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=== Nonnegative rank factorization ===
In case the [[Nonnegative rank (linear algebra)|nonnegative rank]] of {{math|'''V'''}} is equal to its actual rank, {{math|1='''V''' = '''WH'''}} is called a nonnegative rank factorization (NRF).<ref name=BermanPlemmons74>{{cite journal|last=Berman|first=A.|author2=R.J. Plemmons |title=Inverses of nonnegative matrices|journal=Linear and Multilinear Algebra|year=1974|volume=2|issue=2|pages=161–172|doi=10.1080/03081087408817055}}</ref><ref name=BermanPlemmons94>{{cite book|author1=A. Berman |author2=R.J. Plemmons |title=Nonnegative matrices in the Mathematical Sciences|year=1994|publisher=SIAM|___location=Philadelphia}}</ref><ref name=Thomas74>{{cite journal|last=Thomas|first=L.B.|title=Problem 73-14, Rank factorization of nonnegative matrices|journal=SIAM Rev.|year=1974|volume=16|issue=3|pages=393–394|doi=10.1137/1016064}}</ref> The problem of finding the NRF of {{math|'''V'''}}, if it exists, is known to be NP-hard.<ref name=Vavasis09>{{cite journal|last=Vavasis|first=S.A.|title=On the complexity of nonnegative matrix factorization|journal=SIAM J. Optim.|year=2009|volume=20|issue=3|pages=1364–1377|doi=10.1137/070709967|arxiv=0708.4149|s2cid=7150400}}</ref>
=== Different cost functions and regularizations ===
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