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Geometrical Formulation of the Nonnegative Matrix Factorization

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Neural Information Processing (ICONIP 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11303))

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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.

Supported by JSPS KAKENHI Grant Number 16K16108, 17H01793.

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Author information

Authors and Affiliations

  1. National Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki, 305-8568, Japan

    Shotaro Akaho

  2. The Institute of Statistical Mathematics, Tachikawa, Tokyo, 190-8562, Japan

    Hideitsu Hino

  3. Waseda University, Shinjuku, Tokyo, 169-0072, Japan

    Neneka Nara & Noboru Murata

Authors
  1. Shotaro Akaho
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  2. Hideitsu Hino
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  3. Neneka Nara
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  4. Noboru Murata
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Corresponding author

Correspondence to Shotaro Akaho .

Editor information

Editors and Affiliations

  1. The Chinese Academy of Sciences, Beijing, China

    Long Cheng

  2. City University of Hong Kong, Kowloon, Hong Kong

    Andrew Chi Sing Leung

  3. Kobe University, Kobe, Japan

    Seiichi Ozawa

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Akaho, S., Hino, H., Nara, N., Murata, N. (2018). Geometrical Formulation of the Nonnegative Matrix Factorization. In: Cheng, L., Leung, A., Ozawa, S. (eds) Neural Information Processing. ICONIP 2018. Lecture Notes in Computer Science(), vol 11303. Springer, Cham. https://doi.org/10.1007/978-3-030-04182-3_46

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  • DOI: https://doi.org/10.1007/978-3-030-04182-3_46

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-04181-6

  • Online ISBN: 978-3-030-04182-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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