Riemannian Tensor Completion with Side Information

Riemannian optimization methods have shown to be both fast and accurate in recovering a large-scale tensor from its incomplete observation. However, in almost all recent Riemannian tensor completion methods, only low rank constraint is considered. Another important fact, side information or features, remains far from exploiting within the Riemannian optimization framework. In this paper, we explicitly incorporate the side information into a Riemannian minimization model. Specifically, a feature-embedded objective is designed to substantially reduce the sample complexity. For such a Riemannian optimization, a particular metric can be constructed based on the curvature of the objective, which leads to a novel Riemannian conjugate gradient descent solver. Numerical experiments suggest that our solver is more efficient than the state-of-the-art when a highly accurate solution is required.