Provided the means to use a machine learning based Eikonal solver to obtain distance functions on arbitrary Riemannian manifolds. This opens numerous opportunities for computing statistics on manifolds. Most notably, with access to a distance function, one can now conduct manifold-based optimisation. Ultimately, this allows us to compute the Frechet mean on the manifold, and conduct unsupervised clustering.
Note
For more information on this, please see the recent preprint:
Computing distances and means on manifolds with a metric-constrained Eikonal approach