Improved Analysis of the Subsamples 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.
© 2012 World Scientific Publishing Company. Received 17 June 2010. Revised 5 November 2010. This Research was supported by ONR award N00014-08-1-0883, DARPA award N66001-08-1-2065, and AFOSR award FA9550-09-1-0643.