## 1 Introduction
First, the experimenter must decide which transformations to apply to the original data so that the data generated by the transformation is similar with that of the real distribution. In other words, the distribution of the transformed dataset must maintain homogeneity for the class to which it belongs, and heterogeneity for other classes to which it does not belong. Second, changes in conventional DA in multi-dimensional data such as images do not sufficiently simulate the distributions of various lesions. It is difficult to simulate new patterns of lesions just by applying the iterative operations of conventional DA to given medical images. For example, when the lesion is diffuse, such as in the deposition of A\(\beta\), it is difficult to define various types of the lesion using iterative operations. In the same vein, another interesting DA is based on the generative adversarial network (GAN), which synthesizes data to be used as training data through a generative model that learns the data distribution instead of defining operations in advance [27; 28]. The GAN utilizes two modules, discriminator and generator, that compete with each other to learn fake distributions that mimic the real distribution [29]. Ideally, if the GAN can generate a real distribution, the generated distribution could show the boundaries between heterogeneous groups and have the potential to improve generalization of the target model by identifying similar patterns that are not in the training set [27]. However, previous studies on GAN-based DA have rarely considered evaluating and selecting samples quantitatively, and in some cases, performance has deteriorated or been minimal after GAN-based DA [24; 28]. Therefore, to successfully drive a stable GAN-based DA, determining whether to enhance the training set using the generated set based on quantitative evaluation could help to preserve and reliably improve the performance of the target model. However, no GAN-synthesized brain images have been evaluated using recently reported quantitative measurements [30] instead of traditional approaches [29; 31], although some simple results of visual evaluations have been reported [32]. Furthermore, according to our investigation, studies on a GAN-based synthetic medical imaging were not addressed with a quantitative evaluation as well as a visual assessment of a brain PET for diagnosis and prognosis of dementia. In this study, we created a conditional GAN to improve the A\(\beta\) estimation model and performed a quantitative evaluation to confirm the similarity that can be expected to improve the generalization performance. This method includes (1) conditional WGAN-GP to learn each axial image distribution extracted from pre-processed 3D FBB images, (2) pre-trained DenseNet121 and model-agnostic metrics to visually and quantitatively measure the generated images, and (3) ML models such as support vector machine (SVM) and neural network (NN) for observing generalization performance after using of generated images for DA. Finally, we will upload the weights of GAN models, and the source code for our experiments ([[https://github.com/kang2000h/GAN_evaluation](https://github.com/kang2000h/GAN_evaluation)]([https://github.com/kang2000h/GAN_evaluation](https://github.com/kang2000h/GAN_evaluation))) so that the experiments we performed have reproducibility and persistence for related works (Supplementary Materials).