R3MC: A Riemannian three-factor algorithm for low-rank matrix completion

  title={R3MC: A Riemannian three-factor algorithm for low-rank matrix completion},
  author={Bamdev Mishra and Rodolphe Sepulchre},
  journal={53rd IEEE Conference on Decision and Control},
We exploit the versatile framework of Riemannian optimization on quotient manifolds to develop R3MC, a nonlinear conjugate-gradient method for low-rank matrix completion. The underlying search space of fixed-rank matrices is endowed with a novel Riemannian metric that is tailored to the least-squares cost. Numerical comparisons suggest that R3MC robustly outperforms state-of-the-art algorithms across different problem instances, especially those that combine scarcely sampled and ill-conditioned… CONTINUE READING
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