English

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

Optimization and Control 2014-09-23 v2 Machine Learning

Abstract

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 data.

Keywords

Cite

@article{arxiv.1306.2672,
  title  = {R3MC: A Riemannian three-factor algorithm for low-rank matrix completion},
  author = {B. Mishra and R. Sepulchre},
  journal= {arXiv preprint arXiv:1306.2672},
  year   = {2014}
}

Comments

Accepted for publication in the proceedings of the 53rd IEEE Conference on Decision and Control, 2014

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