The Johnson-Lindenstrauss Lemma and the sphericity of some graphs
Journal of Combinatorial Theory Series A
Randomized algorithms
Modern computer algebra
An elementary proof of a theorem of Johnson and Lindenstrauss
Random Structures & Algorithms
Database-friendly random projections: Johnson-Lindenstrauss with binary coins
Journal of Computer and System Sciences - Special issu on PODS 2001
Algorithmic Applications of Low-Distortion Geometric Embeddings
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Finding frequent items in data streams
Theoretical Computer Science - Special issue on automata, languages and programming
Improved Approximation Algorithms for Large Matrices via Random Projections
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
On variants of the Johnson–Lindenstrauss lemma
Random Structures & Algorithms
Numerical linear algebra in the streaming model
Proceedings of the forty-first annual ACM symposium on Theory of computing
Feature hashing for large scale multitask learning
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
The Fast Johnson-Lindenstrauss Transform and Approximate Nearest Neighbors
SIAM Journal on Computing
Fast Dimension Reduction Using Rademacher Series on Dual BCH Codes
Discrete & Computational Geometry
A sparse Johnson: Lindenstrauss transform
Proceedings of the forty-second ACM symposium on Theory of computing
Fast moment estimation in data streams in optimal space
Proceedings of the forty-third annual ACM symposium on Theory of computing
Johnson-Lindenstrauss lemma for circulant matrices
Random Structures & Algorithms
Almost optimal explicit Johnson-Lindenstrauss families
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Sparser Johnson-Lindenstrauss transforms
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
SIAM Journal on Computing
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
Low rank approximation and regression in input sparsity time
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Sparsity lower bounds for dimensionality reducing maps
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
OSNAP: Faster Numerical Linear Algebra Algorithms via Sparser Subspace Embeddings
FOCS '13 Proceedings of the 2013 IEEE 54th Annual Symposium on Foundations of Computer Science
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We give two different and simple constructions for dimensionality reduction in ℓ2 via linear mappings that are sparse: only an O(ϵ)-fraction of entries in each column of our embedding matrices are non-zero to achieve distortion 1 + ϵ with high probability, while still achieving the asymptotically optimal number of rows. These are the first constructions to provide subconstant sparsity for all values of parameters, improving upon previous works of Achlioptas [2003] and Dasgupta et al. [2010]. Such distributions can be used to speed up applications where ℓ2 dimensionality reduction is used.