Abstract
We present a new, simple, and computationally efficient iterative method for low rank matrix completion. Our method is inspired by the class of factorization-type iterative algorithms, but substantially differs from them in the way the problem is cast. Precisely, given a target rank $r$, instead of optimizing on the manifold of rank $r$ matrices, we allow our interim estimated matrix to have a specific overparametrized rank $2r$ structure. Our algorithm, denoted R2RILS, for rank $2r$ iterative least squares, thus has low memory requirements, and at each iteration it solves a computationally cheap sparse least squares problem. We motivate our algorithm by its theoretical analysis for the simplified case of a rank 1 matrix. Empirically, R2RILS is able to recover ill-conditioned low rank matrices from very few observations---near the information limit---and it is stable to additive noise.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.