# Partial Discharge Data Augmentation and Pattern Recognition Method Based on DAE-GAN +
## 4 Case Analysis
### Evaluation of Data Augmentation Capability of the DAE-GAN Model
#### 4.2.2 Evaluation of Model-Generated Sample Diversity and Distribution Similarity  
Taking surface discharge as an illustrative example, the t-distributed stochastic neighbor embedding (t-SNE) algorithm [30] was utilized to perform dimensionality reduction on both real samples and a selection of generated samples from each model. This method allows for visualizing the high-dimensional data in a more interpretable, low-dimensional space. The resulting visual representations of these samples are provided in Figure 8.  
As clearly shown in Figure 8, both BEGAN and VAE models experienced mode collapse, with the generated samples concentrated in a small area near the real samples. In contrast, CWGAN-GP and DAE-GAN, which account for the 1-Lipschitz continuity condition, have their generated samples scattered within the distribution range of the real samples, indicating better diversity. Figure 8: The dimension reduction results of PD samples. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & **Tip** & **Floating** & **Bubble** & **Surface** & **MS-SSIM** \\  & **Discharge** & **Discharge** & **Discharge** & **Discharge** & **Mean Value** \\ \hline CWGAN-GP & 0.9175 & 0.9449 & 0.9732 & 0.9728 & 0.9521 \\ BEGAN & 0.9197 & 0.7932 & 0.9995 & 0.9551 & 0.9169 \\ VAE & 0.8470 & 0.9023 & 0.956 & 0.9383 & 0.9109 \\ DAE-GAN & 0.9504 & 0.9993 & 0.9995 & 0.9763 & 0.9814 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: MS-SSIM index of different models. While diversity gives an indication of variety, another crucial aspect of generative model evaluation is how well the generated samples align with the original data's underlying distribution. A well-performing generative model should not only produce diverse samples but also accurately replicate the statistical properties of the real data. In this context, examining the probability distribution of the generated samples provides deeper insights into how closely the model captures the real data structure. Therefore, it is essential to assess not only the spread of the generated samples but also their probability density relative to the original dataset. The generative capability of a model is primarily reflected in the accuracy of fitting the original distribution. Evaluating model performance solely based on diversity has certain limitations. Using the 'ksdensity' function in MATLAB to approximate the distribution of the dimensionally reduced samples, the probability distributions of the real samples and the generated samples from each model are compared in Figure 9. The 3D probability distribution plot illustrates the distribution of samples after dimensionality reduction. The \(X\)-axis and \(Y\)-axis represent the two dimensions of the samples, while the \(Z\)-axis and color indicate the probability density of the samples at different positions. This visualization helps to intuitively display the distribution characteristics and correlations between variables. A comparison of subfigures (a) and (b) in Figure 9 shows that the probability distributions of samples generated by BEGAN and VAE are confined to specific regions, displaying significant differences from the distribution of real samples. While CWGAN-GP generates probabilities closer to the real samples, some small areas exhibit excessively high probabilities. The 3D visualizations reveal that the probability distribution of samples generated by DAE-GAN closely aligns with that of real samples. The reason is that the autoencoder first reduces the dimensionality of the original samples and then maps them back to the high-dimensional sample space. This two-step process allows the model to preserve the essential features of the original data while effectively reconstructing them in higher dimensions. As a result, the generated samples maintain key characteristics of the real data, leading to a probability distribution that more accurately reflects that of the original samples.