## 2 Related Work
### The Data Argumentation Based on the GAN  
Data augmentation is effective for expanding the scale of data and has been widely used in image processing, natural language processing, and other fields. Data augmentation can enrich the dataset itself and improve the generalization performance of the model. According to the different ways of data augmentation, current data augmentation techniques can be divided into supervised and unsupervised data augmentation. Supervised data argumentation mainly includes single-sample data argumentation techniques (such as the geometric transformation of rotation, cropping, and color transformation) and multi-sample data argumentation techniques (such as SMOTE, SamplePairing, and Mixup) [26; 27]. Data augmentation techniques are mainly based on deep learning, such as generative adversarial networks (GANs) [9; 28].  
In view of geographic data sparsity, it is necessary to choose an appropriate data argumentation method. The single-sample data argumentation technology is relatively straightforward. However, this method causes inconsistencies with the distribution of the original data. Multi-sample data argumentation techniques, such as the Mixup algorithm based on linear interpolation, although simple to implement, can only be effective when the data distribution exhibits a linear law. However, most of the geographic data present the characteristics of nonlinear distribution, and it is difficult to achieve good results using this method [22]. A generative adversarial network is a data augmentation technology based on deep learning and can solve the above two problems.  
The theory of the generative adversarial network comes from the two-person zero-sum game in game theory [9], and its structure is shown in Figure 1. The network has a generator (denoted by G) and a discriminator (denoted by D), where neural networks are used. The role of the generator is to capture and learn the distribution of sample data, and the role of the discriminator is to judge data authenticity. There are no mandatory restrictions on the choice of the two models. The task of [PERSON] is to generate a sample Xfake that is as close to the real distribution as possible, and its input is random noise Z. D is a binary classifier whose task is to judge the authenticity of the data for its input, a generated sample Xfake and real data Xreal. G and D are independent of each other and are alternately iteratively trained. Eventually, the data generated by [PERSON] become so close to the real data that D cannot tell whether the samples it inputs are generated data or real data.  
The training process of the GAN is a min-max game, which means that [PERSON] will minimize the errors when discriminating between true and false data and [PERSON] will maximize the probability of [PERSON]'s discriminating errors. Therefore, in the actual training process, [PERSON] will sample from the real data x and the data G(z) generated by [PERSON] Then, [PERSON] will bring the probability as close to 1 as possible when determining x as real data and bring the probability as close to 0 as possible when determining x as fake data.  
At the beginning of training, due to poor performance, [PERSON] does not generate good data samples, so D is easily judged to be false. However, it will become increasingly accurate because with the existence of [PERSON], [PERSON] can learn to approximate the real data samples without a lot of prior knowledge and prior distribution and finally generate samples that are realistic enough to be similar to the true data.