## 4 Experimental Environment and Results
### Experimental Results  
The initial performance test of the proposed model, the ablation study, and the benchmark models (previously proposed anomaly detection model [25], Skip-GANomaly [30], GANomaly [10], EGBAD [28], and AnoGAN [4] is done by calculating the area under the curve (AUC) of the receiver operating characteristics (ROC). AUC is a function created using true-positive rates (TPR) and false-positive rates (FPR) with different threshold values during the inference process. The results for all the models can be seen in Table 3.  
A qualitative evaluation metric called Frechet Inception Distance (FID) [42] is calculated for the proposed model and the benchmark models. This method is designed to evaluate the generated image quality by calculating the distance of feature vectors between the real image and the corresponding reconstructed image. This estimation is done using the Inception-v3 [43] image classification model. The conditional class probability and the confidence score of each image are combined. This is shown as:  
\[FID=|\mu_{r}-\mu_{g}|^{2}+Tr(\sum_{r}+\sum_{g}-2(\sum_{r}\sum_{r}\sum_{g}-1/2) \tag{7}\]  
where \(X_{r}\sim N(\mu_{r},\sum_{r})\) and \(X_{g}\sim N(\mu_{g},\sum_{g})\) are 2048-dimensional final average pooling activations (which is the default layer selected in this study) for real input images and the corresponding generated images. If both images are identical, the score should be 0. Although a lower score means better performance, an acceptable value for unsupervised learning is generally not known. In this study, a total of 500 constructed images from all three classes (adult, child, and elderly) are compared with their real counterparts, and an average FID score for all classes is obtained. The FID score comparison between the proposed model and the benchmark models can be seen in Table 4. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Normal**} & \multirow{2}{*}{**Anomaly**} & \multirow{2}{*}{**Proposed**} & \multirow{2}{*}{**Conv**} & \multirow{2}{*}{**D. Conv.**} & \multirow{2}{*}{**Previous**} & \multirow{2}{*}{**Skip-GANomaly**} & \multirow{2}{*}{**GANomaly**} & \multirow{2}{*}{**EGAD**} & \multirow{2}{*}{**AnoGAN**} \\  & & & **Only** & & **Only** & & **Model**[25] & [90] & [10] & [28] & [4] \\ \hline Adult + Elderly & Child & 88.45 & 82.36 & 75.84 & 85.07 & 83.34 & 80.45 & 79.63 & 78.57 \\ Child + Adult & Elderly & 83.43 & 81.66 & 73.01 & 80.44 & 79.32 & 78.82 & 76.16 & 74.53 \\ Child + Elderly & Adult & 84.16 & 80.72 & 71.58 & 82.89 & 81.25 & 80.01 & 75.34 & 73.42 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The results for the area under the curve (AUC) of receiver operating characteristics (ROC) of the proposed model, the previously proposed model for Alzheimer’s disease anomaly detection, the ablation study of the single convolutional pipeline as well as the single dilated convolutional pipeline, Skip-GANomaly, GANomaly, EGBAD, and AnoGAN. Figure 4: Anomaly scores for three different cases. The normalization of the anomaly value for each image of the test dataset forms a normal distribution in the histogram. It is expected that the normal inference images will form a normal distribution closer to zero, and the abnormal inference images will form a normal distribution closer to one. The third performance metric used for inference is classification accuracy. To achieve this, the parallel encoder network using both the CNN and the DCN has a Softmax layer (three nodes representing the three classes), added to the end of its feature vector, and supervised training is performed. For this training, stochastic gradient descent (SGD) with lambda decay and Nesterov momentum with the initial learning rate \(10^{-2}\) is used for the proposed model and the benchmark models. Both the proposed model and the benchmark models are trained for 40 epochs. The benchmark models such as DenseNet-169 [44], Inception-v4 [45], ResNet-101 [46], and VGG19 [47] are compared with the proposed model's classification accuracy.