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Geometric Science of Information

5th International Conference, GSI 2021, Paris, France, July 21–23, 2021, Proceedings

  • Conference proceedings
  • © 2021

Overview

Editors:
  1. Frank Nielsen

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

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    You can also search for this editor in PubMed   Google Scholar

  2. Frédéric Barbaresco

    1. THALES Land & Air Systems, Meudon, France

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Lecture Notes in Computer Science (LNCS, volume 12829)

Part of the book sub series: Image Processing, Computer Vision, Pattern Recognition, and Graphics (LNIP)

Included in the following conference series:

Conference proceedings info: GSI 2021.

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Table of contents (98 papers)

  1. Front Matter

    Pages i-xxix
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  2. Probability and Statistics on Riemannian Manifolds

    1. Front Matter

      Pages 1-1
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    2. From Bayesian Inference to MCMC and Convex Optimisation in Hadamard Manifolds

      • Salem Said, Nicolas Le Bihan, Jonathan H. Manton
      Pages 3-11

    3. Finite Sample Smeariness on Spheres

      • Benjamin Eltzner, Shayan Hundrieser, Stephan Huckemann
      Pages 12-19

    4. Gaussian Distributions on Riemannian Symmetric Spaces in the Large N Limit

      • Simon Heuveline, Salem Said, Cyrus Mostajeran
      Pages 20-28

    5. Smeariness Begets Finite Sample Smeariness

      • Do Tran, Benjamin Eltzner, Stephan Huckemann
      Pages 29-36

    6. Online Learning of Riemannian Hidden Markov Models in Homogeneous Hadamard Spaces

      • Quinten Tupker, Salem Said, Cyrus Mostajeran
      Pages 37-44

  3. Sub-Riemannian Geometry and Neuromathematics

    1. Front Matter

      Pages 45-45
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    2. Submanifolds of Fixed Degree in Graded Manifolds for Perceptual Completion

      • Giovanna Citti, Gianmarco Giovannardi, Manuel Ritoré, Alessandro Sarti
      Pages 47-55

    3. An Auditory Cortex Model for Sound Processing

      • Rand Asswad, Ugo Boscain, Giuseppina Turco, Dario Prandi, Ludovic Sacchelli
      Pages 56-64

    4. Conformal Model of Hypercolumns in V1 Cortex and the Möbius Group. Application to the Visual Stability Problem

      • Dmitri Alekseevsky
      Pages 65-72

    5. Extremal Controls for the Duits Car

      • Alexey Mashtakov
      Pages 73-81

    6. Multi-shape Registration with Constrained Deformations

      • Rosa Kowalewski, Barbara Gris
      Pages 82-90

  4. Shapes Spaces

    1. Front Matter

      Pages 91-91
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    2. Geodesics and Curvature of the Quotient-Affine Metrics on Full-Rank Correlation Matrices

      • Yann Thanwerdas, Xavier Pennec
      Pages 93-102

    3. Parallel Transport on Kendall Shape Spaces

      • Nicolas Guigui, Elodie Maignant, Alain Trouvé, Xavier Pennec
      Pages 103-110

    4. Diffusion Means and Heat Kernel on Manifolds

      • Pernille Hansen, Benjamin Eltzner, Stefan Sommer
      Pages 111-118

    5. A Reduced Parallel Transport Equation on Lie Groups with a Left-Invariant Metric

      • Nicolas Guigui, Xavier Pennec
      Pages 119-126

    6. Currents and K-functions for Fiber Point Processes

      • Pernille E. H. Hansen, Rasmus Waagepetersen, Anne Marie Svane, Jon Sporring, Hans J. T. Stephensen, Stine Hasselholt et al.
      Pages 127-134

  5. Geometry of Quantum States

    1. Front Matter

      Pages 135-135
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  1. Geometric Science of Information

Keywords

About this book

This book constitutes the proceedings of the 5th International Conference on Geometric Science of Information, GSI 2021, held in Paris, France, in July 2021.

The 98 papers presented in this volume were carefully reviewed and selected from 125 submissions. They cover all the main topics and highlights in the domain of geometric science of information, including information geometry manifolds of structured data/information and their advanced applications. The papers are organized in the following topics: Probability and statistics on Riemannian Manifolds; sub-Riemannian geometry and neuromathematics; shapes spaces; geometry of quantum states; geometric and structure preserving discretizations; information geometry in physics; Lie group machine learning; geometric and symplectic methods for hydrodynamical models; harmonic analysis on Lie groups; statistical manifold and Hessian information geometry; geometric mechanics; deformed entropy, cross-entropy, and relative entropy; transformation information geometry; statistics, information and topology; geometric deep learning; topological and geometrical structures in neurosciences; computational information geometry; manifold and optimization; divergence statistics; optimal transport and learning; and geometric structures in thermodynamics and statistical physics.

Editors and Affiliations

  • Sony Computer Science Laboratories Inc., Tokyo, Japan

    Frank Nielsen

  • THALES Land & Air Systems, Meudon, France

    Frédéric Barbaresco

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