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Johnson‐Lindenstrauss lemma for circulant matrices**
Aicke Hinrichs (Austrian Academy of Sciences, Johann Radon Institute for Computational and Applied Mathematics), Jan Vybíral (Austrian Academy of Sciences, Johann Radon Institute for Computational and Applied Mathematics)
Abstract: Abstract We prove a variant of a Johnson‐Lindenstrauss lemma for matrices with circulant structure. This approach allows to minimize 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 log3 n) instead of the classical bound k = O(ε−2 log n). © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2011