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Geometrical Formulation of the Nonnegative Matrix Factorization

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Neural Information Processing (ICONIP 2018)

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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Correspondence to Shotaro Akaho .

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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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