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Near Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
, 2004
"... Suppose we are given a vector f in RN. How many linear measurements do we need to make about f to be able to recover f to within precision ɛ in the Euclidean (ℓ2) metric? Or more exactly, suppose we are interested in a class F of such objects— discrete digital signals, images, etc; how many linear m ..."
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Cited by 1513 (20 self)
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law), then it is possible to reconstruct f to within very high accuracy from a small number of random measurements. typical result is as follows: we rearrange the entries of f (or its coefficients in a fixed basis) in decreasing order of magnitude f  (1) ≥ f  (2) ≥... ≥ f  (N), and define the weakℓp ball
Finding motifs using random projections
, 2001
"... Pevzner and Sze [23] considered a precise version of the motif discovery problem and simultaneously issued an algorithmic challenge: find a motif Å of length 15, where each planted instance differs from Å in 4 positions. Whereas previous algorithms all failed to solve this (15,4)motif problem, Pevz ..."
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Cited by 285 (6 self)
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, Pevzner and Sze introduced algorithms that succeeded. However, their algorithms failed to solve the considerably more difficult (14,4), (16,5), and (18,6)motif problems. We introduce a novel motif discovery algorithm based on the use of random projections of the input’s substrings. Experiments
Databasefriendly Random Projections
, 2001
"... A classic result of Johnson and Lindenstrauss asserts that any set of n points in ddimensional Euclidean space can be embedded into kdimensional Euclidean space  where k is logarithmic in n and independent of d  so that all pairwise distances are maintained within an arbitrarily small factor. Al ..."
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Cited by 240 (3 self)
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. All known constructions of such embeddings involve projecting the n points onto a random kdimensional hyperplane. We give a novel construction of the embedding, suitable for database applications, which amounts to computing a simple aggregate over k random attribute partitions.
Signal reconstruction from noisy random projections
 IEEE Trans. Inform. Theory
, 2006
"... Recent results show that a relatively small number of random projections of a signal can contain most of its salient information. It follows that if a signal is compressible in some orthonormal basis, then a very accurate reconstruction can be obtained from random projections. We extend this type of ..."
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Cited by 239 (26 self)
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Recent results show that a relatively small number of random projections of a signal can contain most of its salient information. It follows that if a signal is compressible in some orthonormal basis, then a very accurate reconstruction can be obtained from random projections. We extend this type
Random projections of smooth manifolds
 Foundations of Computational Mathematics
, 2006
"... We propose a new approach for nonadaptive dimensionality reduction of manifoldmodeled data, demonstrating that a small number of random linear projections can preserve key information about a manifoldmodeled signal. We center our analysis on the effect of a random linear projection operator Φ: R N ..."
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Cited by 144 (26 self)
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We propose a new approach for nonadaptive dimensionality reduction of manifoldmodeled data, demonstrating that a small number of random linear projections can preserve key information about a manifoldmodeled signal. We center our analysis on the effect of a random linear projection operator Φ: R
Random projections for . . .
"... We propose a novel method for linear dimensionality reduction of manifold modeled data. First, we show that with a small number M of random projections of sample points in R N belonging to an unknown Kdimensional Euclidean manifold, the intrinsic dimension (ID) of the sample set can be estimated to ..."
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We propose a novel method for linear dimensionality reduction of manifold modeled data. First, we show that with a small number M of random projections of sample points in R N belonging to an unknown Kdimensional Euclidean manifold, the intrinsic dimension (ID) of the sample set can be estimated
Random projection in dimensionality reduction: applications to image and text data,”
 in Proceedings of the 7th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD ’01),
, 2001
"... ABSTRACT Random projections have recently emerged as a powerful method for dimensionality reduction. Theoretical results indicate that the method preserves distances quite nicely; however, empirical results are sparse. We present experimental results on using random projection as a dimensionality r ..."
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Cited by 245 (0 self)
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ABSTRACT Random projections have recently emerged as a powerful method for dimensionality reduction. Theoretical results indicate that the method preserves distances quite nicely; however, empirical results are sparse. We present experimental results on using random projection as a dimensionality
Experiments with Random Projections for Machine Learning
 In KDD ’03: Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining
, 2003
"... Dimensionality reduction via Random Projections has attracted considerable attention in recent years. The approach has interesting theoretical underpinnings and offers computational advantages. In this paper we report a number of experiments to evaluate Random Projections in the context of inductive ..."
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Cited by 67 (0 self)
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Dimensionality reduction via Random Projections has attracted considerable attention in recent years. The approach has interesting theoretical underpinnings and offers computational advantages. In this paper we report a number of experiments to evaluate Random Projections in the context
A Random Introduction To Random Projections
"... The idea of random projections is now pervasive in machine learning literature, ..."
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The idea of random projections is now pervasive in machine learning literature,
Results 1  10
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