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Geometric Structures of Information

  • Frank Nielsen

Part of the Signals and Communication Technology book series (SCT)

About this book

Introduction

This book focuses on information geometry manifolds of structured data/information and their advanced applications featuring new and fruitful interactions between several branches of science: information science, mathematics and physics. It addresses interrelations between different mathematical domains like shape spaces, probability/optimization & algorithms on manifolds, relational and discrete metric spaces, computational and Hessian information geometry, algebraic/infinite dimensional/Banach information manifolds, divergence geometry, tensor-valued morphology, optimal transport theory, manifold & topology learning, and applications like geometries of audio-processing, inverse problems and signal processing.The book collects the most important contributions to the conference GSI’2017 – Geometric Science of Information.

Keywords

Hessian Information Geometry Shape Space Monotone Embedding Stochastic Geometric Mechanics Riemannian Manifolds Geometric Deep Learning Lie Group Thermodynamics Probability Density Estimation Geometry of quantum states GSI’2017

Editors and affiliations

  1. 1.Sony Computer Science Laboratories, Inc.TokyoJapan

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-02520-5
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-030-02519-9
  • Online ISBN 978-3-030-02520-5
  • Series Print ISSN 1860-4862
  • Series Online ISSN 1860-4870
  • Buy this book on publisher's site
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