with other methods. Therefore, this study adopts the REDCAP algorithm under the full-order-CLK configuration. This study sets a unified input sequence length (i.e., 10 steps) and sliding window step length (i.e., 1 step) for the selected prediction model. The prediction output sequence length is set to 1 step (each step corresponds to 1 monitoring interval). These settings ensure that the model effectively captures short-term dynamic changes in land subsidence, providing accurate data support for prediction analysis. This study uses the KNN algorithm to find the 10 nearest neighbors around each point to establish spatial connections and uses the spatial distance between points as the weight of the edges to construct a spatial graph. Figure 4: Silhouette coefficient of REDCAP algorithm clustering results. Figure 3: Spatial distribution of land subsidence data of (**a**) timestamp 10, (**b**) timestamp 20, (**c**) timestamp 30, (**d**) timestamp 40, (**e**) timestamp 50, (**f**) timestamp 60, (**g**) timestamp 70. The dataset was split into training and testing sets with an 80-20 ratio, meaning 80% of the data was used for training the model, while the remaining 20% was reserved for testing its performance. This 80-20 split is a common practice in machine learning, as it provides a balanced approach: the majority of the data is used to train the model, allowing it to learn effectively, while a sufficient portion is held back to evaluate how well the model generalizes to unseen data. Within the training set, 20% was further utilized to train the ensemble learner. This step ensures that the ensemble learner, which typically combines predictions from multiple models, is trained on diverse subsets of the data, enhancing its robustness. A potential bias of the 80-20 split is that the model may not encounter all data variations during training, particularly in small or unevenly distributed datasets. To mitigate this, techniques such as cross-validation can be employed, where the training set is split into multiple subsets, and the model is trained and validated on these different subsets iteratively. This approach ensures the model is trained on the maximum data variation, reducing the risk of overfitting or underfitting. Overall, the 80-20 split was chosen to balance model training efficiency and evaluation reliability, while potential biases were addressed through careful validation strategies.