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In sparse recovery we are given a matrix $A$ (the dictionary) and a vector of the form $A X$ where $X$ is sparse, and the goal is to recover $X$.
A bound on tail probabilities for quadratic forms in independent random variables
D. Hanson and F. Wright · 1971
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Perturbation bounds in connection with singular value decompositions
P. Wedin · 1972
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Matrix analysis
R. Horn and C. Johnson · 1990
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Piercing convex sets and the hadwigder debrunner ( p , q ) (p,q) -problem
N. Alon and D. Kleitman · 1992
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Independent component analysis: A new concept?
P. Comon · 1994
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Learning linear transformations
A. Frieze, M. Jerrum, and R. Kannan · 1996
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Matrix computations
G. Golub and C. van Loan · 1996
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Greedy adaptive approximations
G. Davis, S. Mallat, and M. Avellaneda · 1997
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Sparse coding with an overcomplete basis set: A strategy employed by v1?
B. Olshausen and B. Field · 1997
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A wavelet tour of signal processing
S. Mallat · 1998
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Uncertainty principles and ideal atomic decomposition
D. Donoho and X. Huo · 1999
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Uncertainty principles and signal recovery
D. Donoho and P. Stark · 1999
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Method of optimal directions for frame design
K. Engan, S. Aase, and J. Hakon-Husoy · 1999
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Random vectors in the isotropic position
M. Rudelson · 1999
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Learning overcomplete representations
M. Lewicki and T. Sejnowski · 2000
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Lectures on discrete geometry
J. Matousek · 2002
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Optimally sparse representation in general (non-orthogonal) dictionaries via ℓ 1 \ell_{1} -minimization
D. Donoho and M. Elad · 2003
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Approximation of functions over redundant dictionaries using coherence
A. Gilbert, S. Muthukrishnan, and M. Strauss · 2003
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Sparse representations in unions of bases
R. Gribonval and M. Nielsen · 2003
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Dictionary learning algorithms for sparse representation
K. Kreutz-Delgado, J. Murray, K. Engan B. Rao, T. Lee, and T. Sejnowski · 2003
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Improved sparse approximation over quasi-incoherent dictionaries
J. Tropp, A. Gilbert, S. Muthukrishnan, and M. Strauss · 2003
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Greed is good: Algorithmic results for sparse approximation
J. Tropp · 2004
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Decoding by linear programming
E. Candes and T. Tao · 2005
Cited alongside, same era.
Overcomplete dictionaries for sparse representation of signals
M. Aharon · 2006
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Sparse and redundant representations
M. Elad · 2010
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Setting the polynomial learnability of mixtures of gaussians
A. Moitra and G. Valiant · 2010
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A spectral algorithm for latent dirichlet allocation
A. Anandkumar, D. Foster, D. Hsu, S. Kakade, and Y. Liu · 2012
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Computing a nonnegative matrix factorization – provably
S. Arora, R. Ge, R. Kannan, and A. Moitra · 2012
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Learning topic models - going beyond svd
S. Arora, R. Ge, and A. Moitra · 2012
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Finding overlapping communities in social networks: Towards a rigorous approach
S. Arora, R. Ge, S. Sachdeva, and G. Schoenebeck · 2012
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K-svd: An algorithm for designing overcomplete dictionaries for sparse representation
M. Aharon, M. Elad, and A. Bruckstein · 2006
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Stable signal recovery from incomplete and inaccurate measurements
E. Candes, J. Romberg, and T. Tao · 2006
Cited alongside, same era.
Image denoising via sparse and redundant representations over learned dictionaries
M. Elad and M. Aharon · 2006
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Efficient sparse coding algorithms
H. Lee, A. Battle, R. Raina, and A. Ng · 2006
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Fourth-order cumulant-based blind identification of underdetermined mixtures
L. De Lathauwer, J Castaing, and J. Cardoso · 2007
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Multi-task feature learning
M. Pontil, A. Argyriou, and T. Evgeniou · 2007
Cited alongside, same era.
Large-scale feature learning with spike-and-slab sparse coding
I. J. Goodfellow, A. Courville, and Y.Bengio · 2012
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Exact recovery of sparsely-used dictionaries
D. Spielman, H. Wang, and J. Wright · 2012
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Learning sparsely used overcomplete dictionaries via alternating minimization
A. Agarwal, A. Anandkumar, P. Jain, P. Netrapalli, and R. Tandon · 2013
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Exact recovery of sparsely used overcomplete dictionaries
A. Agarwal, A. Anandkumar, and P. Netrapalli · 2013
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Finding endogenously formed communities
M. Balcan, C. Borgs, M. Braverman, J. Chayes, and S-H Teng · 2013
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On the local correctness of ℓ 1 \ell_{1} -minimization for dictionary learning
Q. Geng, H. Wang, and J. Wright · 2013
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On the provable convergence of alternating minimization for matrix completion
M. Hardt · 2013
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Low rank matrix completion using alternating minimization
P. Jain, P. Netrapalli, and S. Sanghavi · 2013
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Truncated power method for sparse eigenvalue problems
X. Yuan and T. Zhang · 2013
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Dictionary learning using sum-of-square hierarchy
Boaz Barak, John Kelner, and David Steurer · 2014
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Fourier pca
N. Goyal, S. Vempala, and Y. Xiao · 2014
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