# Data Mining Approaches for Landslide Susceptibility Mapping in Unyeonsan, Seoul, South Korea
## 4 Methodology
### Artificial Neural Network  
An ANN is a statistical learning algorithm that describes a neuronal signaling system. The human brain regulates the connection strength of synapses between neurons and determines whether signals are delivered or not; the ANN learns to derive the results with minimum error by adjusting the weight between input data and output data. The unit of the ANN is the perceptron, which is divided into an input layer and an output layer. The input layers are represented by nodes, which are linked to an edge having the weight of each node [57]. The model outputs 1 when the sum of the values of each layer multiplied by the weight is greater than or equal to the threshold; otherwise, the output is \(-1\). This type of perceptron can only be applied to a linear classification and is not applicable in most cases.  
In this study, multi-layered perceptrons allowing classification of nonlinear data were used with a hidden layer between the input and output layers. A feed-forward network was used for the map learning. The learning of neural networks progressed via a backpropagation algorithm that propagates the errors generated in the output layer to each layer and corrects the weights. In other words, the backpropagation algorithm learns the neural network by inverting the step, and the result most similar to the output layer value is derived based on the input layer. The process can be simplified as a combination of nodes and edges [58]. The backpropagation algorithm can be expressed by the following equation:  
\[\omega_{k}^{up}=\ \omega_{k}-\eta^{*}\frac{\partial E_{total}}{\omega_{k}} \tag{16}\]  
where \(\omega_{k}\) is the updated weight for connection \(k\) and \(\eta\) is the learning rate. The initial value of weight \(\omega_{0}\) is given randomly. \(E_{total}\) is the error of the final output result when the expected output value is assumed to be \(T\), according to the input data [59].  
\[E_{total}=\ \frac{1}{2}\sum_{j}^{n}\Bigl{(}T_{j}-out_{oj}\Bigr{)}^{2} \tag{17}\]  
where \(j\) is the number assigned to the node in each layer, and \(n\) is the number of output layers. Because the backpropagation algorithm updates the weights while propagating the error generated from the output to the input direction, it updates the weights starting from the portion from the output. \(E_{total}\) is calculated repeatedly using the updated weight so as to be minimized; the differentiation of \(E_{total}\) is fundamental. Therefore, when the calculated value is passed to the next layer or is expected to be the final result, an activation function is used to convert it to a range of values. In this study, a unipolar sigmoid function was used. The equation of the unipolar sigmoid function is as follows:  
\[f(x)=\frac{1}{1+e^{-x}} \tag{18}\]  
Using the activation function, the output value of each layer is adjusted from 0 to 1.  
In this study, the ANN model was processed using MATLAB R2015a software (MathWorks, Massachusetts, MA, USA). Areas where the slope data were 0 were set as areas not prone to landslide occurrence and used for training data; landslide occurrence point data were also allocated to the training set. The backpropagation algorithm of the ANN was applied to estimate the weights between the input and the hidden layers, and between the hidden and the output layers by updating the hidden nodes and the learning rate. In this study, the input data were normalized to the range of 0.1-0.9 and a 17 \(\times\) 34 \(\times\) 1 structure was selected for the networks. The learning rate was set to 0.01 with a randomly selected initial weight. The number of epochs was set to 2000, and the root mean square error value was set to 0.1, which was used for the stopping criterion.