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Geometric Structures of Information de Frank Nielsen

Geometric Structures of Information: Signals and Communication Technology

Editat de Frank Nielsen
en Limba Engleză Hardback – 29 noi 2018
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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Specificații

ISBN-13: 9783030025199
ISBN-10: 3030025195
Pagini: 368
Ilustrații: VIII, 392 p. 49 illus., 36 illus. in color.
Dimensiuni: 155 x 235 mm
Greutate: 0.74 kg
Ediția:1st ed. 2019
Editura: Springer International Publishing
Colecția Springer
Seria Signals and Communication Technology

Locul publicării:Cham, Switzerland

Cuprins

Rho-Tau Embedding of Statistical Models.- A class of non-parametric deformed exponential

statistical models.- Statistical Manifolds Admitting Torsion and Partially Flat Spaces.- Conformal attening on the probability simplex and its applications to Voronoi partitions and centroids Atsumi Ohara.- Monte Carlo Information-Geometric Structures.- Information geometry in portfolio theory.- Generalising Frailty Assumptions in Survival Analysis: a Geometric Approach.- Some Universal Insights on Divergences for
Statistics, Machine Learning and Articial Intelligence.- Information-Theoretic Matrix
Inequalities and Diusion Processes on Unimodular Lie Groups.

Notă biografică

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.

Textul de pe ultima copertă

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.

Caracteristici

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  


Descriere

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.