On variants of the Johnson–Lindenstrauss lemma

  title={On variants of the Johnson–Lindenstrauss lemma},
  author={Jiř{\'i} Matou{\vs}ek},
  journal={Random Structures \& Algorithms},
  • J. Matoušek
  • Published 1 September 2008
  • Mathematics, Computer Science
  • Random Structures & Algorithms
The Johnson–Lindenstrauss lemma asserts that an n‐point set in any Euclidean space can be mapped to a Euclidean space of dimension k = O(ε‐2 log n) so that all distances are preserved up to a multiplicative factor between 1 − ε and 1 + ε. Known proofs obtain such a mapping as a linear map Rn → Rk with a suitable random matrix. We give a simple and self‐contained proof of a version of the Johnson–Lindenstrauss lemma that subsumes a basic versions by Indyk and Motwani and a version more suitable… 

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