The Johnson-Lindenstrauss Lemma and the sphericity of some graphs
Journal of Combinatorial Theory Series A
Approximate nearest neighbors: towards removing the curse of dimensionality
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Fast computation of low rank matrix approximations
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Fast Monte-Carlo Algorithms for finding low-rank approximations
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Database-friendly random projections: Johnson-Lindenstrauss with binary coins
Journal of Computer and System Sciences - Special issu on PODS 2001
Fast Monte-Carlo Algorithms for Approximate Matrix Multiplication
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
A Replacement for Voronoi Diagrams of Near Linear Size
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Sampling algorithms for l2 regression and applications
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Approximate nearest neighbors and the fast Johnson-Lindenstrauss transform
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Improved Approximation Algorithms for Large Matrices via Random Projections
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Fast dimension reduction using Rademacher series on dual BCH codes
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Sampling algorithms and coresets for ℓp regression
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Faster least squares approximation
Numerische Mathematik
Optimized Projections for Compressed Sensing
IEEE Transactions on Signal Processing
IEEE Transactions on Information Theory
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
IEEE Transactions on Information Theory
Near Optimal Dimensionality Reductions That Preserve Volumes
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Accelerating Feature Based Registration Using the Johnson-Lindenstrauss Lemma
MICCAI '09 Proceedings of the 12th International Conference on Medical Image Computing and Computer-Assisted Intervention: Part I
Fast locality-sensitive hashing
Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining
Optimal bounds for Johnson-Lindenstrauss transforms and streaming problems with sub-constant error
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
An almost optimal unrestricted fast Johnson-Lindenstrauss transform
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Randomized Algorithms for Matrices and Data
Foundations and Trends® in Machine Learning
An Almost Optimal Unrestricted Fast Johnson-Lindenstrauss Transform
ACM Transactions on Algorithms (TALG) - Special Issue on SODA'11
Optimal Bounds for Johnson-Lindenstrauss Transforms and Streaming Problems with Subconstant Error
ACM Transactions on Algorithms (TALG) - Special Issue on SODA'11
Linear regression with random projections
The Journal of Machine Learning Research
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Random projection methods give distributions over k×dmatrices such that if a matrix 茂戮驴(chosen according to the distribution) is applied to a vector the norm of the resulting vector, , is up to distortion 茂戮驴equal to the norm of xw.p. at least 1 茂戮驴 茂戮驴. The Johnson Lindenstrauss lemma shows that such distributions exist over densematrices for k(the target dimension) in . Ailon and Chazelle and later Matousek showed that there exist entry-wise i.i.d. distributions over sparsematrices 茂戮驴which give the same guaranties for vectors whose 茂戮驴茂戮驴is bounded away from their 茂戮驴2norm. This allows to accelerate the mapping x茂戮驴茂戮驴x. We claim that setting 茂戮驴as any column normalized deterministic densematrix composed with random ±1 diagonal matrix also exhibits this property for vectors whose 茂戮驴p(for any p 2) is bounded away from their 茂戮驴2norm. We also describe a specific tensor product matrix which we term lean Walsh. It is applicable to any vector in in O(d) operations and requires a weaker 茂戮驴茂戮驴bound on xthen the best current result, under comparable running times, using sparse matrices due to Matousek.