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A number of conditions are characterized by pathologies that form continuous or nearly-continuous spectra spanning from the absence of pathology to very pronounced pathological changes (e.g., normal aging, mild cognitive impairment, Alzheimer's). Moreover, diseases are often highly heterogeneous with a number of diagnostic subcategories or subconditions lying within the spectra (e.g., autism spectrum disorder, schizophrenia). Discovering coherent subpopulations of subjects within the spectrum of pathological changes may further our understanding of diseases, and potentially identify subconditions that require alternative or modified treatment options. In this paper, we propose an approach that aims at identifying coherent subpopulations with respect to the underlying MRI in the scenario where the condition is heterogeneous and pathological changes form a continuous spectrum. We describe a joint maximum-margin classification and clustering (JointMMCC) approach that jointly detects the pathologic population via semi-supervised classification, as well as disentangles heterogeneity of the pathological cohort by solving a clustering subproblem. We propose an efficient solution to the nonconvex optimization problem associated with JointMMCC. We apply our proposed approach to an medical resonance imaging study of aging, and identify coherent subpopulations (i.e., clusters) of cognitively less stable adults.