Riemannian Tensor Completion with Side Information

TL;DR

This paper introduces a new Riemannian tensor completion model that effectively incorporates side information, leading to more accurate results while maintaining computational efficiency.

Contribution

A novel Riemannian model that seamlessly integrates side information into tensor completion, along with an efficient conjugate gradient solver based on a curvature-aware metric.

Findings

The proposed method outperforms state-of-the-art in accuracy.

The solver maintains efficiency comparable to existing methods.

Numerical experiments validate the effectiveness of the approach.

Abstract

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.