When does non-negative matrix factorization give a correct decomposition into parts?

David Donoho, Victoria Stodden

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We interpret non-negative matrix factorization geometrically, as the problem of finding a simplicial cone which contains a cloud of data points and which is contained in the positive orthant. We show that under certain conditions, basically requiring that some of the data are spread across the faces of the positive orthant, there is a unique such simplicial cone. We give examples of synthetic image articulation databases which obey these conditions; these require separated support and factorial sampling. For such databases there is a generative model in terms of 'parts' and NMF correctly identifies the 'parts'. We show that our theoretical results are predictive of the performance of published NMF code, by running the published algorithms on one of our synthetic image articulation databases.

Original languageEnglish (US)
Title of host publicationAdvances in Neural Information Processing Systems 16 - Proceedings of the 2003 Conference, NIPS 2003
PublisherNeural information processing systems foundation
ISBN (Print)0262201526, 9780262201520
StatePublished - Jan 1 2004
Externally publishedYes
Event17th Annual Conference on Neural Information Processing Systems, NIPS 2003 - Vancouver, BC, Canada
Duration: Dec 8 2003Dec 13 2003

Publication series

NameAdvances in Neural Information Processing Systems
ISSN (Print)1049-5258

Other

Other17th Annual Conference on Neural Information Processing Systems, NIPS 2003
CountryCanada
CityVancouver, BC
Period12/8/0312/13/03

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing

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  • Cite this

    Donoho, D., & Stodden, V. (2004). When does non-negative matrix factorization give a correct decomposition into parts? In Advances in Neural Information Processing Systems 16 - Proceedings of the 2003 Conference, NIPS 2003 (Advances in Neural Information Processing Systems). Neural information processing systems foundation.