## 2 Materials and Methods
### Methods
#### 2.2.1 Multilayer Perceptron  
MLP is a multilayer feed-forward network model with one-way error propagation, and it is one of the most widely used ANNs. MLP can solve the problems of pattern recognition, time series prediction, and so forth [34; 57]. The evolution of a landslide, which is a complex physical process, is also a nonlinear system affected by the natural environment and human engineering activities [58; 59]. Therefore, compared with deterministic models or general linear statistical methods, the MLP model has excellent nonlinear mapping ability for performing LSP [33]. The MLP model is composed of input, hidden, and output layers, all of which are composed of similar neurons (Figure 4). The connections between the input and hidden layers and between the hidden and output layers are all processed by the weight values. By training and testing these weight values, neural networks form an orderly and stable structure with decision-making ability. Since an MLP with a single hidden layer can approximate a nonlinear system with arbitrary accuracy, this paper mainly studied the single-hidden-layer MLP model [60]. For MLP model with multi-input variables and multi-output variables, the number of neurons in input layer \(X=[x_{1},x_{2}\cdots,x_{m0}]\), hidden layer and output layer is respectively set as \(n_{0}\), \(n_{1}\) and \(n_{2}\), so that the inputs and outputs of hidden layer neurons are:  
\[z_{j}=\sum_{i=1}^{n_{0}}w_{ij}x_{i}+b_{j} \tag{1}\] \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Factors**} & \multirow{2}{*}{**Data Type**} & \multirow{2}{*}{**Value**} & **Grids in** & **Grid** & **Landslide** & **Grid** & **Frequency** \\  & & & **Domain** & **(\%)** & **Grid** & **Proportion** & **Ratio** \\ \hline \multirow{8}{*}{NDVI} & \multirow{8}{*}{Continuous} & 0–0.205 & 21,416 & 1.2 & 18 & 0.7 & 0.545 \\  & & 0.205–0.363 & 48,274 & 2.7 & 133 & 4.9 & 1.787 \\  & & 0.363–0.46 & 140,192 & 8.0 & 353 & 13.0 & 1.633 \\  & & 0.46–0.53 & 277,504 & 15.8 & 584 & 21.6 & 1.365 \\  & & 0.53–0.593 & 412,360 & 23.5 & 663 & 24.5 & 1.043 \\  & & 0.593–0.651 & 382,238 & 21.8 & 460 & 17.0 & 0.781 \\  & & 0.651–0.721 & 322,632 & 18.4 & 384 & 14.2 & 0.772 \\  & & 0.72–1 & 152,721 & 8.7 & 1114 & 4.2 & 0.484 \\ \hline \multirow{8}{*}{Total} & \multirow{8}{*}{Continuous} & 0–0.459 & 10,052 & 0.6 & 10 & 0.4 & 0.645 \\  & & 0.459–0.592 & 27,582 & 1.6 & 56 & 2.1 & 1.317 \\ \cline{1-1}  & & 0.592–0.678 & 61,099 & 3.5 & 80 & 3.0 & 0.849 \\ \cline{1-1}  & & 0.678–0.753 & 111,044 & 6.3 & 172 & 6.3 & 1.005 \\ \cline{1-1}  & & 0.753–0.816 & 170,418 & 9.7 & 297 & 11.0 & 1.131 \\ \cline{1-1}  & & 0.816–0.875 & 262,906 & 15.0 & 400 & 14.8 & 0.987 \\ \cline{1-1}  & & 0.875–0.929 & 409,406 & 23.3 & 550 & 20.3 & 0.872 \\ \cline{1-1}  & & 0.929–1 & 704,830 & 40.1 & 1144 & 42.2 & 1.053 \\ \hline \multirow{8}{*}{Population} & \multirow{8}{*}{Continuous} & 0–0.678 & 20,286 & 1.2 & 7 & 0.3 & 0.224 \\ \cline{1-1}  & & 0.678–0.733 & 78,566 & 4.5 & 80 & 3.0 & 0.661 \\ \cline{1-1}  & & 0.733–0.776 & 116,553 & 6.6 & 102 & 3.8 & 0.568 \\ \cline{1-1}  & & 0.776–0.820 & 200,139 & 11.4 & 266 & 9.8 & 0.862 \\ \cline{1-1}  & & 0.820–0.863 & 257,308 & 14.6 & 300 & 11.1 & 0.756 \\ \cline{1-1}  & & 0.863–0.906 & 311,063 & 17.7 & 543 & 20.0 & 1.132 \\ \cline{1-1}  & & 0.906–0.949 & 380,425 & 21.6 & 657 & 24.3 & 1.120 \\ \cline{1-1}  & & 0.949–1 & 392,997 & 22.4 & 754 & 27.8 & 1.245 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Cont. \[y_{i}=f\!\left(\!z_{j}\!\right)=\left(1+e^{-z_{j}}\right)^{-1} \tag{2}\]  
where \(z_{j}\), \(b_{j}\) and \(y_{j}\) are respectively the input, the threshold and the output of the \(j\)th neuron in hidden layer of MLP; \(w_{ij}\) is the weight value between the \(i\)th input neuron and the \(j\)th neuron in the hidden layer; \(f\!\left(\!z_{j}\!\right)\) is the activation function.