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Towards Quotient Barycentric Subspaces

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  • معلومة اضافية
    • Contributors:
      Université Côte d'Azur (UniCA); E-Patient : Images, données & mOdèles pour la médeciNe numériquE (EPIONE); Inria Sophia Antipolis - Méditerranée (CRISAM); Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria); CB - Centre Borelli - UMR 9010 (CB); Service de Santé des Armées-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Ecole Normale Supérieure Paris-Saclay (ENS Paris Saclay)-Université Paris Cité (UPCité); The authors have received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement G-Statistics N° 786854). It was also supported by the French government through the 3IA Côte d’Azur Investments ANR-19-P3IA-0002 managed by the National Research Agency.; ANR-19-P3IA-0002,3IA@cote d'azur,3IA Côte d'Azur(2019); European Project: 786854,H2020 Pilier ERC,ERC AdG(2018)
    • بيانات النشر:
      HAL CCSD
      Springer Nature Switzerland
    • الموضوع:
      2023
    • Collection:
      Archive ouverte du Service de Santé des Armées (HAL)
    • الموضوع:
      France
    • الموضوع:
      Saint-Malo (France), France
    • نبذة مختصرة :
      International audience ; Barycentric Subspaces have been defined in the context of manifolds using the notion of exponential barycenters. In this work, we extend the definition to quotient spaces which are not necessary manifolds. We define an alignment map and an horizontal logarithmic map to introduce Quotient Barycentric Subspaces (QBS). Due to the discrete group action and the quotient structure, the characterization of the subspaces and the estimation of the projection of a point onto the subspace is far from trivial. We propose two algorithms towards the estimation of the QBS and we discussed the results, underling the possible next steps for a robust estimation and their application to different data types.
    • Relation:
      info:eu-repo/grantAgreement//786854/EU/G-Statistics - Foundations of Geometric Statistics and Their Application in the Life Sciences/ERC AdG
    • الرقم المعرف:
      10.1007/978-3-031-38271-0_36
    • الدخول الالكتروني :
      https://inria.hal.science/hal-04162647
      https://inria.hal.science/hal-04162647v1/document
      https://inria.hal.science/hal-04162647v1/file/Towards_Quotient_Barycentric_Subspaces.pdf
      https://doi.org/10.1007/978-3-031-38271-0_36
    • Rights:
      http://creativecommons.org/licenses/by/ ; info:eu-repo/semantics/OpenAccess
    • الرقم المعرف:
      edsbas.11427696