## 3 Results
### Model Performances and Comparisons
#### 3.3.1 The Case of Larger Inventory Polygons  
The prediction results of No. 1 models obtained using the RF and cost-sensitive analysis are presented in Figure 7(a). The examination of this figure reveals that a cost of 5000 provided more favorable results, with the accuracy reaching over 80% in most indices. However, the evaluations of SVM-based approaches in consideration of linear, the first- to third-order polynomial, and radial basis functions are displayed in Figure 7(b). Overall, the second-order polynomial function outperformed others. Compared with previous LR results, Figure 7(c) indicates that the developed model in Section 3.2 obtained the highest accuracies, although the UA of the landslide source was slightly lower. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **No. 1** & **No. 2** & **No. 3** & **No. 4** & **No. 5** \\ \hline \multirow{4}{*}{Algorithm\_Cost} & RF\_3000 & RF\_3000 & RF & RF\_2000 & RF \\  & RF\_5000 & RF\_4000 & RF\_1000 & RF\_3000 & RF\_2000 \\ \cline{1-1}  & RF\_6000 & RF\_5000 & & RF\_4000 & \\ \cline{1-1}  & RF\_7000 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The representative models using the random forests (RF) algorithm with the costs for verifications based on previous comparisons. For example, RF\_3000 indicates that the RF algorithm with a cost of 3000 was used. Figure 8: Performances (\(Y\)-axis) of No. 1 model, where OA, AUC, PA, UA, S, and R represent the overall accuracy, area under the ROC curve, producer’s accuracy, user’s accuracy, landslide source, and runout, respectively. (**a**) Using the algorithm with the costs; (**b**) using the support vector machine (SVM) with linear, the first- to third-order polynomial, and radial basis (RBF) functions; (**c**) comparing the optimal results of (**a**) and (**b**) by using logistic (Logis) regression. Similar procedures to those used to verify the No. 2 model were applied to assess the algorithms of RF with the cost-sensitive analysis, SVM, and LR. Figure 9a further compares the RF with costs, as displayed in the third column in Table 3. Based on this figure, the RF algorithm appeared to outperform the other models without increasing costs. As illustrated in Figure 9b, the accuracies of all the functions of SVM modeling were similar, with higher missing errors for detecting landslide sources. The RF and the second-order polynomial function of SVM were compared with LR, as illustrated in Figure 9c, which revealed that the AUC of the LR was the highest. The accuracies of the three other approaches were similar. For the No. 3 model, Table 4 presents the comparison of the RF algorithm and cost-sensitive analysis. The results indicate that the original RF algorithms provided higher accuracy, whereas the RF method with a cost of 1000 had lower PA and UA for the runout and landslide source classes, respectively. In the SVM case, Figure 10a reveals that the RBF obtained the least accurate results, especially PA and UA for the runout and landslide source signatures. The performances of linear and the first-order polynomial functions were similar. A further comparison of these models, illustrated in Figure 10b, revealed that the results produced by the RF method were more favorable in most cases, especially UA for the landslide source class. The No. 4 models were also examined as illustrated in Figure 11. The RF method without costs also provided the most accurate results, as presented in Figure 11a. Similarly, the performances of the linear and first-order polynomial functions outperformed the RBF method in SVM-based computation, as illustrated in Figure 11b. The comparison based on the aforementioned methods is illustrated in Figure 11c. The findings indicated that the AUC result of SVM was slightly higher than the other indices of the RF, SVM, and LR, which were similar. In the No.