Barycentric Discriminant Analysis (BADIA)

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 1) to assign subjects to a given diagnostic group (i.e., Alzheimer’s disease, other dementia, normal aging) on the basis on brain imaging data or psychological tests (here the a-priori categories are the clinical groups), 2) 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), 3) to use brain scans taken on a given participant to determine what type of object (e.g., a face, a cat, a chair) was watched by the participant when the scans were taken (here the a-priori categories are the types of object), (4) to use DNA measurements to predict if a person is at risk for a given health problem (here the a-priori categories are the types of health problem).