## 3 Results and Discussion  
### Data Augmentation  
The augmented data were affected by the PDF of the random noise, as shown in Figures 5 and 6. The GNDv1 with a small \(\beta\) exhibited a high central density, as shown in Figure 1a. Subsequently, most artificial data samples tended to be close to each other, as shown in Figure 5b. Furthermore, the GNDv1 with a small \(\beta\) exhibited a higher probability density at its tail than that with a large \(\beta\). Thus, few samples exhibited extreme fluctuations, as shown in Figure 5b. When \(\beta\) was large, the samples were widely distributed, as shown in Figure 5c,d. However, extremely fluctuating samples were not generated for a large \(\beta\).  
The GNDv2 with a negative \(\kappa\) had a higher density on the negative side than on the positive side. Thus, the generated samples tended to be skewed toward lower values, as shown in Figure 6b. Additionally, a negative \(\kappa\) yielded a higher density, at larger positive values, than a positive \(\kappa\), resulting in occasional fluctuation to the positive side in a few samples. Conversely, when \(\kappa\) was positive, most generated samples were skewed toward higher values, as shown in Figure 6d; this was because the PDF of the random noise was skewed toward the positive side. Some artificial samples of positive \(\kappa\) exhibited negative amplitudes because the corresponding GNDv2 had a considerable probability density for negative random noise, as shown in Figure 3a. Thus, negative amplitudes could downgrade the classification accuracy because they were not observed in the original data.  
Figure 5: Artificial data generated with GNDv1. The \(y\)-axis represents the normalized amplitude in the frequency domain.  
A cut-off on the PDF of the random noise can be used to prevent negative amplitudes in the artificial data. Specifically, random noise values less than a threshold \(e_{\text{th}}\) can be excluded when augmenting the data, as shown in Figure 7. Figure 8 shows the augmented data when \(\kappa=0.5\) and \(e_{\text{th}}=-2\), \(-1\), and \(-0.5\). When \(e_{\text{th}}=-0.5\) and \(-1\), no negative amplitudes were generated. Moreover, they exhibited a pattern similar to that of the original data.  
Figure 6: Artificial data generated with GNDvw2. The \(y\)-axis represents the normalized amplitude in the frequency domain.  
Figure 7: Cut-off for the PDF of GNDv2.  
To investigate the effects of this cut-off technique on classification accuracy, a CNN classifier was trained with the augmented data. Then, the accuracy values in the absence/presence of the cut-off were obtained and compared, as presented in Table 1. When the cut-off was applied, the augmented data presented greater similarity to the original data; therefore, we expected the accuracy to increase over \(e_{\text{th}}\). However, the accuracy decreased as more of the PDF was removed.  
This result was obtained because sample variation was important for accurate classification. The sample variation decreased significantly when the cut-off was applied to the random noise, as shown in Figure 8. Additionally, the number of low-quality samples (i.e., samples with negative amplitudes) is very small; thus, their effect on the classification can be deemed negligible. Consequently, the cut-off technique was not used.