Corpus ID: 15673678

# Low-rank Solutions of Linear Matrix Equations via Procrustes Flow

@inproceedings{Tu2016LowrankSO,
title={Low-rank Solutions of Linear Matrix Equations via Procrustes Flow},
author={Stephen Tu and Ross Boczar and Max Simchowitz and M. Soltanolkotabi and B. Recht},
booktitle={ICML},
year={2016}
}
• Stephen Tu, +2 authors B. Recht
• Published in ICML 2016
• Mathematics, Computer Science
• 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 \$n_1 \times n_2… CONTINUE READING