There is ample evidence for the heterogeneous nature of diseases. For example, Alzheimer’s Disease, Schizophrenia and Autism Spectrum Disorder are typical disease examples that are characterized by high clinical heterogeneity, and likely by heterogeneity in the underlying brain phenotypes. Parsing this heterogeneity as captured by neuroimaging studies is important both for better understanding of disease mechanisms, and for building subtype-specific classifiers. However, few existing methodologies tackle this problem in a principled machine learning framework. In this work, we developed a novel non-linear learning algorithm for integrated binary classification and subpopulation clustering. Non-linearity is introduced through the use of multiple linear hyperplanes that form a convex polytope that separates healthy controls from pathologic samples. Disease heterogeneity is disentangled by implicitly clustering pathologic samples through their association to single linear sub-classifiers. We show results of the proposed approach from an imaging study of Alzheimer’s Disease, which highlight the potential of the proposed approach to map disease heterogeneity in neuroimaging studies.