The Johnson-Lindenstrauss Lemma and the sphericity of some graphs
Journal of Combinatorial Theory Series A
Approximate counting via random optimization
Random Structures & Algorithms
Approximate nearest neighbors: towards removing the curse of dimensionality
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Efficient search for approximate nearest neighbor in high dimensional spaces
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Linear-size approximate voronoi diagrams
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Lectures on Discrete Geometry
An elementary proof of a theorem of Johnson and Lindenstrauss
Random Structures & Algorithms
RANDOM '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
On Approximate Nearest Neighbors in Non-Euclidean Spaces
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Stable distributions, pseudorandom generators, embeddings and data stream computation
FOCS '00 Proceedings of the 41st 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
A Replacement for Voronoi Diagrams of Near Linear Size
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Bounded Geometries, Fractals, and Low-Distortion Embeddings
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
On the Impossibility of Dimension Reduction in \ell _1
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Navigating nets: simple algorithms for proximity search
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Metric structures in L1: dimension, snowflakes, and average distortion
European Journal of Combinatorics
Embeddings of surfaces, curves, and moving points in euclidean space
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Ultra-low-dimensional embeddings for doubling metrics
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Random projection trees and low dimensional manifolds
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Tighter bounds for random projections of manifolds
Proceedings of the twenty-fourth annual symposium on Computational geometry
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
Random Projection RBF Nets for Multidimensional Density Estimation
International Journal of Applied Mathematics and Computer Science - Issues in Fault Diagnosis and Fault Tolerant Control
Ultra-low-dimensional embeddings for doubling metrics
Journal of the ACM (JACM)
How to complete a doubling metric
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Which spatial partition trees are adaptive to intrinsic dimension?
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
Lower bounds for sparse recovery
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
ICAISC'10 Proceedings of the 10th international conference on Artificial intelligence and soft computing: Part I
Approximate nearest neighbor search for low dimensional queries
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
A nonlinear approach to dimension reduction
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
A tree-based regressor that adapts to intrinsic dimension
Journal of Computer and System Sciences
Optimal lower bound for differentially private multi-party aggregation
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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In this article we introduce the notion of nearest-neighbor-preserving embeddings. These are randomized embeddings between two metric spaces which preserve the (approximate) nearest-neighbors. We give two examples of such embeddings for Euclidean metrics with low “intrinsic” dimension. Combining the embeddings with known data structures yields the best-known approximate nearest-neighbor data structures for such metrics.