# Spatio-Temporal Heterogeneous Ensemble Learning Method for Predicting Land Subsidence
###### Abstract  
The prediction of land subsidence is of significant value for the early warning and prevention of geological disasters. Although numerous land subsidence prediction methods are currently available, two obstacles still exist: (i) spatio-temporal heterogeneity of land subsidence is not well considered, and (ii) the prediction performance of individual models is unsatisfactory when the data do not meet their assumptions. To address these issues, we developed a spatio-temporal heterogeneous ensemble learning method for predicting land subsidence. Firstly, a two-stage hybrid spatio-temporal clustering method was proposed to divide the dataset into internally homogeneous spatio-temporal clusters. Secondly, within each spatio-temporal cluster, an ensemble learning strategy was employed to combine one time series prediction model and three spatio-temporal prediction models to reduce the prediction uncertainty of an individual model. Experiments on a land subsidence dataset from Cangzhou, China, show that the prediction accuracy of the proposed method is significantly higher than that of four individual prediction models. land subsidence prediction; spatio-temporal heterogeneity; spatio-temporal clustering; ensemble learning +
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simple, easy to use, and low-cost. However, these methods require data to meet certain ideal assumptions, which often conflict with the complex nonlinear characteristics of land subsidence data, resulting in poor prediction results. Machine learning algorithms have been widely used in land subsidence prediction tasks due to their powerful ability to extract high-dimensional, nonlinear features from data, including backpropagation (BP) algorithms, CART, support vector regression (SVR), convolutional neural networks (CNNs), Bayesian models, fuzzy set theory, and long short-term memory (LSTM) networks [15, 16, 17, 18, 19, 20, 21]. However, the underlying assumptions of these algorithms may be not satisfied in various scenarios, leading to limited generalization performance. Consequently, ensemble learning methods, which combine multiple individual base learners to improve prediction accuracy, have been applied to land subsidence prediction [23, 24, 25, 26]. [PERSON] et al. [27] proposed a land subsidence prediction model based on XGBoost for the Beijing Plain. [PERSON], [PERSON], [PERSON], and [PERSON] [24] combined the Gradient Boosting Decision Tree (GBDT) and Random Forest (RF) methods to predict land subsidence. Both boosting and bagging strategies combine the same base model multiple times, thus categorizing them as homogeneous ensemble learning methods. Despite the development of various prediction models, a critical gap remains in addressing the spatio-temporal heterogeneity of subsidence data and the inconsistent performance of individual models. Specifically, two obstacles still exist:  
1. The spatio-temporal heterogeneity of land subsidence is not adequately considered in existing prediction models. Spatio-temporal heterogeneity refers to the variation in observed values of a spatio-temporal object across time, space, or both. Land subsidence is a spatio-temporally dynamic process, and its spatio-temporal heterogeneity is difficult to characterize. Existing land subsidence prediction methods primarily focus on time series analysis of historical data, often neglecting the spatial dependence of land subsidence data [27]. Recently, some methods have incorporated spatial clustering or time series clustering to consider spatial or temporal heterogeneity in land subsidence prediction [12, 21]. However, these methods still struggle to effectively model the spatio-temporal heterogeneity of land subsidence, directly impacting the accuracy and reliability of predictions. 2. The prediction performance of individual models is unsatisfactory when the data deviate from the models' assumptions.