# Generative Adversarial Network for Class-Conditional Data Augmentation
## 4 Experiments
### Data Classification Comparison  
Validation-score: We evaluate the classification performance using the validation score (V-Score) [38]. The V-Score can measure the clustering accuracy. To calculate the V-Score, we need to compute two terms, which are homogeneity and completeness. On one hand, homogeneity \(v_{h}\) determines if each cluster has only the same label. On the other hand, completeness \(v_{c}\) measures if all data points of the same class label belong to the same cluster, which can be numerically evaluated as follows,  
\[v_{h} =\begin{cases}1,&\text{if }H(C,K)=0,\\ 1-\frac{H(C|K)}{H(C)},&\text{otherwise.}\end{cases} \tag{7}\] \[v_{c} =\begin{cases}1,&\text{if }H(K,C)=0,\\ 1-\frac{H(K|C)}{H(K)},&\text{otherwise.}\end{cases},\]  
where \(C=\{c_{1},\cdots,c_{n}\}\) denotes a set of classes, and \(K=\{k_{1},\cdots,k_{m}\}\) denotes a set of clusters. In (7), we normalize the conditional entropy \(H(C|K)\) and \(H(K|C)\) using \(H(C)\) and \(H(K)\), respectively, to remove class size dependencies.  
Then, the V-Score \(\mathcal{V}_{\beta}\) is the weighted mean of \(v_{c}\) and \(v_{h}\):  
\[\mathcal{V}_{\beta}=\frac{(1+\beta)v_{h}v_{c}}{\beta v_{h}+v_{c}}, \tag{8}\]  
where parameter \(\beta\) can be adjusted to favor either homogeneity or completeness. In our experiment, we set \(\beta\) to 1, giving the same weight to both metrics. The V-score results are obtained with the proposed conditional denoising autoencoder initialization only and not with adversarial training We apply the V-Score to the latent space obtained by the proposed conditional autoencoder and compared the latent space of our GANDA to that of BAGAN. As shown in Table 3, our method outperforms BAGAN. The performance improvements on V-Score can be obtained owing to explicit class conditioning in the latent space. For this experiment, we use the k-means algorithm to cluster the latent space and MNIST as the testing dataset, which consists of 10 classes. Please note that the number of class labels, the number of classes, the size of the data, and the clustering algorithm are independent of each other. Thus, the V-Score can accurately evaluate the quantitative classification performance.  
**Classification score:** Tables 4 and 5 show the effects of using the generated samples as augmented data for classification tasks. We conduct this experiment by changing the removal ratio for the minority class. For the MNIST [34] dataset, we compare the existing methods (i.e., Vanilla GAN [1], ACGAN [7], and BAGAN [2]) with the proposed GANDA. Our GANDA outperforms state-of-the-art methods in various removal ratios. The CelebA [35] dataset consists of very high-resolution images, where the proposed GANDA also outperforms state-of-the-art methods. The classification accuracy in Tables 4 and 5 are not empirically affected by slight changes in the specific network architecture in Table 1.  
\begin{table}
\begin{tabular}{c c} \hline \hline  & **V-Score (K-Means)** \\ \hline GANDA (conditional denoising autoencoder initialization) & 0.779 \\ \hline BAGAN (denoising autoencoder initialization) & 0.739 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of the proposed GANDA with BAGAN in terms of V-Score.