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We study the Riemannian optimization methods on the embedded manifold of low rank matrices for the problem of matrix completion, which is about recovering a low rank matrix from its partial entries.
A practical algorithm for the determination of the phase from image and diffraction plane pictures
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Semidefinite programming
L. Vandenberghe and S. Boyd · 1996
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Strong converse for identification via quantum channels
R. Ahlswede and A. Winter · 2002
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Matrix rank minimization with applications
M. Fazel · 2002
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The complexity of matrix completion
N. J. A. Harvey, D. R. Karger, and S. Yekhanin · 2006
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Numerical Optimization
J. Nocedal and S. J. Wright · 2006
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Uncovering shared structures in multiclass classification
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Matrix Methods in Data Mining and Pattern Recogonization
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Optimization Algorithms on Matrix Manifolds
P.-A. Absil, R. Mahony, and R. Sepulchre · 2008
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Tight oracle bounds for low-rank matrix recovery from a minimal number of random measurements
E. J. Candès and Y. Plan · 2009
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Exact matrix completion via convex optimization
E. J. Candès and B. Recht · 2009
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The power of convex relaxation: Near-optimal matrix completion
E. J. Candès and T. Tao · 2009
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Rank-constrained solutions to linear matrix equations using PowerFactorization
J. P. Haldar and D. Hernando · 2009
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Interior-point method for nuclear norm approximation with application to system identification
Z. Liu and L. Vandenberghe · 2009
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A singular value thresholding algorithm for matrix completion
J.-F. Cai, E. J. Candès, and Z. Shen · 2010
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Guaranteed rank minimization via singular value projection
P. Jain, R. Meka, and I. Dhillon · 2010
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Matrix completion from a few entries
R. H. Keshavan, A. Montanari, and S. Oh · 2010
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ADMiRA: Atomic decomposition for minimum rank approximation
K. Lee and Y. Bresler · 2010
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Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization
B. Recht, M. Fazel, and P. A. Parrilo · 2010
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RTRMC: A Riemannian trust-region method for low-rank matrix completion
N. Boumal and P.-A. Absil · 2011
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Convergence of fixed-point continuation algorithms for matrix rank minimization
D. Goldfarb and S. Ma · 2011
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Recovering low-rank matrices from few coefficients in any basis
D. Gross · 2011
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A simpler approach to matrix completion
B. Recht · 2011
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CGIHT: Conjugate gradient iterative hard thresholding for compressed sensing and matrix completion
J. Blanchard, J. Tanner, and K. Wei · 2015
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Phase retrieval via Wirtinger flow: Theory and algorithms
E. J. Candès, X. Li, and M. Soltanolkotabi · 2015
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Incoherence-optimal matrix completion
Y. Chen · 2015
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Solving random quadratic systems of equations is nearly as easy as solving linear systems
Y. Chen and E. J. Candès · 2015
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Y. Chen and M. J. Wainwright · 2015
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Fast exact matrix completion with finite samples
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Low-rank matrix completion using alternating minimization
P. Jain, P. Netrapalli, and S. Sanghavi · 2012
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Efficient algorithms for collaborative filtering
R. H. Keshavan · 2012
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Scaled gradients on Grassmann manifolds for matrix completion
T. Ngo and Y. Saad · 2012
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Solving a low-rank factorization model for matrix completion by a non-linear successive over-relaxation algorithm
Z. Wen, W. Yin, and Y. Zhang · 2012
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Blind deconvolution using convex programming
A. Ahmed, B. Recht, and J. Romberg · 2013
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Phase retrieval via matrix completion
E. J. Candès, Y. Eldar, T. Strohmer, and V. Voroninski · 2013
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P. Jain and P. Netrapalli · 2015
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Blind deconvolution meets blind demixing: Algorithms and performance bounds
S. Ling and T. Strohmer · 2015
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Global convergence of stochastic gradient descent for some nonconvex matrix problems
C. De Sa, K. Olukotun, and C. Ré · 2015
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Guaranteed matrix completion via non-convex factorization
R. Sun and Z. Luo · 2015
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Solving systems of phaseless equations via Kaczmarz methods: A proof of concept study
K. Wei · 2015
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Guarantees of Riemannian optimization for low rank matrix recovery
K. Wei, J.-F. Cai, T. F. Chan, and S. Leung · 2015
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The local convexity of solving systems of quadratic equations
C. D. White, S. Sanghavi, and R. Ward · 2015
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Nonconvex low rank matrix factorization via inexact first order oracle
T. Zhao, Z. Wang, and H. Liu · 2015
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A convergent gradient descent algorithm for rank minimization and semidefinite programming from random linear measurements
Q. Zheng and J. Lafferty · 2015
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A geometric analysis of phase retrieval
J. Sun, Q. Qu, and J. Wright · 2016
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Low rank matrix completion by alternating steepest descent methods
J. Tanner and K. Wei · 2016
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Low-rank solutions of linear matrix equations via Procrustes flow
S. Tu, R. Boczar, M. Simchowitz, M. Soltanolkotabi, and B. Recht · 2016
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