Note: low-rank tensor train completion with side information based on Riemannian optimization

Understand

We consider the low-rank tensor train completion problem when additional side information is available in the form of subspaces that contain the mode-$k$ fiber spans.

• We propose an algorithm based on Riemannian optimization to solve the problem.
• Numerical experiments show that the proposed algorithm requires far fewer known entries to recover the tensor compared to standard tensor train completion methods.