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Nonnegative matrix factorization requires irrationality

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Chistikov, Dmitry, Kiefer, Stefan, Marušić, Ines, Shirmohammadi, Mahsa and Worrell, James (2017) Nonnegative matrix factorization requires irrationality. SIAM Journal on Applied Algebra and Geometry, 1 (1). pp. 285-307. doi:10.1137/16M1078835

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Official URL: https://doi.org/10.1137/16M1078835

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Abstract

Nonnegative matrix factorization (NMF) is the problem of decomposing a given nonnegative n × m matrix M into a product of a nonnegative n × d matrix W and a nonnegative d × m matrix H. A longstanding open question, posed by Cohen and Rothblum in 1993, is whether a rational matrix M always has an NMF of minimal inner dimension d whose factors W and H are also rational. We answer this question negatively, by exhibiting a matrix for which W and H require irrational entries.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Computer Science
Library of Congress Subject Headings (LCSH): Non-negative matrices, Decomposition (Mathematics), Factorization (Mathematics)
Journal or Publication Title: SIAM Journal on Applied Algebra and Geometry
Publisher: SIAM
ISSN: 2470-6566
Official Date: 2017
Dates:
DateEvent
2017Published
29 June 2017Available
10 March 2017Accepted
Volume: 1
Number: 1
Page Range: pp. 285-307
DOI: 10.1137/16M1078835
Status: Peer Reviewed
Publication Status: Published
Publisher Statement: © 2017 SIAM
Access rights to Published version: Open Access
Copyright Holders: Society for Industrial and Applied Mathematics
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
648701 European Research Councilhttp://viaf.org/viaf/130022607
UNSPECIFIED[RS] Royal Societyhttp://dx.doi.org/10.13039/501100000288
UNSPECIFIED[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
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