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Consider an m by N matrix Phi with the Restricted Isometry Property of order k and level delta, that is, the norm of any k-sparse vector in R^N is preserved to within a multiplicative factor of 1 +- delta under application of Phi.
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W. B. Johnson and J. Lindenstrauss · 1984
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The Johnson-Lindenstrauss Lemma and the sphericity of some graphs
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Algorithmic applications of low-distortion embeddings
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Concentration inequalities using the entropy method
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An elementary proof of a theorem of Johnson and Lindenstrauss
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For most large underdetermined systems of linear equations the minimal ℓ 1 \ell^{1} solution is also the sparsest solution
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Improved approximation algorithms for large matrices via random projections
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Randomized algorithms for the low-rank approximation of matrices
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A sparse Johnson-Lindenstrauss transform
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Almost optimal unrestricted fast Johnson-Lindenstrauss transform
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