Local and Global Linear Convergence of General Low-rank Matrix Recovery Problems.
作者： Javad Lavaei , Yingjie Bi , Haixiang Zhang
DOI:
关键词: Local search (optimization) 、 Matrix (mathematics) 、 Gradient descent 、 Mathematics 、 Low-rank approximation 、 Restricted isometry property 、 Convergence (routing) 、 Local convergence 、 Rate of convergence 、 Applied mathematics
摘要: … The low-rank matrix recovery problem is to recover an unknown low-rank ground truth matrix from … In this paper, we consider two variants of the low-rank matrix recovery problem with a …
arxiv.org参考文章(30)
Yehuda Koren, Robert Bell, Chris Volinsky, Matrix Factorization Techniques for Recommender Systems IEEE Computer. ,vol. 42, pp. 30- 37 ,(2009) , 10.1109/MC.2009.263
Xiaowei Zhou, Can Yang, Weichuan Yu, Moving Object Detection by Detecting Contiguous Outliers in the Low-Rank Representation IEEE Transactions on Pattern Analysis and Machine Intelligence. ,vol. 35, pp. 597- 610 ,(2013) , 10.1109/TPAMI.2012.132
Benjamin Recht, Maryam Fazel, Pablo A. Parrilo, Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization Siam Review. ,vol. 52, pp. 471- 501 ,(2010) , 10.1137/070697835
Emmanuel J Candès, Y Plan, Tight Oracle Inequalities for Low-Rank Matrix Recovery From a Minimal Number of Noisy Random Measurements IEEE Transactions on Information Theory. ,vol. 57, pp. 2342- 2359 ,(2011) , 10.1109/TIT.2011.2111771
Zhaoran Wang, Tuo Zhao, Han Liu, A nonconvex optimization framework for low rank matrix estimation neural information processing systems. ,vol. 28, pp. 559- 567 ,(2015)
Jason D Lee, Max Simchowitz, Michael I Jordan, Benjamin Recht, None, Gradient Descent Only Converges to Minimizers conference on learning theory. ,vol. 49, pp. 1246- 1257 ,(2016)
Zhihui Zhu, Qiuwei Li, Gongguo Tang, Michael B. Wakin, Global optimality in low-rank matrix optimization ieee global conference on signal and information processing. ,vol. 66, pp. 3614- 3628 ,(2017) , 10.1109/TSP.2018.2835403
Rong Ge, Chi Jin, Yi Zheng, No spurious local minima in nonconvex low rank problems: a unified geometric analysis international conference on machine learning. pp. 1233- 1242 ,(2017)
Yu Zhang, Ramtin Madani, Javad Lavaei, Conic Relaxations for Power System State Estimation With Line Measurements IEEE Transactions on Control of Network Systems. ,vol. 5, pp. 1193- 1205 ,(2018) , 10.1109/TCNS.2017.2691473
Quanquan Gu, Lingxiao Wang, Yaodong Yu, Xiao Zhang, A Primal-Dual Analysis of Global Optimality in Nonconvex Low-Rank Matrix Recovery international conference on machine learning. pp. 5857- 5866 ,(2018)