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Minor edit. That reference is not actual development of the method, but pure application among tons of other applications. Tag: references removed |
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=== Astronomy ===
In astronomy, NMF is a promising method for [[dimension reduction]] in the sense that astrophysical signals are non-negative. NMF has been applied to the spectroscopic observations<ref name=":0">{{Cite journal |last1=Berné |first1=O. |last2=Joblin |first2=C.|author2-link=Christine Joblin |last3=Deville |first3=Y. |last4=Smith |first4=J. D. |last5=Rapacioli |first5=M. |last6=Bernard |first6=J. P. |last7=Thomas |first7=J. |last8=Reach |first8=W. |last9=Abergel |first9=A. |date=2007-07-01 |title=Analysis of the emission of very small dust particles from Spitzer spectro-imagery data using blind signal separation methods |url=https://www.aanda.org/articles/aa/abs/2007/26/aa6282-06/aa6282-06.html |journal=Astronomy & Astrophysics |language=en |volume=469 |issue=2 |pages=575–586 |doi=10.1051/0004-6361:20066282 |issn=0004-6361|doi-access=free }}</ref><ref name="blantonRoweis07">{{Cite journal |arxiv=astro-ph/0606170|last1= Blanton|first1= Michael R.|title= K-corrections and filter transformations in the ultraviolet, optical, and near infrared |journal= The Astronomical Journal|volume= 133|issue= 2|pages= 734–754|last2= Roweis|first2= Sam |year= 2007|doi= 10.1086/510127|bibcode = 2007AJ....133..734B |s2cid= 18561804}}</ref> and the direct imaging observations<ref name = "ren18">{{Cite journal|arxiv=1712.10317|last1= Ren|first1= Bin |title= Non-negative Matrix Factorization: Robust Extraction of Extended Structures|journal= The Astrophysical Journal|volume= 852|issue= 2|pages= 104|last2= Pueyo|first2= Laurent|last3= Zhu | first3 = Guangtun B.|last4= Duchêne|first4= Gaspard |year= 2018|doi= 10.3847/1538-4357/aaa1f2|bibcode = 2018ApJ...852..104R |s2cid= 3966513}}</ref> as a method to study the common properties of astronomical objects and post-process the astronomical observations. The advances in the spectroscopic observations by Blanton & Roweis (2007)<ref name="blantonRoweis07" /> takes into account of the uncertainties of astronomical observations, which is later improved by Zhu (2016)<ref name="zhu16">{{Cite arXiv|last=Zhu|first=Guangtun B.|date=2016-12-19|title=Nonnegative Matrix Factorization (NMF) with Heteroscedastic Uncertainties and Missing data |eprint=1612.06037|class=astro-ph.IM}}</ref> where missing data are also considered and [[parallel computing]] is enabled. Their method is then adopted by Ren et al. (2018)<ref name="ren18" /> to the direct imaging field as one of the [[methods of detecting exoplanets]], especially for the direct imaging of [[circumstellar disks]].
Ren et al. (2018)<ref name="ren18" /> are able to prove the stability of NMF components when they are constructed sequentially (i.e., one by one), which enables the [[linearity]] of the NMF modeling process; the [[linearity]] property is used to separate the stellar light and the light scattered from the [[exoplanets]] and [[circumstellar disks]].
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