On randomness reduction in the Johnson-Lindenstrauss lemma

Details On randomness reduction in the Johnson-Lindenstrauss lemma On randomness reduction in the Johnson-Lindenstrauss lemma

2012-02-24

arxiv.org/abs/1202.5500v1

Mathematics

Probability

Scientific paper

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.

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