Journal article
Nonnegative matrix factorization requires irrationality
- Abstract:
- Nonnegative matrix factorization (NMF) is the problem of decomposing a given nonnegative n x m matrix M into a product of a nonnegative n x d matrix W and a nonnegative d x 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.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 439.8KB, Terms of use)
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- Publisher copy:
- 10.1137/16M1078835
Authors
+ European Research Council
More from this funder
- Funder identifier:
- http://dx.doi.org/10.13039/501100000288
- Funding agency for:
- Chistikov, D
- Grant:
- AVS-ISS (648701
- Publisher:
- Society for Industrial and Applied Mathematics
- Journal:
- SIAM Journal on Applied Algebra and Geometry More from this journal
- Volume:
- 1
- Issue:
- 1
- Pages:
- 285-307
- Publication date:
- 2017-06-29
- Acceptance date:
- 2017-03-10
- DOI:
- EISSN:
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2470-6566
- Keywords:
- Pubs id:
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pubs:686674
- UUID:
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uuid:09b91dd8-c9b8-4571-9bec-014a72f996ea
- Local pid:
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pubs:686674
- Deposit date:
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2017-03-22
Terms of use
- Copyright holder:
- c 2017 Chistikov, et al
- Copyright date:
- 2017
- Notes:
- This is the publisher's version of the article. The final version is available online from Society for Industrial and Applied Mathematics at: 10.1137/16M1078835
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