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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.

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

Full citation:

Divergence functions and geometric structures they induce on a manifold

Zhang Jun

1-30

Geometry on positive definite matrices deformed by v-potentials and its submanifold structure

Ohara Atsumi; Eguchi Shinto

31-55

Hessian structures and divergence functions on deformed exponential families

Matsuzoe Hiroshi; Henmi Masayuki

57-80

Harmonic maps relative to $$alpha $$-connections

Uohashi Keiko

81-96

A Riemannian geometry in the $$$$-exponential banach manifold induced by $$$$-divergences

Quiceno Héctor R.; Loaiza Gabriel I.; Arango Juan C.

97-117

Computational algebraic methods in efficient estimation

Kobayashi Kei; Wynn Henry P.

119-140

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

Barbaresco Frédéric

141-217

Distances on spaces of high-dimensional linear stochastic processes

Afsari Bijan; Vidal René

219-242

Discrete ladders for parallel transport in transformation groups with an affine connection structure

Lorenzi Marco; Pennec Xavier

243-271

Diffeomorphic iterative centroid methods for template estimation on large datasets

Cury Claire; Colliot Olivier

273-299

Hartigan's method for $$$$-mle

Saint-Jean Christophe; Nielsen Frank

301-330

Morphological processing of univariate gaussian distribution-valued images based on Poincaré upper-half plane representation

Angulo Jesús; Velasco-Forero Santiago

331-366

Dimensionality reduction for classification of stochastic texture images

Dodson C. T. J.; Sampson W. W.

367-388