## 3 Results and Discussion
### Accuracy Improvement  
The accuracy was obtained for various shape parameters over different augmented data samples; the shape parameter \(\beta\) of GNDv1 was varied from 0.2 to 3.5, while the parameter \(\kappa\) of GNDv2 was varied from \(-2\) to 2. A total of 80, 160, 480, and 800 artificial samples were generated per class. Then, the artificial and original datasets were used for training the CNN classifier. For a reliable comparison, the effects of the initial weight of the CNN classifier and the augmentation randomness on accuracy need to be minimized. To this end, the accuracies for various initial weights and several augmentation trials were obtained. The final accuracy \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{1}{c}{**Number of**} & \multicolumn{4}{c}{\(e_{\text{th}}\)} \\ \cline{2-5}
**Augmented Data** & **No** & \(-\)**2** & \(-\)**1** & \(-\)**0.5** \\
**Per Class** & **Cut-Off** & & & \\ \hline
0 & \multicolumn{4}{c}{71.2} \\ \multicolumn{1}{c}{(Original)} & \multicolumn{4}{c}{(0.663)} \\
80 & 74.12 (0.543) & 72.48 (0.473) & 71.2 (0.476) & 70.04 (0.531) \\
160 & 76.52 (0.444) & 74.48 (0.724) & 71.84 (0.594) & 70.80 (0.493) \\
480 & 79.72 (0.604) & 75.08 (0.557) & 71.68 (0.340) & 70.40 (0.400) \\
800 & 78.08 (0.476) & 76.68 (0.403) & 71.64 (0.500) & 69.00 (0.370) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Effects of data cut-off on classification accuracy. The GNDv2 with \(\kappa\) = 0.5 was used. The numbers in parentheses represent the standard errors. Figure 8: Augmented data of Class 1 with GNDv2: (**a**) \(\kappa=0.5\) and no cut-off; (**b**) \(\kappa=0.5\) and \(e_{\text{th}}=-2\); (**c**) \(\kappa=0.5\) and \(c_{\text{th}}=-1\); (**d**) \(\kappa=0.5\) and \(e_{\text{th}}=-0.5\). When the augmented dataset was added to the training dataset, the accuracy significantly increased in most cases compared to when the original dataset was used alone. In the case of the dataset generated using GNDv1 (Figure 9), the accuracy increases as \(\beta\) increases for \(\beta<1\). This suggests that a smoother distribution is more effective for generating high-quality brainwave data. For \(\beta>1\), the effects of \(\beta\) on accuracy were negligible because the changes in the PDF were not considerable, as shown in Figure 2a. Furthermore, the accuracy increased as the number of samples with the artificial dataset increased. For example, for a large \(\beta\), the accuracy improvement was approximately 2% when 80 samples were augmented. The improvement was approximately 7% when 800 samples were added. When artificial data were created using GNDv2, high accuracy was achieved for \(0<\kappa<1\), as shown in Figure 10. This suggests that high-quality brainwave signals can be generated when the PDF of the random noise is slightly skewed toward the positive side. The accuracy also improved as the number of artificial samples increased. However, when \(\kappa>0.3\), a higher level of accuracy was achieved with 480 samples than with 800 samples. We speculate that this counterintuitive result was obtained because the effect of negative amplitudes was considerable only when the number of artificial samples was very large. Specifically, when \(\kappa\) was positive, negative amplitudes were generated, which were not observed in the original dataset. However, negative amplitudes would be rare if the number of samples was not sufficiently large (i.e., less than 480). Thus, the effect of negative amplitudes was small. Therefore, if a sufficiently large number of samples is created, the training dataset is likely to contain a considerable number of negative amplitudes, leading to accuracy degradation. Thus, a lower accuracy was achieved with 800 artificial samples than with 480 samples. To verify that the accuracy could be improved by the flexible CMD in other bio-signals, the model was applied to an electromyography (EMG) signal.