Riemannian Tensor Completion with Side Information
This work addresses tensor completion for data analysis applications, representing an incremental improvement by incorporating side information into existing Riemannian methods.
The paper tackled the problem of low rank tensor completion by integrating side information into Riemannian optimization, resulting in a solver that is more accurate than state-of-the-art methods while maintaining efficiency.
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.