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Abstract: Let X be a subset of n points of the Euclidean space, and let 0 < " < 1. A classical result of Johnson and Lindenstrauss [JL84] states that there is a projection of X onto a subspace of dimension O(" log n), with distortion 1 + ". Here we show a natural extension of the above result, to a stronger preservation of the geometry of nite spaces. By a k-fold increase of the number of dimensions used compared to [JL84], a good preservation of volumes and of distances between points and ane ... (Update)
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BibTeX entry: (Update)
A. Magen. Dimensionality reductions that preserve volumes and distance to ane spaces, and its algorithmic applications. Submitted to STOC 2002, 2001. http://citeseer.ist.psu.edu/magen01dimensionality.html More
@misc{ magen02dimensionality,
author = "A. Magen",
title = "Dimensionality reductions that preserve volumes and distance to ane spaces",
text = "A. Magen. Dimensionality reductions that preserve volumes and distance
to ane spaces, and its algorithmic applications. Submitted to STOC 2002,
2001.",
year = "2002",
url = "citeseer.ist.psu.edu/magen01dimensionality.html" }
Citations (may not include all citations):227 An elementary proof of the johnson-lindenstrauss lemma - Dasgupta, Gupta - 1999
170 The geometry of graphs and some of its algorithmic applicati.. - Linial, London et al. - 1995
165 Approximate nearest neighbor: towards removing the curse of .. - Indyk, Motwani - 1998
79 Extensions of Lipschitz mappings into a Hilbert space (context) - Johnson, Lindenstrauss - 1984
37 Approximating the bandwidth via volume respecting embeddings - Feige - 2000
35 The johnson lindenstrauss lemma and the sphericity of some g.. (context) - Frankl, Mahera - 1988
27 Point location in arrangements of hyperplanes (context) - Meiser - 1993
25 Database-friendly random projections - Achlioptas - 2001
25 Small distortion and volume preserving embeddings for planar.. (context) - Rao - 1999
17 An algorithmic theory of learning: Robust concepts and rando.. (context) - Arriaga, Vempala - 1999
9 Derandomized dimensionality reduction with applications - Engebretsen, Indyk et al. - 2002
8 Projective clustering in high dimensions using core-sets (context) - Har-Peled, Varadarajan - 2002
2 Approximating vlsi layout problems (context) - Vempala - 1998
2 Approximation algortihms for strip cover in the plane (context) - Agarwal, Procopiuc - 2000
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