Journal
ADVANCES IN DATA SCIENCE AND ADAPTIVE ANALYSIS
Volume 3, Issue 1-2, Pages 115-126Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S1793536911000787
Keywords
Dimension reduction; numerical linear algebra; random matrix; Walsh-Hadamard matrix
Categories
Funding
- ONR [N00014-08-1-0883]
- DARPA [N66001-08-1-2065]
- AFOSR [FA9550-09-1-0643]
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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.
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