  Existing approaches for diffusion on graphs, e.g., for label propagation, are
mainly focused on isotropic diffusion, which is induced by the commonly-used
graph Laplacian regularizer. Inspired by the success of diffusivity tensors for
anisotropic diffusion in image processing, we presents anisotropic diffusion on
graphs and the corresponding label propagation algorithm. We develop positive
definite diffusivity operators on the vector bundles of Riemannian manifolds,
and discretize them to diffusivity operators on graphs. This enables us to
easily define new robust diffusivity operators which significantly improve
semi-supervised learning performance over existing diffusion algorithms.
