## 4 Experimental Environment and Results
### Model Evaluation  
Model performance is evaluated through multiple methods. First, a classification inference is performed with the parallel model to check whether the parallel encoder module is working accurately. Trained parallel model weights are frozen, a classification layer (softmax) is added, and fine-tuning is performed with the same training hyperparameters, with the categorical cross-entropy loss. Same hyperparameters are used to train the benchmark classification models. The benchmark result with other classification models is given in Table 3, and the confusion matrix of the parallel model can be seen in Figure 4.  
Class activation maps are helpful to highlight the regions where the model's attention is focused on in data visualization. These regions shown in Figure 3 are relevant to each different class. Thus, the greater the variance between these regions is, the more accurate the model performs. Looking at the model's class activation maps, both CNN and DCN  
Figure 4: Confusion matrix for the parallel model inference. The confusion matrix is drawn with the results from the inference using true labels and the model’s predicted labels. activation areas are complementary to each other in a given brain image. The four activation images on the left-hand side are from the CNN, whereas the four activation images on the right-hand side are from the DCN. Although the DCN has a lower activation area overall, the values in these areas are higher than the CNN activation values, indicating that the DCN features are distinct and unique. The second evaluation method is the area under the curve (AUC) [63]. It is a function that uses true positive rates (\(TPR\)) and false-positive rates (\(FPR\)) with varying threshold values from the inference data. \[TPR=\frac{TP}{TP+FN}\quad,\quad\quad FPR=\frac{FP}{FP+TN} \tag{5}\]  
where \(TP\) is a true positive, \(FN\) is a false negative, \(FP\) is a false positive, and \(TN\) is a true negative. The model's performance is compared with recent anomaly detection works such as GANomaly [29], Skip-GANomaly [56], EGBAD [32], and AnoGAN [23]. Additionally, an ablation study is performed on CNN pipeline and DCN pipeline networks. The comparison can be seen in Table 4.  
A qualitative evaluation method called Frechet Inception Distance (FID) [64] is applied as a metric. This method is used to evaluate the quality of the generated images by calculating the distance of feature vectors between the real and the generated images. The estimation is done via the Inception-V3 [60] model which was built on the original GoogLeNet architecture [65] classifies the generated image. The conditional class probability and the confidence of each image are combined. This is defined as [64]:  
\[FID=|\mu_{r}-\mu_{g}|^{2}+Tr(\sum_{r}+\sum_{g}-2(\sum_{r}\sum_{r}\sum_{g})^{-1/ 2}) \tag{6}\]  
where \(X_{r}\sim N(\mu_{r},\sum_{r})\) and \(X_{g}\sim N(\mu_{g},\sum_{g})\) are 2048-dimensional activations of the pool3 layer for real and generated samples. If both images are identical, the score should ideally be 0. Since there is no clear given metric value that is acceptable for unsupervised learning in the literature, there might be problems with what the acceptable value. A total of 1000 constructed images gathered from each class were compared with the correspond \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **AD-NC** & **MCI-NC** & **AD-MCI** \\ \hline GANomaly [29] & 59.31 & 57.33 & 48.34 \\ EGBAD [32] & 58.46 & 60.31 & 54.71 \\ AnoGAN [23] & 55.71 & 52.93 & 48.11 \\ Skip-GANomaly [56] & 71.42 & 67.02 & 68.56 \\ Ablation-Conv. & 68.71 & 65.34 & 61.25 \\ Ablation-Dilated Conv. & 60.82 & 54.02 & 52.40 \\ Proposed Model & 75.21 & 70.84 & 71.85 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Area under the curve (AUC) results of benchmark models GANomaly, EGBAD, AnoGAN, Skip-GAN, and ablation study of the proposed model, and the proposed model itself.