Improved analysis of the subsampled randomized Hadamard transform

Abstract

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.

8 pages. To appear, Advances in Adaptive Data Analysis, special issue "Sparse Representation of Data and Images." v2--v4 include minor corrections