Johnson-Lindenstrauss lemma for circulant matrices

Authors:
Aicke Hinrichs;Jan Vybíral
Affiliations:
Department of Mathematics, Universität Jena, 07740 Jena, Germany;Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, A-4040 Linz, Austria
Venue:
Random Structures & Algorithms
Year:
2011

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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 (Supported by DFG Heisenberg (HI 584/3-2); FWF START-Preis Sparse Approximation and Optimization in High Dimensions (Y 432-N15).)