Luminal-A breast cancer is a subtype with the largest number of patients, about 40% of all breast cancer patients. The biggest characteristic of luminal-A breast cancer patients is a wide range of variation in prognosis for endocrine therapy. Therefore, this research divides the luminal-A breast cancer patients into the two distinct prognostic subgroups. The latent features generated through denoising autoencoders that extract and compress gene expression patterns of luminal-A breast cancer patients identify the two prognostic subgroups. The significance difference in overall survival between two subgroups are shown via log-rank test that is a hypothesis test to compare the survival distributions of two samples. In addition, through biological pathway analysis, it is found that the autophagy-lysosome pathways are more activated in the better prognostic subgroups. It is expected that this research can be used for personalized breast cancer treatment.