Abstract
When learning functions on manifolds, we can improve performance by regularizing with respect to the intrinsic manifold
geometry rather than the ambient space. However, when regularizing tensor learning, calculating the derivatives along this
intrinsic geometry is not possible, and so existing approaches
are limited to regularizing in Euclidean space. Our new method
for intrinsically regularizing and learning tensors on Riemannian manifolds introduces a surrogate object to encapsulate the
geometric characteristic of the tensor. Regularizing this instead
allows us to learn non-symmetric and high-order tensors. We
apply our approach to the relative attributes problem, and we
demonstrate that explicitly regularizing high-order relationships
between pairs of data points improves performance