Optimal Design of Experiments on Riemannian Manifolds

Traditional optimal design of experiment theory is developed on Euclidean space. In this paper, new theoretical results of optimal design of experiments on Riemannian manifolds are provided. In particular, it is shown that D-optimal and G-optimal designs are equivalent on manifolds and provide a lower bound for the maximum prediction variance. In addition, a converging algorithm that finds the optimal experimental design on manifold data is proposed. Numerical experiments demonstrate the competitive performance of the new algorithm.