Alzheimer’s disease (AD) is a complex and heterogeneous disease that can be affected by various genetic factors. Although the cause of AD is not yet known and there is no treatment to cure this disease, its progression can be delayed. AD has recently been recognized as a brain-specific type of diabetes called type 3 diabetes. Several studies have shown that people with type 2 diabetes (T2D) have a higher risk of developing AD. Therefore, it is important to identify subgroups of patients with AD that may be more likely to be associated with T2D. We here describe a new approach to identify the correlation between AD and T2D at the genetic level. Subgroups of AD and T2D were each generated using a non-negative matrix factorization (NMF) approach, which generated clusters containing subsets of genes and samples. In the gene cluster that was generated by conventional gene clustering method from NMF, we selected genes with significant differences in the corresponding sample cluster by Kruskal–Wallis and Dunn-test. Subsequently, we extracted differentially expressed gene (DEG) subgroups, and candidate genes with the same regulation direction can be extracted at the intersection of two disease DEG subgroups. Finally, we identified 241 candidate genes that represent common features related to both AD and T2D, and based on pathway analysis we propose that these genes play a role in the common pathological features of AD and T2D. Moreover, in the prediction of AD using logistic regression analysis with an independent AD dataset, the candidate genes obtained better prediction performance than DEGs. In conclusion, our study revealed a subgroup of patients with AD that are associated with T2D and candidate genes associated between AD and T2D, which can help in providing personalized and suitable treatments.