## 5 Conclusions  
In this work, an analysis of Alzheimer's Disease as an anomaly in PET images using an unsupervised anomaly detection model featuring a parallel feature extractor is conducted. The parallel feature extractor consists of a CNN and a DCN. Latent vectors obtained from both pipelines are concatenated and used as the main feature vector to reconstruct the input image. The discriminator takes both the original input image and the reconstructed image as input and labels them as either real or fake. As it is shown in Tables 4 and 5, the proposed model outperforms the previous anomaly models both quantitatively and qualitatively by having a classification accuracy of 96.03%, 0.59% higher than DenseNet169, and an AUC score of 75.21%, 3.79% higher than Skip-GANomaly. The ablation study shows that the proposed model also outperforms ablation study sub-networks. The narrow activation areas with high values seen in the DCN class activation maps provide a boosting effect to the CNN's wider, but much lower value areas. The justification of the superior performance in the classification of the parallel feature extractor model is given in Table 3 and the proof is given in the form of class activation maps, as shown in Figure 3. Although there are no solid metric values of the optimal performance for the unsupervised models, comparison based on the FID score shows that the model produces images similar to the real ones.The score comparisons are given in Table 5, and a sample batch of images is shown in Figure 5. There are multiple discussions to be made in future studies:  
* Among the three loss functions, the importance of each loss function can be evaluated. A genetic algorithm or a grid search can be used to assign weights for each loss function to observe its effect on the model. * The depth of the parallel model can be altered by using other parameter search algorithms. A deeper model may increase the computational cost while improving the accuracy. * The skip connections used in autoencoders have been showing promising results [57]. The possibility and feasibility of skip connections will be investigated to further improve the performance of the model. * Probable ways to improve the AUC score further will be investigated. Figure 6: Anomaly score distributions for test images. Note that the anomaly scores are normalized to \([0,1]\), and the images with higher anomaly scores are reflected with values closer to 1 while the normal images are closer to 0. (**a**) AD-NC case. AD is considered the anomaly, which reflects a higher anomaly score in the distribution. (**b**) MCI-NC case. MCI is considered the anomaly, which reflects a higher anomaly score in the distribution. (**c**) AD-MCI case. AD is considered the anomaly, which reflects a higher anomaly score in the distribution. **Author Contributions:** Conceptualization, H.B.B., J.-S.P., and D.-Y.K. ; methodology, H.B.B. and J.-S.P. ; software, H.B.B. ; validation, H.B.B., J.-S.P., and D.-Y.K. ; formal analysis, H.B.B. and J.-S.P. ; investigation, H.B.B., J.-S.P., and D.-Y.K. ; resources, ADNI; data curation, ADNI; writing--original draft preparation, H.B.B. ; writing--review and editing, J.-S.P., and D.-Y.K. ; visualization, H.B.B., supervision, J.-S.P., and D.-Y.K. ; project administration, J.-S.P., and D.-Y.K. ; funding acquisition, J.-S.P., and D.-Y.K. All authors have read and agreed to the published version of the manuscript. **Funding:** This research was supported by the National Research Foundation (NRF) funded by the Ministry of Science, ICT & Future Planning (NRF-2018R1A2B2008178) & Brain Busan 21+ Program. **Institutional Review Board Statement:** The study was conducted according to the guidelines of the Declaration of Helsinki, and approved by the Institutional Review Boards of both Kyungsung University and Dong-A University. **Informed Consent Statement:** All subjects gave their informed consent for inclusion before they participated in the study.