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Souriau Exponential Map Algorithm for Machine Learning on Matrix Lie Groups

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Geometric Science of Information (GSI 2019)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 11712))

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Abstract

Jean-Marie Souriau extended Urbain Jean Joseph Leverrier algorithm to compute characteristic polynomial of a matrix in 1948. This Souriau algorithm could be used to compute exponential map of a matrix that is a challenge in Lie Group Machine Learning. Main property of Souriau Exponential Map numerical scheme is its scalability with highly parallelization.

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Acknowledgement

I would like to show my gratitude Ms. Danielle Fortuné from University of Poitiers, for giving me some documents from Claude Vallée and Jean-Marie Souriau archives.

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Authors and Affiliations

  1. Thales Land & Air Systems, 91470, Limours, France

    Frédéric Barbaresco

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  1. Frédéric Barbaresco
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Correspondence to Frédéric Barbaresco .

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Editors and Affiliations

  1. Sony Computer Science Laboratories, Inc., Tokyo, Japan

    Frank Nielsen

  2. Thales, Limours, France

    Frédéric Barbaresco

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Barbaresco, F. (2019). Souriau Exponential Map Algorithm for Machine Learning on Matrix Lie Groups. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2019. Lecture Notes in Computer Science(), vol 11712. Springer, Cham. https://doi.org/10.1007/978-3-030-26980-7_10

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  • DOI: https://doi.org/10.1007/978-3-030-26980-7_10

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