On the Impossibility of Dimension Reduction in l1

Abstract

The Johnson--Lindenstrauss lemma shows that any <i>n</i> points in Euclidean space (i.e., &#x211D;<sup><i>n</i></sup> with distances measured under the &ell;<inf>2</inf> norm) may be mapped down to <i>O</i>((log <i>n</i>)/&epsi;<sup>2</sup>) dimensions such that no pairwise distance is distorted by more than a (1 &plus; &epsi;) factor. Determining whether… (More)
DOI: 10.1145/1089023.1089026

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@inproceedings{Brinkman2003OnTI, title={On the Impossibility of Dimension Reduction in l1}, author={Bo Brinkman and Moses Charikar}, booktitle={FOCS}, year={2003} }