Overview
- Features new and fruitful interactions between several branches of science: information science, mathematics and physics
- Addresses interrelations between different mathematical domains like shape spaces, probability/optimization & algorithms on manifolds
- Collects the most important contributions to the conference GSI’2017 – Geometric Science of Information
Part of the book series: Signals and Communication Technology (SCT)
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About this book
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.
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Keywords
Table of contents (12 chapters)
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Front Matter
Editors and Affiliations
About the editor
Frank Nielsen is Professor at the Laboratoire d'informatique de l'École polytechnique, Paris, France. His research aims at understanding the nature and structure of information and randomness in data, and exploiting algorithmically this knowledge in innovative imaging applications. For that purpose, he coined the field of computational information geometry (computational differential geometry) to extract information as regular structures whilst 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 such or such particular data representation.
Bibliographic Information
Book Title: Geometric Structures of Information
Editors: Frank Nielsen
Series Title: Signals and Communication Technology
DOI: https://doi.org/10.1007/978-3-030-02520-5
Publisher: Springer Cham
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Hardcover ISBN: 978-3-030-02519-9Published: 29 November 2018
eBook ISBN: 978-3-030-02520-5Published: 19 November 2018
Series ISSN: 1860-4862
Series E-ISSN: 1860-4870
Edition Number: 1
Number of Pages: VIII, 392
Number of Illustrations: 13 b/w illustrations, 36 illustrations in colour
Topics: Communications Engineering, Networks, Coding and Information Theory, Global Analysis and Analysis on Manifolds