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Fixed-Rank Approximation of a Positive-Semidefinite Matrix from Streaming Data

Tropp, Joel A. and Yurtsever, Alp and Udell, Madeleine and Cevher, Volkan (2017) Fixed-Rank Approximation of a Positive-Semidefinite Matrix from Streaming Data. ACM Technical Reports, 2017-03. California Institute of Technology , Pasadena, CA. (Unpublished) http://resolver.caltech.edu/CaltechAUTHORS:20170620-081901312

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Abstract

Several important applications, such as streaming PCA and semidefinite programming, involve a large-scale positive-semidefinite (psd) matrix that is presented as a sequence of linear updates. Because of storage limitations, it may only be possible to retain a sketch of the psd matrix. This paper develops a new algorithm for fixed-rank psd approximation from a sketch. The approach combines the Nyström approximation with a novel mechanism for rank truncation. Theoretical analysis establishes that the proposed method can achieve any prescribed relative error in the Schatten 1-norm and that it exploits the spectral decay of the input matrix. Computer experiments show that the proposed method dominates alternative techniques for fixed-rank psd matrix approximation across a wide range of examples.


Item Type:Report or Paper (Technical Report)
Related URLs:
URLURL TypeDescription
http://users.cms.caltech.edu/~jtropp/reports/TYUC17-Fixed-Rank-Approximation-TR.pdfAuthorReport
http://resolver.caltech.edu/CaltechAUTHORS:20180829-073029156Related ItemDiscussion Paper
ORCID:
AuthorORCID
Tropp, Joel A.0000-0003-1024-1791
Group:Applied & Computational Mathematics
Other Numbering System:
Other Numbering System NameOther Numbering System ID
ACMTR2017-03
DOI:10.7907/QJE2-RP11
Record Number:CaltechAUTHORS:20170620-081901312
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170620-081901312
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78360
Collection:CaltechACMTR
Deposited By: Sydney Garstang
Deposited On:21 Jun 2017 20:58
Last Modified:29 Mar 2019 18:54

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