Geometric Theory of Information [electronic resource] / edited by Frank Nielsen.

By: Nielsen, Frank [editor.]Contributor(s): SpringerLink (Online service)Material type: TextTextLanguage: English Series: Signals and Communication Technology: Publisher: Cham : Springer International Publishing : Imprint: Springer, 2014Description: XII, 392 p. 81 illus., 60 illus. in color. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783319053172Subject(s): Engineering | Remote sensing | Data mining | Global differential geometry | Engineering | Signal, Image and Speech Processing | Differential Geometry | Data Mining and Knowledge Discovery | Mathematical Applications in Computer Science | Remote Sensing/PhotogrammetryAdditional physical formats: Printed edition:: No titleDDC classification: 621.382 LOC classification: TK5102.9TA1637-1638TK7882.S65Online resources: Click here to access online
Contents:
Preface -- Divergence Functions and Geometric Structures They Induce on a Manifold -- Geometry on Positive Definite Matrices Deformed by V-potentials and Its Submanifold Structure -- Hessian structures and divergence functions on deformed exponential families -- Harmonic maps relative to α-connections -- A Riemannian geometry in the q-exponential Banach manifold induced by q-divergences -- Computational algebraic methods in efficient estimation.
In: Springer eBooksSummary: 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.
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Preface -- Divergence Functions and Geometric Structures They Induce on a Manifold -- Geometry on Positive Definite Matrices Deformed by V-potentials and Its Submanifold Structure -- Hessian structures and divergence functions on deformed exponential families -- Harmonic maps relative to α-connections -- A Riemannian geometry in the q-exponential Banach manifold induced by q-divergences -- Computational algebraic methods in efficient estimation.

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.

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