On randomness reduction in the Johnson-Lindenstrauss lemma
Probability
2012-11-09 v2 Functional Analysis
Abstract
A refinement of so-called fast Johnson-Lindenstrauss transform, due to Ailon and Chazelle (2006), and Matou\v{s}ek (2008), is proposed. While it preserves the time efficiency and simplicity of implementation of the original construction, it reduces randomness used to generate the random transformation. In the analysis of the construction two auxiliary results are established which might be of independent interest: a Bernstein-type inequality for a sum of a random sample from a family of independent random variables and a normal approximation result for such a sum.
Keywords
Cite
@article{arxiv.1202.5500,
title = {On randomness reduction in the Johnson-Lindenstrauss lemma},
author = {Paweł Wolff},
journal= {arXiv preprint arXiv:1202.5500},
year = {2012}
}