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

共 50 条

[41] Efficient Recovery of Low-Rank Matrix via Double Nonconvex Nonsmooth Rank Minimization
Zhang, Hengmin
Gong, Chen
Qian, Jianjun
Zhang, Bob
Xu, Chunyan
Yang, Jian
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, 2019, 30 (10) : 2916 - 2925
[42] Rank Consistency Induced Multiview Subspace Clustering via Low-Rank Matrix Factorization
Guo, Jipeng
Sun, Yanfeng
Gao, Junbin
Hu, Yongli
Yin, Baocai
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, 2022, 33 (07) : 3157 - 3170
[43] Low-Rank Solutions of Matrix Inequalities With Applications to Polynomial Optimization and Matrix Completion Problems
Madani, Ramtin
Fazelnia, Ghazal
Sojoudi, Somayeh
Lavaei, Javad
2014 IEEE 53RD ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC), 2014, : 4328 - 4335
[44] A Converse to Low-Rank Matrix Completion
Pimentel-Alarcon, Daniel L.
Nowak, Robert D.
2016 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY, 2016, : 96 - 100
[45] Enhanced Low-Rank Matrix Approximation
Parekh, Ankit
Selesnick, Ivan W.
IEEE SIGNAL PROCESSING LETTERS, 2016, 23 (04) : 493 - 497
[46] DECENTRALIZED LOW-RANK MATRIX COMPLETION
Ling, Qing
Xu, Yangyang
Yin, Wotao
Wen, Zaiwen
2012 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP), 2012, : 2925 - 2928
[47] Quantization for low-rank matrix recovery
Lybrand, Eric
Saab, Rayan
INFORMATION AND INFERENCE-A JOURNAL OF THE IMA, 2019, 8 (01) : 161 - 180
[48] Sensitivity of low-rank matrix recovery
Breiding, Paul
Vannieuwenhoven, Nick
NUMERISCHE MATHEMATIK, 2022, 152 (04) : 725 - 759
[49] Low-rank matrix completion via preconditioned optimization on the Grassmann manifold
Boumal, Nicolas
Absil, P. -A.
LINEAR ALGEBRA AND ITS APPLICATIONS, 2015, 475 : 200 - 239
[50] TRANSIENT INTERFERENCE SUPPRESSION VIA STRUCTURED LOW-RANK MATRIX DECOMPOSITION
Li, Mao
He, Zishu
2015 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING (ICASSP), 2015, : 3746 - 3750

← 1 2 3 4 5 →