In this paper, we propose a novel method for magnetic resonance imaging based Alzheimer's disease (AD) or mild cognitive impairment (MCI) diagnosis that systematically integrates voxel-based, region-based, and patch-based approaches into a unified framework. Specifically, we parcellate the brain into predefined regions based on anatomical knowledge (i.e., templates) and derive complex nonlinear relationships among voxels, whose intensities denote volumetric measurements, within each region. Unlike existing methods that use cubical or rectangular shapes, we consider the anatomical shapes of regions as atypical patches. Using complex nonlinear relationships among voxels in each region learned by deep neural networks, we extract a "regional abnormality representation." We then make a final clinical decision by integrating the regional abnormality representations over the entire brain. It is noteworthy that the regional abnormality representations allow us to interpret and understand the symptomatic observations of a subject with AD or MCI by mapping and visualizing these observations in the brain space. On the baseline MRI dataset from the Alzheimer's Disease Neuroimaging Initiative (ADNI) cohort, our method achieves state-of-the-art performance for four binary classification tasks and one three-class classification task. Additionally, we conducted exhaustive experiments and analysis to validate the efficacy and potential of our method.