  Faithful visualizations of data residing on manifolds must take the
underlying geometry into account when producing a flat planar view of the data.
In this paper, we extend the classic stochastic neighbor embedding (SNE)
algorithm to data on general Riemannian manifolds. We replace standard Gaussian
assumptions with Riemannian diffusion counterparts and propose an efficient
approximation that only requires access to calculations of Riemannian distances
and volumes. We demonstrate that the approach also allows for mapping data from
one manifold to another, e.g. from a high-dimensional sphere to a
low-dimensional one.
