# Landslide Susceptibility Modeling Using a Deep Random Neural Network
## 4 Results and Discussion
### Performance Evaluation and Comparison  
In this study, the performance of the DRNN was evaluated using the overall accuracy (OA), kappa coefficient (K), F-measure (F), Matthews correlation coefficient (MCC), and receiver operating characteristic (ROC) curve. The performance evaluation was conducted using both the training data and the testing data (Table 3). On the basis of training data, the fitting power of models was measured. All models achieve a high level of goodness of fit. Note that the CNN shows higher values of OA, K, F, and MCC than DRNN, DNN, and ADAANN, proving the excellent feature extraction capability of the convolution structure. The proposed DRNN achieves the second-best fitting performance, yielding OA, K, F, and MCC values of 91.16%, 0.823, 0.912, and 0.823, respectively. By comparison, DNN and ADAANN obtain nearly equal performances in terms of goodness of fit. In terms of  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Class**} & \multicolumn{3}{c}{**ADAANN**} & \multicolumn{3}{c}{**DNN**} & \multicolumn{3}{c}{**CNN**} & \multicolumn{3}{c}{**DRNN**} \\ \cline{2-11}  & **PC(\%)** & **PL(\%)** & **LD** & **PC(\%)** & **PL(\%)** & **LD** & **PC(\%)** & **PL(\%)** & **LD** & **PC(\%)** & **PL(\%)** & **LD** \\ \hline Very low & 19.73 & 0.00 & 0.00 & 19.76 & 0.00 & 0.00 & 40.17 & 0.00 & 0.00 & 34.15 & 0.00 & 0.00 \\ Low & 17.78 & 0.00 & 0.00 & 18.46 & 0.48 & 0.03 & 9.04 & 0.73 & 0.08 & 19.05 & 1.03 & 0.05 \\ Moderate & 14.51 & 1.45 & 0.10 & 14.99 & 1.94 & 0.13 & 10.36 & 2.42 & 0.23 & 11.08 & 5.93 & 0.53 \\ High & 29.21 & 30.51 & 1.04 & 28.60 & 30.99 & 1.08 & 23.46 & 33.90 & 1.44 & 19.06 & 36.34 & 1.91 \\ Very high & 18.57 & 68.04 & 3.66 & 18.22 & 66.59 & 3.65 & 16.98 & 62.95 & 3.71 & 16.66 & 63.14 & 3.79 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Landslide density analysis on landslide susceptibility maps.  
generalization performance, our method achieves the highest OA, K, F, and MCC, with values of 91.46%, 0.829, 0.914, and 0.828, respectively. In addition, CNN also achieves satisfactory performance, with OA, K, F, and MCC values of 88.41%, 0.7767, 0.883, and 0.767, respectively. DNN and ADANN perform comparably regarding the generalization ability. The ROC curves of various models are shown in Figure 8. The area under the ROC curve (AUC) quantitatively depicts the model's performance. On the training data, CNN achieves the highest AUC (0,981). It is followed by the DRNN (0.967), DNN (0.940), and ADAANN (0.936). On the testing data, the proposed DRNN holds the best prediction performance in AUC (0.946), followed by CNN (0.942), DNN (0.936), and ADAANN (0.916).  
Figure 7: Landslide susceptibility mapping using (**a**) ADAANN, (**b**) DNN, (**c**) CNN, (**d**) DRNN.  
Similar results can be found in previous landslide studies. For example, [PERSON] et al. (2022) assessed the landslide susceptibility of the Yaan-Linzhi area on the basis of deep learning methods [78]. They found that the accuracy of CNN is greater than that of the DNN in both the training and testing stages. [PERSON] et al. (2022) analyzed the performance of different CNN structures in landslide modeling and proved the advantages of CNN relative to DNN [79]. [PERSON] and [PERSON] (2021) compared deep learning and ensemble learning methods for landslide spatial probability prediction and concluded that CNN significantly outperforms DNN and ensemble models including RF and Adaboost [80]. In the present study, CNN achieves the best prediction accuracy on training data but encounters a slight overfitting problem. The proposed DRNN effectively alleviates this limitation by using the random mechanism. The random mechanism expands the data space, allowing the model to receive diverse information for full training. Additionally, the random rule acts as regularization, which helps mitigate overfitting. The DRNN achieves desirable and comprehensive performances, which may be suitable for landslide susceptibility assessment in the study area.