Alzheimer's disease (AD) varies a great deal cognitively regarding symptoms, test findings, the rate of progression, and neuroradiologically in terms of atrophy on magnetic resonance imaging (MRI). We hypothesized that an unbiased analysis of the progression of AD, regarding clinical and MRI features, will reveal a number of AD phenotypes. Our objective is to develop and use a computational method for multi-modal analysis of changes in cognitive scores and MRI volumes to test for there being multiple AD phenotypes. In this retrospective cohort study with a total of 857 subjects from the AD (n = 213), MCI (n = 322), and control (CN, n = 322) groups, we used structural MRI data and neuropsychological assessments to develop a novel computational phenotyping method that groups brain regions from MRI and subsets of neuropsychological assessments in a non-biased fashion. The phenotyping method was built based on coupled nonnegative matrix factorization (C-NMF). As a result, the computational phenotyping method found four phenotypes with different combination and progression of neuropsychologic and neuroradiologic features. Identifying distinct AD phenotypes here could help explain why only a subset of AD patients typically respond to any single treatment. This, in turn, will help us target treatments more specifically to certain responsive phenotypes.