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On the Fisher-Rao Information Metric in the Space of Normal Distributions

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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

The Fisher-Rao distance between two probability distribution functions, as well as other divergence measures, is related to entropy and is in the core of the research area of information geometry. It can provide a framework and enlarge the perspective of analysis for a wide variety of domains, such as statistical inference, image processing (texture classification and inpainting), clustering processes and morphological classification. We present here a compact summary of results regarding the Fisher-Rao distance in the space of multivariate normal distributions including some historical background, closed forms in special cases, bounds, numerical approaches and references to recent applications.

Supported by FAPESP (13/25997-7) and CNPq (313326/2017-7) foundations.

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Author information

Authors and Affiliations

  1. CETEC, Federal University of Recôncavo of Bahia, Cruz das Almas, Brazil

    Julianna Pinele

  2. Institute of Mathematics, University of Campinas, Campinas, Brazil

    Sueli I. R. Costa

  3. School of Applied Sciences, University of Campinas, Campinas, Brazil

    João E. Strapasson

Authors
  1. Julianna Pinele
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  2. Sueli I. R. Costa
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  3. João E. Strapasson
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Corresponding author

Correspondence to Julianna Pinele .

Editor information

Editors and Affiliations

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

    Frank Nielsen

  2. Thales, Limours, France

    Frédéric Barbaresco

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Pinele, J., Costa, S.I.R., Strapasson, J.E. (2019). On the Fisher-Rao Information Metric in the Space of Normal Distributions. 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_70

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  • DOI: https://doi.org/10.1007/978-3-030-26980-7_70

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-26979-1

  • Online ISBN: 978-3-030-26980-7

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