## 3 Methodology
### Decomposition-Ensemble Learning Model for Landslide Displacement Prediction
#### 3.4.2 Individual Prediction  
In the present study, 124 measurements from October 2006 to January 2017 were used as the training set for the prediction model, and 21 measurements from February 2017 to October 2018 were treated as testing data. According to previous research on landslide displacement prediction [46; 47], the trend components are mainly controlled by internal geological conditions and can be perfectly predicted by polynomial regression fitting. In contrast, the periodic component is mainly controlled by external triggering factors, such as rainfall intensity and reservoir fluctuation. The major difficulty in landslide displacement prediction is accurate prediction of the periodic components. Therefore, polynomial regression fitting was treated as an individual prediction model to predict trend components. The trend component shown in Figure 7 can be fitted as follows:  
\[y_{T}(t)=-0.0337t^{2}+21.7046t+7.1479 \tag{18}\]  
The coefficient of determination (R\({}^{2}\)) for the trend component is 1000, which indicates a perfect model for the prediction of the trend component.  
Aiming at interpreting the behaviors between input candidates and model outputs and excluding irrelevant and redundant variables to develop accurate and cost-effective prediction models [48], the RNN with MIC-based input variable selection was implemented for individual prediction of periodic components. Based on previous research related to landslide displacement prediction [49], seven commonly used variables were selected as input candidates, including three state candidates and four trigger candidates. The selected four trigger input candidates are one-month antecedent rainfall (\(x_{1}\)), two-month antecedent rainfall (\(x_{2}\)), average values of reservoir level for the current month (\(x_{3}\)), and reservoir fluctuation for the current month (\(x_{4}\)). The state candidates are displacement in the past month (\(x_{5}\)), displacement of landslides in the past two months (\(x_{6}\)), and displacement of landslides in the past three months (\(x_{7}\)). Pair plots and MICs between the input candidates and periodic components are shown in Figure 8. The pair plots show an approximately linear dependency between the periodic components (\(y_{P}\)) and state candidates (\(x_{5}\), \(x_{6}\), and \(x_{7}\)). The MICs indicate that the seven input candidates have significant dependency on the  
Figure 7: Decomposition results of landslide displacement using the EEMD method and time series of original landslide displacement and the trend and periodic components.  
periodic components, with MIC values larger than 0.2. Therefore, seven input candidates were treated as the input for individual prediction of periodic components.  
The landslide measurements were first normalized in the range of 0 to 1 by min-max feature scaling. After the outputs from the EEMD-RNN approach were renormalized, the final displacement predictions were obtained. The simple trial and error method was adopted for the parameter tuning in RNN, GRU, and LSTM networks. The results from trial-and-error analysis show that RNN, GRU, and LSTM networks with one hidden layer for landslide displacement prediction is better than using a multi-layer network. Therefore, one hidden layer with topologies of 7-50-1, 7-55-1, and 7-50-1 was set up for RNN, LSTM, and GRU in the present study. The epoch strategy referring to the process by which all data are sent into the network to complete an iterative calculation was adopted. The epoch sizes were set to 1000, 400, and 100, respectively. Moreover, learning rate scheduling was adopted for faster convergence and convergence to a better minimum [50]. The corresponding learning rate parameters for RNN, LSTM, and GRU were set to 0.6, 0.7, and 0.5, respectively. More details about the parameter settings in the comparative studies are shown in Table 2.  
Figure 8: Pair plots and MICs between the input candidates and periodic components.