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Alzheimer's disease (AD) and Parkinson's disease (PD) are the two most common neurodegenerative disorders in humans. Because a significant percentage of patients have clinical and pathological features of both diseases, it has been hypothesized that the patho-cascades of the two diseases overlap. Despite this evidence, these two diseases are rarely studied in a joint manner. In this paper, we utilize clinical, imaging, genetic, and biospecimen features to cluster AD and PD patients into the same feature space. By training a machine learning classifier on the combined feature space, we predict the disease stage of patients two years after their baseline visits. We observed a considerable improvement in the prediction accuracy of Parkinson's dementia patients due to combined training on Alzheimer's and Parkinson's patients, thereby affirming the claim that these two diseases can be jointly studied.