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Signals and Communication Technology

Progress in Information Geometry

Theory and Applications

Editors: Nielsen, Frank (Ed.)

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  • Features new and fruitful interactions between several branches of science: information science, mathematics and physics
  • Offers a substantial information source for industry and academia
  • Collects the most important contributions to the conference GSI’2019 – Geometric Science of Information
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eBook $119.00
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  • ISBN 978-3-030-65459-7
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  • Immediate eBook download after purchase
Hardcover $159.99
price for USA in USD
  • ISBN 978-3-030-65458-0
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
About this book

This book focuses on information-geometric manifolds of structured data and models and related applied mathematics. It features new and fruitful interactions between several branches of science: Advanced Signal/Image/Video Processing, Complex Data Modeling and Analysis, Statistics on Manifolds, Topology/Machine/Deep Learning and Artificial Intelligence. The selection of applications makes the book a substantial information source, not only for academic scientist but it is also highly relevant for industry. 

The book project was initiated following discussions at the international conference GSI’2019 – Geometric Science of Information that was held at ENAC, Toulouse (France).


About the authors

Frank Nielsen is Senior Researcher at Sony Computer Science Laboratories Inc, Tokyo, Japan and a fellow of the European Laboratory for Learning and Intelligent Systems (ELLIS). He taught at Ecole Polytechnique (Palaiseau, France) visual computing and high performance computing (HPC) for data science. His research aims at understanding the nature and structure of information and variability in data and exploiting algorithmically this knowledge in innovative imaging and machine learning applications. For that purpose, he coined the field of computational information geometry (computational differential geometry) to extract information as regular structures while taking into account variability in datasets by grounding them in geometric spaces. Geometry beyond Euclidean spaces has a long history of revolutionizing the way we perceived reality. Curved spacetime geometry sustained relativity theory and fractal geometry unveiled the scale-free properties of nature. In the digital world, geometry is data-driven and allows intrinsic data analytics by capturing the very essence of data through invariance principles without being biased by any particular data representation. He is an editor of the journal Entropy (MDPI) and of the journal Information Geometry (INGE, Springer), and co-organize the biannual internation conference on the Geometric Sciences of Information (GSI).

Table of contents (10 chapters)

Table of contents (10 chapters)
  • Information Geometry of Smooth Densities on the Gaussian Space: Poincaré Inequalities

    Pages 1-17

    Pistone, Giovanni

  • On Normalization Functions and $$\varphi $$-Families of Probability Distributions

    Pages 19-36

    de Andrade, Luiza H. F. (et al.)

  • Affine Connections with Torsion in (Para-)complexified Structures

    Pages 37-56

    Zhang, Jun (et al.)

  • Contact Hamiltonian Systems for Probability Distribution Functions and Expectation Variables: A Study Based on a Class of Master Equations

    Pages 57-87

    Goto, Shin-itiro (et al.)

  • Invariant Koszul Form of Homogeneous Bounded Domains and Information Geometry Structures

    Pages 89-126

    Barbaresco, Frédéric

Buy this book

eBook $119.00
price for USA in USD
  • ISBN 978-3-030-65459-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $159.99
price for USA in USD
  • ISBN 978-3-030-65458-0
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Progress in Information Geometry
Book Subtitle
Theory and Applications
Editors
  • Frank Nielsen
Series Title
Signals and Communication Technology
Copyright
2021
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-65459-7
DOI
10.1007/978-3-030-65459-7
Hardcover ISBN
978-3-030-65458-0
Series ISSN
1860-4862
Edition Number
1
Number of Pages
XII, 274
Number of Illustrations
70 b/w illustrations, 35 illustrations in colour
Topics