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Based on a new atomic norm, we propose a new convex formulation for sparse matrix factorization problems in which the number of nonzero elements of the factors is assumed fixed and known.
On bounds for the normal integral
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Summing and Nuclear Norms in Banach Space Theory
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Large cliques elude the Metropolis process
M. Jerrum · 1992
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Characterization of the subdifferential of some matrix norms
G. A. Watson · 1992
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Matrix analysis
R. Bhatia · 1997
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Geometry of Cuts and Metrics , volume 15 of Algorithms and Combinatorics
M. M. Deza and M. Laurent · 1997
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Convex Analysis
R.T. Rockafellar · 1997
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Local operator theory, random matrices and Banach spaces
K. R. Davidson and S. J. Szarek · 2001
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Spectral bounds for sparse PCA: Exact and greedy algorithms
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H. Zou, T. Hastie, and R. Tibshirani · 2006
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A direct formulation for sparse PCA using semidefinite programming
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Efficient sparse coding algorithms
H. Lee, A. Battle, R. Raina, and A. Y. Ng · 2007
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Convex sparse matrix factorizations
F. Bach, J. Mairal, and J. Ponce · 2008
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Optimal solutions for sparse principal component analysis
A. d’Aspremont, F. Bach, and L. El Ghaoui · 2008
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Sparse regression as a sparse eigenvalue problem
B. Moghaddam, A. Gruber, Y. Weiss, and S. Avidan · 2008
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High-dimensional analysis of semidefinite relaxations for sparse principal components
A. A. Amini and M. J. Wainwright · 2009
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Group lasso with overlap and graph lasso
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Deflation methods for sparse PCA
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A coordinate gradient descent method for nonsmooth separable minimization
P. Tseng and S. Yun · 2009
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Information-theoretic limits on sparsity recovery in the high-dimensional and noisy setting
M. J. Wainwright · 2009
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A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis
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Living on the edge: Phase transitions in convex programs with random data
D. Amelunxen, M. Lotz, M. B. McCoy, and J. A. Tropp · 2013
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Convex relaxations of structured matrix factorizations
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Complexity theoretic lower bounds for sparse principal component detection
Q. Berthet and P. Rigollet · 2013
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PhaseLift: Exact and stable signal recovery from magnitude measurements via convex programming
E. J. Candès, T. Strohmer, and V. Voroninski · 2013
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Online learning for matrix factorization and sparse coding
J. Mairal, F. Bach, J. Ponce, and G. Sapiro · 2010
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Optimization with sparsity-inducing penalties
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Nuclear norm penalization and optimal rates for noisy matrix completion
V. Koltchinskii, K. Lounici, and A. B. Tsybakov · 2011
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Sparse prediction with the k k -support norm
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Structured sparsity through convex optimization
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The convex geometry of linear inverse problems
V. Chandrasekaran, B. Recht, P. A. Parrilo, and A. S. Willsky · 2012
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Finding approximately rank-one submatrices with the nuclear norm and ℓ 1 \ell_{1} norms
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Do semidefinite relaxations really solve sparse PCA?
R. Krauthgamer, B. Nadler, and D. Vilenchik · 2013
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Conditional gradient algorithms for rank-one matrix approximations with a sparsity constraint
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Sharp mse bounds for proximal denoising
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The squared-error of generalized LASSO: A precise analysis
S. Oymak, C. Thrampoulidis, and B. Hassibi · 2013
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Intersecting singularities for multi-structured estimation
E. Richard, F. Bach, and J.-P. Vert · 2013
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Provable subspace clustering: When LRR meets SSC
Y.-X. Wang, H. Xu, and C. Leng · 2013
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Truncated power method for sparse eigenvalue problems
X.-T. Yuan and T. Zhang · 2013
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Link prediction in graphs with autoregressive features
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