There is a wide variety of effects of Alzheimer’s disease (AD), a neurodegenerative disease that can lead to cognitive decline, deterioration of daily life, and behavioral and psychological changes. A polymorphism of the ApoE gene ε 4 is considered a genetic risk factor for Alzheimer’s disease. The purpose of this paper is to demonstrate that single-nucleotide polymorphic markers (SNPs) have a causal relationship with quantitative PET imaging traits. Additionally, the classification of AD is based on the frequency of brain tissue variations in PET images using a combination of k-nearest-neighbor (KNN), support vector machine (SVM), linear discrimination analysis (LDA), and convolutional neural network (CNN) techniques. According to the results, the suggested SNPs appear to be associated with quantitative traits more strongly than the SNPs in the ApoE genes. Regarding the classification result, the highest accuracy is obtained by the CNN with 91.1%. These results indicate that the KNN and CNN methods are beneficial in diagnosing AD. Nevertheless, the LDA and SVM are demonstrated with a lower level of accuracy.