Improved analysis of the subsampled randomized Hadamard transform
This paper presents an improved analysis of a structured dimension-reduction map called the subsampled randomized Hadamard transform. This argument demonstrates that the map preserves the Euclidean geometry of an entire subspace of vectors. The new proof is much simpler than previous approaches, and it offers---for the first time---optimal constants in the estimate on the number of dimensions required for the embedding.
© 2011 World Scientific Publishing. Date: 17 June 2010. Revised 5 November 2010 and 17 July 2011. This note will appear in Advances in Adaptive Data Analysis, special issue "Sparse Representation of Multiscale Data and Images."
Accepted Version - 1011.1595.pdf