Geometrical formulation of the nonnegative matrix factorization

Shotaro Akaho*, Hideitsu Hino, Neneka Nara, Noboru Murata

*Corresponding author for this work

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

2 Citations (Scopus)


Nonnegative matrix factorization (NMF) has many applications as a tool for dimension reduction. In this paper, we reformulate the NMF from an information geometrical viewpoint. We show that a conventional optimization criterion is not geometrically natural, thus we propose to use more natural criterion. By this formulation, we can apply a geometrical algorithm based on the Pythagorean theorem. We also show the algorithm can improve the existing algorithm through numerical experiments.

Original languageEnglish
Title of host publicationNeural Information Processing - 25th International Conference, ICONIP 2018, Proceedings
EditorsLong Cheng, Seiichi Ozawa, Andrew Chi Sing Leung
PublisherSpringer Verlag
Number of pages10
ISBN (Print)9783030041816
Publication statusPublished - 2018
Event25th International Conference on Neural Information Processing, ICONIP 2018 - Siem Reap, Cambodia
Duration: 2018 Dec 132018 Dec 16

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11303 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other25th International Conference on Neural Information Processing, ICONIP 2018
CitySiem Reap


  • Dimension reduction
  • Information geometry
  • Topic model

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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