## 1 Introduction
As an example, during the feature selection process, features that are related to AD are chosen from various modalities which may include cortical thickness, brain glucose metabolism, subcortical volumes, and cerebral A\(\beta\) accumulation in regions of interest (ROI), such as the hippocampus [16]. Recent works make use of multi modalities of MRI, PET, and fMRI images, and use various preprocessing techniques such as segmentation [17] to improve the accuracy of their proposed models [18]. Recent developments in deep learning technology have led to a massive surge of constantly-improving models, especially in the computer vision area, mainly due to the improvements brought by convolutional neural networks (CNNs). These models learn to extract meaningful features from inputs and produce highly accurate results. The replacement of human experts with automated systems in the near future is being discussed due to the reduced cost and relatively similar performance [19]. Anomaly detection is defined as the recognition of an unexpected pattern that is significantly different from the rest of the data. The majority of the challenges include a proper feature extraction method, imbalance in the data distribution, variance in anomalous cases, and environmental conditions. In the field of computer vision, anomaly detection is recently gaining more attention due to the advancements in the machine learning area. A key handicap with the public datasets is that most of these datasets have an imbalance among the classes they contain. The bias makes using such datasets difficult, especially in medical imaging, causing trained models to have less than desired performance [20]. Furthermore, manual labeling of the medical imaging data is a costly and labor-intensive process, and considering the deep learning models thriving with large amounts of data, developed systems may end up with limited utility and poor generalization [21]. In such scenarios, an unsupervised approach to data distribution modeling can be feasible, where the majority of the normal case data is used for training, and abnormal case data and the remainder of the normal case data are used to find outlier cases during the inference. For a variety of domains [22; 23; 24], different approaches to anomaly detection [25; 26; 27] have been proposed in the past. It is generally assumed that the anomalies differ in lower dimensions as well as in high-dimensional space, meaning the latent space mapping is a vital point in anomaly detection. Recent studies that include generative adversarial networks (GANs) [28] in their models are highly effective in mapping the data distribution. GANs being efficient in mapping both high-dimensional and low-dimensional features with very little information loss has sparked a new interest in anomaly detection works [29]. In medical imaging, GANs are generally used for AD diagnosis [30], and data generation to be used in training the deep learning models [31]. Anomaly detection can be used to differentiate normal brain images and the abnormal brain images is not very well researched. In this study, the analysis of Alzheimer's disease as an anomaly using the proposed model is researched. In the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset, there are three classes which are AD, MCI, and normal control (NC). The proposed model is trained using the unsupervised method. The anomaly analysis is performed on these classes in the following cases: AD-NC, MCI-NC, AD-MCI, the initial class is the anomaly class, and the latter class, the normal class. The area under the curve (AUC) is calculated for each of these comparisons to evaluate the performance of the model, as per previous work in the field [32; 33], as well as Frechet Inception Distance as a qualitative evaluation. Contributions of this paper are as follows:  
* Novelty--the Alzheimer's disease anomaly analysis of PET images using a proposed unsupervised adversarially trained model with a unique feature extractor model.