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An algorithm for approximate closest-point queries
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Two algorithms for nearest-neighbor search in high dimensions
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Nearest neighbor queries in metric spaces
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Approximate nearest neighbor queries revisited
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Approximate nearest neighbors: towards removing the curse of dimensionality
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
An optimal algorithm for approximate nearest neighbor searching fixed dimensions
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Lower bounds for high dimensional nearest neighbor search and related problems
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Approximate nearest neighbor queries in fixed dimensions
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
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Locally lifting the curse of dimensionality for nearest neighbor search (extended abstract)
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We introduce a new low-distortion embedding of l2d into lpO(log n) (p=1,2), called the Fast-Johnson-Linden-strauss-Transform. The FJLT is faster than standard random projections and just as easy to implement. It is based upon the preconditioning of a sparse projection matrix with a randomized Fourier transform. Sparse random projections are unsuitable for low-distortion embeddings. We overcome this handicap by exploiting the "Heisenberg principle" of the Fourier transform, ie, its local-global duality. The FJLT can be used to speed up search algorithms based on low-distortion embeddings in l1 and l2. We consider the case of approximate nearest neighbors in l2d. We provide a faster algorithm using classical projections, which we then further speed up by plugging in the FJLT. We also give a faster algorithm for searching over the hypercube.