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Geometric theory of information

edited byFrank Nielsen

Abstract

This book brings together geometric tools and their applications for Information analysis. It collects current and many uses of in the interdisciplinary fields of Information Geometry Manifolds in Advanced Signal, Image & Video Processing, Complex Data Modeling and Analysis, Information Ranking and Retrieval, Coding, Cognitive Systems, Optimal Control, Statistics on Manifolds, Machine Learning, Speech/sound recognition, and natural language treatment which are also substantially relevant for the industry.

Details | Table of Contents

Divergence functions and geometric structures they induce on a manifold Jun Zhang

pp.1-30

https://doi.org/10.1007/978-3-319-05317-2_1

Geometry on positive definite matrices deformed by v-potentials and its submanifold structure Atsumi Ohara Shinto Eguchi

pp.31-55

https://doi.org/10.1007/978-3-319-05317-2_2

Hessian structures and divergence functions on deformed exponential families Hiroshi Matsuzoe Masayuki Henmi

pp.57-80

https://doi.org/10.1007/978-3-319-05317-2_3

Harmonic maps relative to $$alpha $$-connections Keiko Uohashi

pp.81-96

https://doi.org/10.1007/978-3-319-05317-2_4

A Riemannian geometry in the $$$$-exponential banach manifold induced by $$$$-divergences Héctor R. Quiceno Gabriel I. Loaiza Juan C. Arango

pp.97-117

https://doi.org/10.1007/978-3-319-05317-2_5

Computational algebraic methods in efficient estimation Kei Kobayashi Henry P. Wynn

pp.119-140

https://doi.org/10.1007/978-3-319-05317-2_6

Eidetic reduction of information geometry through legendre duality of Koszul characteristic function and entropy

from Massieu–Duhem potentials to geometric Souriau temperature and Balian quantum Fisher metric

Frédéric Barbaresco

pp.141-217

https://doi.org/10.1007/978-3-319-05317-2_7

Distances on spaces of high-dimensional linear stochastic processes

a survey

Bijan Afsari René Vidal

pp.219-242

https://doi.org/10.1007/978-3-319-05317-2_8

Discrete ladders for parallel transport in transformation groups with an affine connection structure Marco Lorenzi Xavier Pennec

pp.243-271

https://doi.org/10.1007/978-3-319-05317-2_9

Diffeomorphic iterative centroid methods for template estimation on large datasets Claire Cury Olivier Colliot

pp.273-299

https://doi.org/10.1007/978-3-319-05317-2_10

Hartigan's method for $$$$-mle

mixture modeling with wishart distributions and its application to motion retrieval

Christophe Saint-Jean Frank Nielsen

pp.301-330

https://doi.org/10.1007/978-3-319-05317-2_11

Morphological processing of univariate gaussian distribution-valued images based on Poincaré upper-half plane representation Jesús Angulo Santiago Velasco-Forero

pp.331-366

https://doi.org/10.1007/978-3-319-05317-2_12

Dimensionality reduction for classification of stochastic texture images C. T. J. Dodson W. W. Sampson

pp.367-388

https://doi.org/10.1007/978-3-319-05317-2_13

Publication details

Publisher: Springer

Place: Dordrecht

Year: 2014

Pages: 392

Series: Signals and Communication Technology

DOI: 10.1007/978-3-319-05317-2

ISBN (hardback): 978-3-319-05316-5

ISBN (digital): 978-3-319-05317-2

Full citation:

Nielsen Frank (2014) Geometric theory of information. Dordrecht, Springer.