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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.

References

  1. Le Bihan, N., Chatelain, F., Manton, J.: Isotropic multiple scattering processes on hyperspheres. IEEE Trans. Inf. Theory 62, 5740–5752 (2016)

    Article  MATH  MathSciNet  Google Scholar 

  2. Chatelain, F., Le Bihan, N., Manton, J.: Parameter estimation for multiple scattering process on the sphere. In: IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (2015)

    Google Scholar 

  3. Chatelain, F., Le Bihan, N.: von-mises fisher approximation of multiple scattering process on the hypershpere. In: IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (2013)

    Google Scholar 

  4. Mardia, K., Jupp, P.: Directional Statistics. Wiley, New York (2000)

    MATH  Google Scholar 

  5. Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables. Dover Publications, New York (1972)

    MATH  Google Scholar 

  6. Kent, J.: Limiting behaviour of the von Mises-Fisher distribution. Math. Proc. Cambridge Philos. Soc. 84, 531–536 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  7. Le Bihan, N., Margerin, L.: Nonparametric estimation of the heterogeneity of a random medium using compound poisson process modeling of wave multiple scattering. Phys. Rev. E 80, 016601 (2009)

    Article  MathSciNet  Google Scholar 

  8. Lefebvre, M.: Applied Stochastic Processes. Springer, New York (2006)

    MATH  Google Scholar 

  9. Saleh, B.: Photoelectron Statistics. Springer, Heidelberg (1978)

    Book  Google Scholar 

  10. Sra, S.: A short note on parameter approximation for von mises-fisher distributions. Comput. Stat. 27, 177–190 (2012)

    Article  MATH  MathSciNet  Google Scholar 

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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

  • eBook Packages: Computer ScienceComputer Science (R0)

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