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Low-rank Solutions of Linear Matrix Equations via Procrustes Flow

2020-03-05 | |  74 |   42 |   0

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 图片.png  matrix of rank r when the number of measurements exceeds a constant times 图片.png

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