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Improved analysis of the subsampled randomized Hadamard transform

Tropp, Joel A. (2011) Improved analysis of the subsampled randomized Hadamard transform. Advances in Adaptive Data Analysis, 3 (1-2). pp. 115-126. ISSN 1793-5369. https://resolver.caltech.edu/CaltechAUTHORS:20180831-112120288

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1142/S1793536911000787DOIArticle
http://arxiv.org/abs/1011.1595arXivDiscussion Paper
ORCID:
AuthorORCID
Tropp, Joel A.0000-0003-1024-1791
Additional Information:© 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.”
Subject Keywords:Dimension reduction, numerical linear algebra, random matrix, Walsh–Hadamard matrix
Issue or Number:1-2
Classification Code:2010 Mathematics Subject Classification. Primary: 15B52
Record Number:CaltechAUTHORS:20180831-112120288
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20180831-112120288
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:89333
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:04 Sep 2018 15:02
Last Modified:03 Oct 2019 20:15

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