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We present a theory for Euclidean dimensionality reduction with subgaussian matrices which unifies several restricted isometry property and Johnson-Lindenstrauss type results obtained earlier for specific data sets.
Error and perturbation bounds for subspaces associated with certain eigenvalue problems
G. Stewart · 1973
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Extensions of Lipschitz mappings into a Hilbert space
W. Johnson and J. Lindenstrauss · 1984
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Regularity of Gaussian processes
M. Talagrand · 1987
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The Johnson-Lindenstrauss lemma and the sphericity of some graphs
P. Frankl and H. Maehara · 1988
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On Milman’s inequality and random subspaces which escape through a mesh in 𝐑 n {\bf R}^{n}
Y. Gordon · 1988
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Riemannian manifolds
J. Lee · 1997
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Approximate nearest neighbors: Towards removing the curse of dimensionality
P. Indyk and R. Motwani · 1998
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Learning mixtures of Gaussians
S. Dasgupta · 1999
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Clustering for edge-cost minimization
L. Schulman · 2000
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Random projection in dimensionality reduction: applications to image and text data
E. Bingham and H. Mannila · 2001
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Majorizing measures without measures
M. Talagrand · 2001
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Database-friendly random projections: Johnson-Lindenstrauss with binary coins
D. Achlioptas · 2003
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Problems and results in extremal combinatorics. I
N. Alon · 2003
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An elementary proof of a theorem of Johnson and Lindenstrauss
S. Dasgupta and A. Gupta · 2003
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The random projection method
S. Vempala · 2004
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Empirical processes and random projections
B. Klartag and S. Mendelson · 2005
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The generic chaining
M. Talagrand · 2005
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Near-optimal signal recovery from random projections: universal encoding strategies?
E. Candès and T. Tao · 2006
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Compressed sensing
D. Donoho · 2006
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Improved approximation algorithms for large matrices via random projections
T. Sarlós · 2006
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Random projections for manifold learning
C. Hegde, M. Wakin, and R. Baraniuk · 2007
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Nearest-neighbor-preserving embeddings
P. Indyk and A. Naor · 2007
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Reconstruction and subgaussian operators in asymptotic geometric analysis
S. Mendelson, A. Pajor, and N. Tomczak-Jaegermann · 2007
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Compressed sensing performance bounds under Poisson noise
M. Raginsky, R. Willett, Z. Harmany, and R. Marcia · 2010
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Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization
B. Recht, M. Fazel, and P. Parrilo · 2010
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Sampling and reconstructing signals from a union of linear subspaces
T. Blumensath · 2011
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Tight oracle inequalities for low-rank matrix recovery from a minimal number of noisy random measurements
E. Candès and Y. Plan · 2011
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Faster least squares approximation
P. Drineas, M. Mahoney, S. Muthukrishnan, and T. Sarlós · 2011
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Disentangling gaussians
A. Kalai, A. Moitra, and G. Valiant · 2012
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A simple proof of the restricted isometry property for random matrices
R. Baraniuk, M. Davenport, R. DeVore, and M. Wakin · 2008
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On the performance of clustering in Hilbert spaces
G. Biau, L. Devroye, and G. Lugosi · 2008
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Tighter bounds for random projections of manifolds
K. Clarkson · 2008
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A theory for sampling signals from a union of subspaces
Y. Lu and M. Do · 2008
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On variants of the Johnson-Lindenstrauss lemma
J. Matoušek · 2008
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Uniform uncertainty principle for Bernoulli and subgaussian ensembles
S. Mendelson, A. Pajor, and N. Tomczak-Jaegermann · 2008
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Linear regression with random projections
O. Maillard and R. Munos · 2012
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Compressive matched-field processing
W. Mantzel, J. Romberg, and K. Sabra · 2012
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Embeddings of surfaces, curves, and moving points in Euclidean space
P. Agarwal, S. Har-Peled, and H. Yu · 2013
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A Mathematical Introduction to Compressive Sensing
S. Foucart and H. Rauhut · 2013
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Greedy-like algorithms for the cosparse analysis model
R. Giryes, S. Nam, M. Elad, R. Gribonval, and M. Davies · 2013
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Optimal bounds for Johnson-Lindenstrauss transforms and streaming problems with subconstant error
T. Jayram and D. Woodruff · 2013
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Parametric estimation of randomly compressed functions
W. Mantzel · 2013
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Compressive parameter estimation
W. Mantzel and J. Romberg · 2013
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The cosparse analysis model and algorithms
S. Nam, M. Davies, M. Elad, and R. Gribonval · 2013
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Distance preserving embeddings for general n n -dimensional manifolds
N. Verma · 2013
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