Metodo

International Studies in Phenomenology and Philosophy

Series | Book

COPR Bookmark
224910

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 OharaShinto 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 MatsuzoeMasayuki 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. QuicenoGabriel I. LoaizaJuan C. Arango

pp.97-117

https://doi.org/10.1007/978-3-319-05317-2_5
Computational algebraic methods in efficient estimation Kei KobayashiHenry 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 AfsariRené 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 LorenziXavier 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 CuryOlivier 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-JeanFrank 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 AnguloSantiago 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. DodsonW. 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.