  By restricting the iterate on a nonlinear manifold, the recently proposed
Riemannian optimization methods prove to be both efficient and effective in low
rank tensor completion problems. However, existing methods fail to exploit the
easily accessible side information, due to their format mismatch. Consequently,
there is still room for improvement in such methods. To fill the gap, in this
paper, a novel Riemannian model is proposed to organically integrate the
original model and the side information by overcoming their inconsistency. For
this particular model, an efficient Riemannian conjugate gradient descent
solver is devised based on a new metric that captures the curvature of the
objective.Numerical experiments suggest that our solver is more accurate than
the state-of-the-art without compromising the efficiency.
