Barycentric discriminant analysis (BADIA) generalizes discriminant analysis, and like discriminant analysis, it is performed when measurements made on some observations are combined to assign these observations, or new observations, to a priori defined categories. For example, BADIA can be used (a) to assign people to a given diagnostic group (e.g., patients with Alzheimer's disease, patients with other dementia, or people aging without dementia) on the basis of brain imaging data or psychological tests (here the a priori categories are the clinical groups), (b) to assign wines to a region of production on the basis of several physical and chemical measurements (here the a priori categories are the regions of production), (c) to use brain scans taken on a given participant to determine what type of ...