Geometrical formulation of the nonnegative matrix factorization

Shotaro Akaho, Hideitsu Hino, Neneka Nara, Noboru Murata

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

    1 Citation (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
    Number of pages10
    ISBN (Print)9783030041816
    Publication statusPublished - 2018 Jan 1
    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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