# Landslide Susceptibility Assessment by Using Convolutional Neural Network
## 3 Materials and Methods
### Model Cross-Verification  
In order to estimate the CNN model performance, which is implemented on the input data for the assessment of landslide susceptibility, the model was verified by obtaining a loss function. For justification and assessment of the model's accuracy, confusion matrix components (i.e., precision, recall, and f1-score) were estimated. The matrix has been calculated from the following equations [44]:  
\[\text{Precision}= \frac{\text{TP}}{\text{TP}+\text{FP}} \tag{1}\] \[\text{Recall}= \frac{\text{TP}}{\text{TP}+\text{FN}}\] (2) \[\text{Accuracy}= \frac{\text{TP}+\text{TN}}{\text{TP}+\text{TN}+\text{FP}+\text{ FN}}\] (3) \[\text{F1}-\text{score}= 2\cdot\frac{\text{Precision}\cdot\text{Recall}}{\text{ Precision}+\text{Recall}} \tag{4}\]  
where, P = positive; N = negative; TP = true positive; FP = false positive; TN = true negative; and FN = false negative. The confusion matrix is a table indicating a detailed analysis of the retrieved documents (estimated by the model) and relevant documents (measured data). For classification tasks, the terms TP, TN, FP, and FN compare the classifier's results under test with trusted external judgments. The terms positive and negative refer to the classifier's prediction, and the terms true and false refer to whether that prediction corresponds to the external judgment. In this regard, the matrix provides the indices which show the \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \# & **Location** & **Height** & **Slope Dip** & **Geology** & **Failure Type** &
\begin{tabular}{c} **Tensile** \\ **Crack** \\ \end{tabular} \\ \hline
1 & 53.038 E & 36.013 N & 120 & 47 & Sediment & Massive & Yes \\
2 & 53.056 E & 35.984 N & 200 & 40 & Sediment & Massive & Yes \\
3 & 53.045 E & 35.987 N & 79 & 46 & Sediment & Planar & Yes \\
4 & 53.044 E & 35.984 N & 35 & 57 & Sediment & Planar & Yes \\
5 & 53.042 E & 35.979 N & 150 & 55 & Sediment & Massive & Yes \\
6 & 53.041 E & 35.976 N & 63 & 50 & Sediment & Massive & Yes \\
7 & 53.051 E & 35.979 N & 47 & 60 & Sediment & Planar & Yes \\
8 & 53.067 E & 35.974 N & 100 & 47 & Sediment & Massive & Yes \\
9 & 53.059 E & 35.954 N & 210 & 63 & Rock & Sliding & No \\  
\hline \hline \end{tabular}
\end{table} 
Table 2: A summary of the historical landslides. reliability of model performance so that for indicators closer to 1 (100%), the accuracy and performance of the model increase [44]. The justification was applied by using common machine-learning classifiers, such as SVM, k-NN, and DT algorithms, based on performance indices. SVM is a supervised learning model with associated learning algorithms that analyzes data for classification and regression analysis purposes. k-NN is a non-parametric method proposed by [PERSON] that is used for classification and regression, which involves the k closest training examples in the feature space. DT is a decision-making tool that employs a tree-like model of decisions and their potential outcomes, such as chance event outcomes, resource costs, and utility. It is one way to show an algorithm that is only made up of conditional control statements. Decision trees are commonly used in operations research, specifically in decision analysis, to help identify a strategy most likely to achieve a goal and are also a popular tool in machine learning [42; 44]. The error models were used to provide the performance analysis for all algorithms, which concluded that the mean squared error (MSE), root mean square error (RMSE), and mean absolute percentage error (MAPE) were used to measure the models' error rates and compared with the others. On the other hand, the receiver operating characteristic (ROC) curve was used to demonstrate the overall accuracy variation for entire models. ROC is a graphical plot that illustrates the diagnostic ability of a binary classifier system as its discrimination threshold varied, which is created by plotting the TP against the FP rates. ROC analysis provides the criterion for changes in machine-learning models based on overall accuracy compression.