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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
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 | ||||||||||||
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| 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 | ||||||||||||
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| 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 | ||||||||||||
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