## 3 Methods for Landslide Identification
### Semi-Supervised Generative Adversarial Network Model Construction
Take the images of \(n\times n\times n_{c}\) as the input, with n as the side length of the image and \(n_{c}\) the number of channels. Fill the image boundary with 0 elements with the number of \(p_{0}\), and slide in the input image using the convolution kernel with a size of \(f_{k}\times f_{k}\times n_{c}\), and the number of \(n_{c}^{\prime}\) at a step distance of h\({}_{c}\). During the sliding process, the convolution kernel and the corresponding image pixel are multiplied and then added, and the calculation result is the updated corresponding pixel value. The operation results of the input image and a convolutional layer are shown in the following formula, where the upper \([l]\) represents the first neural layer; \([. ]\) represents rounding down. \[n^{[l+1]}=\left\lfloor\frac{n^{[l]}+2p_{0}-f_{k}}{h_{c}}+1\right\rfloor\times \left\lfloor\frac{n^{[l]}+2p_{0}-f_{k}}{h_{c}}+1\right\rfloor\times n_{c}^{ \prime} \tag{2}\]  
The pooling layer serves a fundamental purpose in CNN by reducing the size of the feature map while preserving essential characteristic information, thus diminishing data redundancy. Following convolution and pooling operations, the CNN extracts these characteristics to construct a feature map. The incorporation of LeakyReLU activation func  
Figure 3: Semi-Supervised Generative Adversarial Network Structure. The red arrow represents the input and discriminant result of the real sample, and the green arrow represents the input and discriminant result of the generated sample. The yellow represents the factor, the red and orange are the labels. Grey represents random noise data vector and input data vector respectively. tions enhances the model's nonlinearity, preventing gradient vanishing, and consequently, improving the model's generalization capabilities. The batch normalization (BN) layer plays a crucial role in accelerating network training while enhancing the model's accuracy and robustness. The fully connected layer is typically located at the final segment of the CNN's hidden layers. It effectively discards the spatial topological relationships within the feature map, converting it into a series of vector-based features. These features are then propagated to the output layer through an activation function. In this particular study, the discriminator ultimately generates three output neurons via the fully connected layer, corresponding to the three categories: non-landslide (0), landslide (1), and fake. The input to the generator is composed of random noise adhering to a normal distribution. This noise undergoes reshaping before being upsampled through transposed convolution. The feature map produced via transposed convolution is progressively remapped to the spatial domain of the original input image. This meticulous process guarantees that the generated image attains a semantic level of interpretation by the discriminator, matching the pixel-level fidelity of an authentic image. The calculation for determining the output feature map size resulting from the transposed convolution operation can be expressed using Formula (3). In this formula, 'k' represents the size of the convolution kernel,'s' indicates the stride, and 'p' denotes image boundary padding. During this operation, both LeakyReLU activation and the batch normalization (BN) layer are applied to expedite the training process and enhance the model's stability  
\[n^{[l+1]}=\lfloor s(i-1)+2p-k+2\rfloor\times\lfloor s(i-1)+2p-k-2\rfloor\times n _{c}^{\prime} \tag{3}\]  
From the perspective of loss function, the model built in this paper mainly uses two types of losses: binary cross-entropy (BCE) and multi-class cross-entropy (MCE). BCE is used to measure the gap between the predicted value of the model and the real label in the binary classification problem, and the calculation is shown in Formula (4), where y is the real label of the sample (the value is 0 or 1), and \(\hat{y}\) is the output category probability value of the model.