Geometrical formulation of the nonnegative matrix factorization

Shotaro Akaho, Hideitsu Hino, Neneka Nara, Noboru Murata

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

    Abstract

    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
    Pages525-534
    Number of pages10
    ISBN (Print)9783030041816
    DOIs
    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

    Other

    Other25th International Conference on Neural Information Processing, ICONIP 2018
    CountryCambodia
    CitySiem Reap
    Period18/12/1318/12/16

    Fingerprint

    Non-negative Matrix Factorization
    Factorization
    Formulation
    Pythagorean theorem
    Dimension Reduction
    Numerical Experiment
    Optimization
    Experiments

    Keywords

    • Dimension reduction
    • Information geometry
    • Topic model

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Computer Science(all)

    Cite this

    Akaho, S., Hino, H., Nara, N., & Murata, N. (2018). Geometrical formulation of the nonnegative matrix factorization. In L. Cheng, S. Ozawa, & A. C. S. Leung (Eds.), Neural Information Processing - 25th International Conference, ICONIP 2018, Proceedings (pp. 525-534). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11303 LNCS). Springer-Verlag. https://doi.org/10.1007/978-3-030-04182-3_46

    Geometrical formulation of the nonnegative matrix factorization. / Akaho, Shotaro; Hino, Hideitsu; Nara, Neneka; Murata, Noboru.

    Neural Information Processing - 25th International Conference, ICONIP 2018, Proceedings. ed. / Long Cheng; Seiichi Ozawa; Andrew Chi Sing Leung. Springer-Verlag, 2018. p. 525-534 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11303 LNCS).

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

    Akaho, S, Hino, H, Nara, N & Murata, N 2018, Geometrical formulation of the nonnegative matrix factorization. in L Cheng, S Ozawa & ACS Leung (eds), Neural Information Processing - 25th International Conference, ICONIP 2018, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11303 LNCS, Springer-Verlag, pp. 525-534, 25th International Conference on Neural Information Processing, ICONIP 2018, Siem Reap, Cambodia, 18/12/13. https://doi.org/10.1007/978-3-030-04182-3_46
    Akaho S, Hino H, Nara N, Murata N. Geometrical formulation of the nonnegative matrix factorization. In Cheng L, Ozawa S, Leung ACS, editors, Neural Information Processing - 25th International Conference, ICONIP 2018, Proceedings. Springer-Verlag. 2018. p. 525-534. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-030-04182-3_46
    Akaho, Shotaro ; Hino, Hideitsu ; Nara, Neneka ; Murata, Noboru. / Geometrical formulation of the nonnegative matrix factorization. Neural Information Processing - 25th International Conference, ICONIP 2018, Proceedings. editor / Long Cheng ; Seiichi Ozawa ; Andrew Chi Sing Leung. Springer-Verlag, 2018. pp. 525-534 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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