Johnson-Lindenstrauss lemma for circulant matrices

Details Johnson-Lindenstrauss lemma for circulant matrices Johnson-Lindenstrauss lemma for circulant matrices

2010-01-27

arxiv.org/abs/1001.4919v1

Mathematics

Functional Analysis

Scientific paper

We prove a variant of a Johnson-Lindenstrauss lemma for matrices with
circulant structure. This approach allows to minimise the randomness used, is
easy to implement and provides good running times. The price to be paid is the
higher dimension of the target space $k=O(\epsilon^{-2}\log^3n)$ instead of the
classical bound $k=O(\epsilon^{-2}\log n)$.

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