Although there is no cure to date, Alzheimer's disease detection in early stages has a significant impact on the patient's life in terms of cost, the progress, and helping to plan in advance for an appropriate healthcare in the life ahead as well as providing clinical etiologies for further research. This paper discusses implementing a feature fusion method utilizing sparse and denoising autoencoders to reveal the stage of Alzheimer's disease. Four cohorts consisted of individuals with Alzheimer's disease, late mild cognitive impairment, early mild cognitive impairment, and normal control groups are classified using multinomial logistic regression fueled by the fusion of high-level and low-level features. The high-level features are extracted from the stacked autoencoders. The results show that feature fusion enhance the performance of typical autoencoders. However, the performance of feature fusion using denoising autoencoders is superior to that of the sparse training of autoencoders in terms of overall accuracy, precision, and recall.