# A Generative Adversarial Network Structure for Learning with Small Numerical Data Sets
## 4 Experimental Study
### Experiment Results  
Table 2 shows the results of generating virtual samples by WGAN_MTD with training dataset having a size of 10 (denoted by 10 TD) from the Wine dataset. The table includes the accuracy of the experiment conducted 30 times, the average accuracy (denoted by average), standard deviation (denoted by stddev), and the \(p\)-value between only small dataset samples (denoted by SDS) and WGAN_MTD (proposed method denoted by PM), in different prediction models (denoted by SVM_poly, SVM_rbf, Decision_Tree, and Naive Bayes). \(p\)-value < 0.05 is denoted by *, \(p\)-value < 0.01 is denoted by **, \(p\)-value < 0.001 is denoted by *** and \(p\)-value > 0.05 means the state is not stable, and is denoted by ns. The experiment shows that our method works better in every prediction model as indicated by the better average accuracy and significant \(p\)-value (under 0.01) for 10 TD in the Wine dataset with 100 virtual samples. Table 3 shows the results of generating virtual samples by WGAN_MTD with a different number of training datasets (10, 15, and 20) in the Wine dataset, omitting the detailed results of the 30 replications of the experiment. With 15 training datasets, as shown in Table 3, the experiment shows that our method works better in the SVM polynomial and decision tree, as indicated by better average accuracy and significant \(p\)-value (under 0.05) when using the Wine training dataset with 100 virtual samples. As reported in Table 3, the experiment also shows that our method works better in both the SVM and decision tree, as indicated by the better average accuracy and significant \(p\)-value (under 0.05) when using 20 training datasets in the Wine dataset with 100 virtual samples. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Datasets**} & \multirow{2}{*}{**Total Samples**} & \multirow{2}{*}{**Input Attributes**} & \multirow{2}{*}{**Output Attributes**} & \multicolumn{3}{c}{**Number of Samples**} \\ \cline{5-6}  & & & & **Class 1** & **Class 2** & **Class 3** \\ \hline Wine & 178 & 13 & 1 & 59 & 71 & 48 \\ \hline Seeds & 210 & 6 & 1 & 70 & 70 & 70 \\ \hline Cervical Cancer & 72 & 18 & 1 & 21 & 51 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Detail of datasets. Table 4 shows the results of generating virtual samples by WGAN_MTD with different numbers of training datasets (10, 15, and 20) in the Seeds datasets when omitting the detailed results of 30 replications of the experiment. When the 10 training datasets are used in the Seeds dataset with 100 virtual samples, the experiment shows that our method works better in the SVM with the polynomial kernel and Naive Bayes, as indicated by the better average accuracy and significant \(p\)-value (under 0.05). The experiment results show that our method only works better in the SVM with the polynomial kernel, as indicated by the better average accuracy and significant \(p\)-value (under 0.01), when the training dataset  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**SVM\_Poly**} & \multicolumn{2}{c}{**SVM\_Rbf**} & \multicolumn{2}{c}{**Decision\_Tree**} & \multicolumn{2}{c}{**Naive\_Bayes**} \\ \cline{2-9}  & **SDS** & **PM** & **SDS** & **PM** & **SDS** & **PM** & **SDS** & **PM** \\ \hline
1 & 58.333\% & 59.524\% & 66.071\  
size increases to 15 and 20 in the Seeds dataset with 100 virtual samples. In Table 5, the experiment results show a similar pattern to that of Table 4; that is, our method only works better in the SVM with the polynomial kernel, as indicated by the better average accuracy and significant \(p\)-value (under 0.01), when the training dataset size increases to 15 and 20 in the Cervical Cancer dataset with 100 virtual samples.