# A Generative Adversarial Network Structure for Learning with Small Numerical Data Sets
###### Abstract
Since the GAN method was published in 2014, it has been regarded as an important method for virtual sample generation of image data. It has also been extensively applied, and many extensions to and improvements of GANs have been made. According to the GAN Zoo website, there are more than 70 types of GAN. [PERSON] and [PERSON] [20] improved the GAN and proposed conditional generative adversarial nets (cGAN), adding additional conditions to the generative and discriminative networks, so that the model can be generated and determined with additional conditions. The improvement also transformed the GAN structure from an unsupervised learning model to a supervised model. [PERSON] et al. [21] proposed the Wasserstein GAN (WGAN) to improve the problem of gradient vanishing, by replacing the sigmoid function for the discriminative network, introducing the concept of Wasserstein Distance, and adding the 1-Lipschitz continuous function. As a result, the output of the discriminative network [0, 1] was changed to the degree of similarity to the training sample. Figure 1: The architecture of GAN. The VSG method provides a good solution for learning with small datasets; however, it cannot verify the quality of the virtual sample it generates. If the generated virtual sample is biased, it leads to biased results of subsequent modelling. Although the GAN and its extension improvement methods enhance the similarity between the generated virtual sample and the real sample, the cost in terms of the time required to train the sample is very large, and the GAN mostly uses vast graphic data sets as its input rather than small sets of numeric data. In addition, the GAN (e.g., its discriminative network) is based on the convolutional neural network (CNN), which is a deep neural network (DNN) and does not apply to data learning scenarios with a sparse sample [22]. The development of a process suitable for small-sample learning under the framework of a GAN, to effectively improve the sample quality generated by the VSG method and thus improve the learning efficiency of small samples, is a topic worth exploring. This study proposed a GAN architecture that can generate effective virtual samples with only a small dataset. Based on the original architecture of GANs, the graphical generation part of the generative network was modified to numerical generation, the MTD virtual sample generation method was modified, and the tanh function was adopted as the activation function of the output layer in the generative network (of the GAN). It aims to facilitate the match between the two so that the random numbers generated by the GAN through Latent Space could be limited by the MTD method and finally restored to a value close to that of the original. In this study, we proposed a new method based on the Wasserstein GAN (WGAN) architecture and modified mega-trend-diffusion (MTD) as a limitation of the GAN generative network to reverse the back-propagation network (BPN) to actually generate and identify the networks of the GAN. Thus, this study used this improved GAN architecture, called WGAN_MTD, so that small-sample data can also be used to generate virtual samples that are similar to real samples through the GAN. We verified the model with two public data sets from the UC Irvine Machine Learning Repository and compared the performance, in terms of accuracy, standard deviation, and \(p\)-value, with other methods of supporting classification models, such as support vector machines (SVM), decision tree (DT), and Naive Bayes. The results showed a better classification performance than those models without generating virtual samples. The following section is dedicated to a review of the related research. Our approach to improve the generating network ability of GANs in the context of the numerical small-sample classifier, based on MTD, is presented in Section 3. The proposed approach was validated based on experiments with two public datasets, as presented in Section 4. Finally, Section 5 concludes the paper.