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Johnson-Lindenstrauss lemma for circulant matrices · arXivDesk

1001.4919Jan 27, 2010

Johnson-Lindenstrauss lemma for circulant matrices

Aicke Hinrichs, Jan Vybíral

Functional Analysis Information Theory

Abstract

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 $k=O(ε^{-2}\log^3n)$ instead of the classical bound $k=O(ε^{-2}\log n)$

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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.

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The paper addresses: Johnson-Lindenstrauss lemma for circulant matrices.
We prove a variant of a Johnson-Lindenstrauss lemma for matrices with circulant structure.

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