# A Generative Adversarial Network Structure for Learning with Small Numerical Data Sets
###### Abstract  
In recent years, generative adversarial networks (GANs) have been proposed to generate simulated images, and some works of literature have applied GAN to the analysis of numerical data in many fields, such as the prediction of building energy consumption and the prediction and identification of liver cancer stages. However, these studies are based on sufficient data volume. In the current era of globalization, the demand for rapid decision-making is increasing, but the data available in a short period of time is scarce. As a result, machine learning may not provide precise results. Obtaining more information from a small number of samples has become an important issue. Therefore, this study aimed to modify the generative adversarial network structure for learning with small numerical datasets, starting with the Wasserstein GAN (WGAN) as the GAN architecture, and using mega-trend-diffusion (MTD) to limit the bound of virtual samples that the GAN generates. The model verification of our proposed structure was conducted with two datasets in the UC Irvine Machine Learning Repository, and the performance was evaluated using three criteria: accuracy, standard deviation, and \(p\)-value. The experiment result shows that, using this improved GAN architecture (WGAN_MTD), small sample data can also be used to generate virtual samples that are similar to real samples through GAN. small datasets; virtual sample; generative adversarial network +
Footnote †: 2021: 14 November 202  
Typically, in statistics, a small sample can be referred to a data set with a sample size of less than 30. However, in real-world problems, the sample size should be determined according to the purpose of the survey. Because a small sample may be a tiny subset of the population, it is not possible to fully express the whole information of the population, which may lead to biased machine learning results and poor prediction performance. Furthermore, an incomplete data structure or imbalanced dataset is also a common problem in small-sample learning. It is believed that small samples still contain the underlying information. Thus, finding the clue hidden inside small samples, and inferring these samples' corresponding population information, is meaningful for practical needs. There are many acceptable methods for small-sample learning, of which virtual sample generation (VSG) is one of the main methods as used, for example, by [PERSON] et al. [14] with the bootstrap method. [PERSON] et al. [15], based on statistical inference mechanisms and using the principle of repeated sampling without replacement, investigated mathematical algorithms for converting limited 2D images into 3D images. [PERSON] et al. [16] produced a functional virtual population through the trial-and-error method. According to [PERSON] [17], in order to solve the problem of incomplete information, the principle of information diffusion on display based on fuzzy theory has a more sufficient and long-term continuity and development. [PERSON] and [PERSON] [18] reasoned that the normal diffusion function infers that each sample point can spread on both sides of two derivative samples, increasing the possibility of improving the accuracy of the neurologic network for learning with a small sample; this approach is called a diffusion neural network. Like the approach of [PERSON] et al. [19], based on the sample derivation formula of [PERSON] and [PERSON] [18], the mega-trend-diffusion (MTD) technique takes into account the overall information of all data, and is proposed to infer the value domain of the parent. Generative adversarial networks (GANs) have become one of the commonly used models for producing virtual samples. The GAN structure is a sample generation method developed by [PERSON] et al. [13] that uses the confrontation between the generative network (the Generator), and the discriminative network (the Discriminator) as the main core to ensure the generated virtual samples are closer to the training samples.