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Density Estimation for Compound Cox Processes on Hyperspheres

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Geometric Science of Information (GSI 2017)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10589))

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Abstract

Cox multiple scattering processes on hyperspheres are a class of doubly stochastic Poisson processes that can be used to describe scattering phenomenon in Physics (optics, micro-waves, acoustics, etc.). In this article, we present an EM (Expectation Maximization) technique to estimate the concentration parameter of a Compound Cox process with values on hyperspheres. The proposed algorithm is based on an approximation formula for multiconvolution of von Mises Fisher densities on spheres of any dimension.

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Notes

  1. 1.

    Here we make use of a notation abuse by expressing \(f(\varvec{x}_t;\mu ,\kappa )\) as a sum of dirac measure and a pdf. It has to be understood the following way: when \(\varvec{x}= \varvec{\mu }\), it equals the dirac mass, and for other cases it equals the density function.

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Author information

Authors and Affiliations

  1. Univ. Grenoble Alpes, CNRS, Grenoble INP, GIPSA-lab (UMR 5216), Grenoble, France

    Florent Chatelain & Nicolas Le Bihan

  2. Department of Electrical and Electronic Engineering, The University of Melbourne, Melbourne, Australia

    Jonathan H. Manton

Authors
  1. Florent Chatelain
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  2. Nicolas Le Bihan
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  3. Jonathan H. Manton
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Corresponding author

Correspondence to Nicolas Le Bihan .

Editor information

Editors and Affiliations

  1. Ecole Polytechnique, Palaiseau, France

    Frank Nielsen

  2. Thales Land and Air Systems, Limours, France

    Frédéric Barbaresco

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Chatelain, F., Le Bihan, N., Manton, J.H. (2017). Density Estimation for Compound Cox Processes on Hyperspheres. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2017. Lecture Notes in Computer Science(), vol 10589. Springer, Cham. https://doi.org/10.1007/978-3-319-68445-1_79

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  • DOI: https://doi.org/10.1007/978-3-319-68445-1_79

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-68444-4

  • Online ISBN: 978-3-319-68445-1

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