# Landslide Susceptibility Modeling Using a Deep Random Neural Network
###### Abstract
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Basic structures** & \multicolumn{1}{c}{**Method Descriptions**} & **References** \\ \hline Deep feedforward neural network (DNN) & \(\bullet\) & A DNN model with greedy unsupervised learning & [52] \\  & \(\bullet\) & SSL-DNN: A novel DNN model with semi-supervised learning & [53] \\  & \(\bullet\) & A kernel-based DNN & [54] \\  & \(\bullet\) & ACO-DBN: The DNN was integrated with the ant colony & [55] \\  & \(\bullet\) & A robust DNN model based on the combination of a DNN, extreme learning machine, ANN, and genetic algorithm & [56] \\  & \(\bullet\) & A DNN model with the particle swarm algorithm & [57] \\  & \(\bullet\) & A DNN model integrated with the SVM & [58] \\ \hline Convolution neural network (CNN) & \(\bullet\) & CNN-1D, CNN-2D, and CNN-3D methods & [33] \\  & \(\bullet\) & The CNN-1D with the Bayesian optimization algorithm & [46] \\  & \(\bullet\) & The CNN integrated with SVM, RF, and logistic regression & [59] \\  & \(\bullet\) & The CNN integrated with the metaheuristic optimization algorithm & [60] \\  & \(\bullet\) & LSGH-Net: A novel CNN method based on the CNN and Gaussian & [61] \\ \hline Recurrent neural network (RNN) & \(\bullet\) & A typical RNN model & [62] \\  & \(\bullet\) & A long-short-term memory (LSTM) model & [63] \\  & \(\bullet\) & A novel RNN model combining LSTM with a conditional random field & [64] \\ \hline Auto-encoder & \(\bullet\) & A typical auto-encoder model & [65] \\  & \(\bullet\) & A fully connected sparse auto-encoder model & [66] \\  & \(\bullet\) & An auto-encoder model integrated with the RF & [67] \\  & \(\bullet\) & A stacked auto-encoder with the sparse optimization & [68] \\ \hline \multirow{4}{*}{Deep learning ensemble methods} & \(\bullet\) & An ensemble model of CNN and RNN based on a stacking algorithm & [40] \\  & \(\bullet\) & An ensemble model of CNN, RNN, and LSTM based on shared blocks & [41] \\  & \(\bullet\) & An ensemble model of CNN, DNN, and ResNet & [42] \\  & \(\bullet\) & An ensemble model of CNN and RNN variants & [43] \\ \hline \multirow{2}{*}{Other methods} & \(\bullet\) & A deep boosting method & [44] \\  & \(\bullet\) & A deep learning tree & [44] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: A summary of the existing deep learning-based LSM methods. the network. The reason is that the size of the limited data does not match the volumes of the parameters of the complex structure, whereas the complex structure may lead to serious overfitting problems when the training data are insufficient. Therefore, the performance of deep learning methods is largely constrained in landslide susceptibility modeling due to the limitation of training data. In machine learning-based landslide susceptibility modeling, ensemble methods that rely on random strategies are usually effective in dealing with limited data. For example, Bagging randomly extracts subsets of samples to estimate landslide susceptibility [22]; rotation forest [70], random subspace [30], and RF adopt random features to improve the model's generalization skill. In wetland classification, [PERSON] et al. (2021) showed that the ANN with rotation forest effectively overcomes the negative impacts of reducing the training data size [32]. Similar techniques, such as DropOut [71], StochasticDepth [72], DropPath [73], and DropBlock [74] are also developed in deep learning. The basic idea of these methods is to insert perturbation into the model's structure randomly to avoid overfitting the training data. For instance, in DropPath, the network's sub-paths in the residual blocks of the FractalNet are randomly removed [73]. In landslide susceptibility modeling, deep learning methods require perturbation to be regularized. Therefore, exploring deep learning landslide models with random strategies can potentially handle limited landslide data. The present study proposes a novel deep learning-based method, named deep random neural network (DRNN), to improve the generalization capability of landslide modeling.