# Susceptibility Mapping on Urban Landslides Using Deep Learning Approaches in Mt. Umyeon
## 3 Methodology  
### Deep Neural Network and Kernel-Based Deep Neural Network  
ANNs are one of the most popular ML methods for prediction and classification across various fields. ANNs are composed of an input layer, a hidden layer, and an output layer; the input layer has as many input variables as the number of input variables in the model, and the output layer represents the prediction result. All layers between the input and output layers are referred to as hidden layers, and the number of hidden layers is determined through an empirical process [73]. The backpropagation algorithm is known to be the commonly used, effective method for training weight determination. Through the backpropagation algorithm, training is performed repeatedly, until a predefined error value is reached and finally is applied to predict for all the data by using the trained model [74].  
DL methodology is an ML method based on this ANN, and it performs prediction and classification in the same way. Like the term \"deep layer\", learning is performed by transforming data levels into different levels in DL methodology [75]. Recent ML studies have proposed various DL architectures (e.g., autoencoders, Restricted Boltzmann Machine (RBM), CNN, and Recurrent Neural Network (RNN)) [76]. In this study, a DNN and kernel-based DNN were applied and compared; the DNN can be interpreted as a deep version of an ANN. As the number of layers increases, the network becomes more complex, and the most appropriate layer for data can be created.  
Specifically, in the case of a DNN using a stochastic gradient descent (SGD) in this study, the architecture was constructed using 100, 100, 50, 50, 25, 25, 10, 10 sequential hidden nodes, as shown in Figure 5 and Table 2. The rectified linear unit (ReLU) was selected as the activation function, and the nonlinear properties of the network were improved through the ReLU activation function [77]. The loss function was designated as the mean squared error (MSE), and the max epochs was set to 300 (Table 1). The batch size and learning rate were set to 150.00 and 0.01, respectively. In the process of calculating the weight for each node during training, the influence of the node becomes too high when the weight of a certain node is high. For example, only the neuron that has the most influence among the input neurons is reflected, and the result may appear as if it was created only by that layer. Therefore, the weight decay was used, which is a concept that prevents the weight of all nodes from becoming larger than necessary. By increasing the weight decay, we kept the overall weight low and used the conditions for all input neurons. Increasing the weight decay keeps the overall weight low and uses the conditions for all input neurons. The weight decay of DNN was set to 0.015 in this study. For a comparison of the results, the DNN and kernel-based DNN were set to the same parameters. The image kernel size was set to only \(7\times 7\) in the case of kernel-based DNN, as shown in the structure from Figure 5b.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model Parameters** & **DNN** & **KDNN** & **CNN** \\ \hline Input data dimension & - & \(7\times 7\) & \(7\times 7\) \\ Filter depth in convolutional layers & - & - & [48; 96; 96; 192; 192] \\ Filter size in convolutional layers & - & - & [3; 3; 3; 3; 1] \\ Number of nodes in fully connected layer & [100; 100; 50; 50; 25; 10; 10] & [96; 48; 24] \\ Activation function & \multicolumn{3}{c}{The rectified linear unit (ReLU)} \\ Optimizer & \multicolumn{3}{c}{Stochastic gradient descent (SGD)} \\ Loss function & \multicolumn{3}{c}{Mean squared error (MSE)} \\ Max epochs & \multicolumn{3}{c}{300.00} \\ Batch size & \multicolumn{3}{c}{150.00} \\ Learning rate & \multicolumn{3}{c}{0.01} \\ Weight decay & 0.015 & 0.015 & 0.030 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Model parameters used in this study.