Low-rank Solutions of Linear Matrix Equations via Procrustes Flow

被引：0

作者：

Tu, Stephen ^{[1
]}

Boczar, Ross ^{[1
]}

Simchowitz, Max ^{[1
]}

Soltanolkotabi, Mahdi ^{[2
]}

Recht, Benjamin ^{[1
]}

机构：

[1] Univ Calif Berkeley, EECS Dept, Berkeley, CA 94720 USA

[2] USC, Ming Hsieh Dept Elect Engn, Los Angeles, CA USA

来源：

INTERNATIONAL CONFERENCE ON MACHINE LEARNING, VOL 48 | 2016年 / 48卷

关键词：

SIGNAL RECOVERY;

D O I：

暂无

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

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) x n(2) matrix of rank r when the number of measurements exceeds a constant times (n(1) + n(2))r.

引用

页数：10

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