## 2 Materials and Methods
### Procedure and Data Mining Algorithms
#### 2.2.1 Developed Models  
The random forests (RF) algorithm [44] is a data mining method used for constructing a classification-based model that employs a supervised strategy. RF is an extension of the tree-based algorithms. The RF employs the information gain (IG) measure or Gini index to determine the degree of impurity of factors or variables, applying the bootstrap and vote operators to improve the results \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Dataset**} & \multicolumn{2}{c}{**Landslide Source**} & \multicolumn{2}{c}{**Runout**} \\ \cline{2-5}  & **Area (m\({}^{2}\))** & **No. of Samples** & **Area (m\({}^{2}\))** & **No. of Samples** \\ \hline No. 1 & 250,493 & 2508 & 385,381 & 3839 \\ No. 2 & 154,709 & 1545 & 239,199 & 2386 \\ No. 3 & 141,574 & 1412 & 206,055 & 2060 \\ No. 4 & 132,005 & 1313 & 197,162 & 1980 \\ No. 5 & 126,636 & 1265 & 190,338 & 1905 \\ \hline \(\geq\)10,000 m\({}^{2}\) * & 155,333 (avg) & 9318 & 162,768 (avg) & 27,640 \\
50,000—100,000 m\({}^{2}\) & 68,670 (avg) & 15,798 & 63,792 (avg) & 8937 \\ \hline \hline \end{tabular}  
* Areas and number of samples in the table include the training polygon samples, but these samples were eliminated during the verified process.  
\end{table} 
Table 1: The training and verification samples extracted from the landslide inventory polygons. Figure 3: The conceptual procedure used in this study to model and verify the separation between landslide source and runout signatures. derived from the tree-based rules. The bootstrap method \"randomly\" selects subtraining data to generate several trees (termed \"forests\") to avoid the overfitting results. The vote component is used to determine the optimal results according to the developed trees, thus improving the RF classifier. A topographic factor with a larger IG or Gini value had to be selected because higher values indicate a higher priority for constructing a tree node, which should be ignored in the next computation. A sequence of tree-based rules was constructed after several iterations. The rules were then used to classify other instances. Nominal (or discrete) and numeric (or continuous) formats are commonly used in the field. Entropy theory was applied to calculate the IG in the nominal case, as displayed in Equations (1)-(3). In these equations, E(A) represents the entropy of all training data; S and R represent the numbers of landslide sources and runout samples, respectively; E'(a) and v are the entropy and number of subsets of a specific topographic factor, respectively; E(a) is the entropy of the subset in a specific topographic factor, calculated using Equation (1); IG(a) represents the IG of a specific topographic factor. The Gini index was applied to determine the IG in the numeric cases, as displayed in Equations (4) and (5), where C represents a segmented point for a specific topographic factor used to divide continuous data into two parts, and N\({}_{1}\) and N\({}_{2}\) represent the numbers of a \(\leq\) C and a \(>\) C, respectively. The steps were detailed by [PERSON] et al. [53]. \[\mathrm{E(A)}\ =\ -\frac{S}{S+R}\log_{2}\frac{S}{S+R}\ -\frac{R}{S+R}\log_{2}\frac{R}{S+R} \tag{1}\]  
\[\mathrm{E^{\prime}(a)}\ =\ \sum_{i=1}^{\mathrm{v}}\frac{S_{i}+R_{i}}{S+R} \mathrm{E(a_{i})} \tag{2}\]  
\[\mathrm{IG(a)}\ =\ \mathrm{E(A)-E^{\prime}(a)} \tag{3}\]  
\[\mathrm{Gini(a\leq C\ or\ a>C)}\ =\ 1-\sum_{i\ =\ 1}^{\mathrm{m}}\frac{n_{i}}{N} \tag{4}\]  
\[\mathrm{IG(a,C)}\ =\frac{N_{1}}{N}\mathrm{Gini(a\leq C)}+\frac{N_{2}}{N} \mathrm{Gini(a>C)} \tag{5}\]  
The strategy of adjusting the decision boundary used in the study is termed as the cost-sensitive analysis. The cost-sensitive analysis is a postclassification method based on the cost matrix that reclassifies the instances and balances the accuracies of certain classes when missing or false alarm errors are unreliable [49; 54; 55]. The dimension of the cost matrix is equal to that of the confusion matrix.