Low-Rank Solutions of Linear Matrix Equations via Procrustes Flow
Abstract
In this paper we study the problem of recovering a low-rank matrix from linear measurements. Our algorithm, which we call Procrustes Flow, starts from an initial estimate obtained by a thresholding scheme followed by gradient descent on a non-convex objective. We show that as long as the measurements obey a standard restricted isometry property, our algorithm converges to the unknown matrix at a geometric rate. In the case of Gaussian measurements, such convergence occurs for a n1 \times n2 matrix of rank r when the number of measurements exceeds a constant times (n1 + n2)r.
Cite
Text
Tu et al. "Low-Rank Solutions of Linear Matrix Equations via Procrustes Flow." International Conference on Machine Learning, 2016.Markdown
[Tu et al. "Low-Rank Solutions of Linear Matrix Equations via Procrustes Flow." International Conference on Machine Learning, 2016.](https://mlanthology.org/icml/2016/tu2016icml-lowrank/)BibTeX
@inproceedings{tu2016icml-lowrank,
title = {{Low-Rank Solutions of Linear Matrix Equations via Procrustes Flow}},
author = {Tu, Stephen and Boczar, Ross and Simchowitz, Max and Soltanolkotabi, Mahdi and Recht, Ben},
booktitle = {International Conference on Machine Learning},
year = {2016},
pages = {964-973},
volume = {48},
url = {https://mlanthology.org/icml/2016/tu2016icml-lowrank/}
}