Computing hulls in positive definite space

P(n): a Riemannian manifold Definition: symmetric positive-definite (n) (n) matrices Applications: Diffusion Tensor MRI (DT-MRI) Flow through voxel modeled in P(3) Elasticity Tensors Modeled by elements of P(6) Machine Learning Used in kernels Convex Hulls Data on P(n): Want to analyze this data Centerpoints, clustering, shape Convex hull (CH) is a useful data analysis tool Describes shape of the data Can use max CH peeling depth to find a centerpoint A framework for analyzing shape in spaces where CH is difficult to work with (ball hull) An approximation to the ball hull (""-ball hull) A way to measure width as a side benefit (extent) Horofunctions provide a good way to analyze manifolds like this