 In the one dimensional case, the hyperplane is the point "y" itself, and the sum of directions simplifies to the (directed) counting measure.The geometric median can be generalized from Euclidean spaces to general Riemannian manifolds (and even metric spaces) using the same idea which is used to define the Fréchet mean on a Riemannian manifold.Let formula_14 be a Riemannian manifold with corresponding distance function formula_15, let formula_16 be formula_17 weights summing to 1, and let formula_18
be formula_17 observations from formula_14.