Visualizing Riemannian data with Rie-SNE
This work addresses the challenge of creating accurate visualizations for data on complex geometric structures, which is incremental as it builds on existing SNE techniques.
The paper tackles the problem of visualizing data on Riemannian manifolds by extending the SNE algorithm to incorporate Riemannian geometry, resulting in a method that efficiently uses distances and volumes for mapping between manifolds.
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.