R3MC: A Riemannian three-factor algorithm for low-rank matrix completion
We exploit the versatile framework of Riemannian optimization on quotient manifolds to implement R3MC, a nonlinear conjugate gradient method optimized for matrix completion. The underlying geometry uses a Riemannian metric tailored to the quadratic cost. Numerical comparisons suggest that R3MC robustly outperforms state-of-the-art algorithms across different synthetic and real datasets especially in instances that combine scarcely sampled and ill-conditioned data.
It comes with state-of-the-art solvers and built-in geometries, so that solving a Riemannian optimization problem essentially reduces to coding its cost and gradient functions.
It is readily possible to solve rank-constrained or orthonormality-constrained problems.
Code and documentation are available from http://www.manopt.org.
- FNRS (Aspirant)Ph.D. candidate, 2011 - present
- IAP DySCOPh.D. candidate, 2010 - 2011
The research deals with the application of manifold optimization techniques to large-scale convex optimization problems whose expected or desired solutions have low rank. We focus specifically on convex relaxations of large-scale rank-constrained problems encountered in machine learning, data reduction and bioinformatics.
- University of LiègeApplied Mathematics, 2010 - present
- Indian Institute of Technology BombayElectrical Engineering, 2005 - 2010