Geometric Theory of Information

1. Front Matter

   Pages i-xii

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2. Divergence Functions and Geometric Structures They Induce on a Manifold

   • Jun Zhang

   Pages 1-30

3. Geometry on Positive Definite Matrices Deformed by V-Potentials and Its Submanifold Structure

   • Atsumi Ohara, Shinto Eguchi

   Pages 31-55

4. Hessian Structures and Divergence Functions on Deformed Exponential Families

   • Hiroshi Matsuzoe, Masayuki Henmi

   Pages 57-80

5. Harmonic Maps Relative to \(\alpha \)-Connections

   • Keiko Uohashi

   Pages 81-96

6. A Riemannian Geometry in the \(q\)-Exponential Banach Manifold Induced by \(q\)-Divergences

   • Héctor R. Quiceno, Gabriel I. Loaiza, Juan C. Arango

   Pages 97-117

7. Computational Algebraic Methods in Efficient Estimation

   • Kei Kobayashi, Henry P. Wynn

   Pages 119-140

8. 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

   Pages 141-217

9. Distances on Spaces of High-Dimensional Linear Stochastic Processes: A Survey

   • Bijan Afsari, René Vidal

   Pages 219-242

10. Discrete Ladders for Parallel Transport in Transformation Groups with an Affine Connection Structure

    • Marco Lorenzi, Xavier Pennec

    Pages 243-271

11. Diffeomorphic Iterative Centroid Methods for Template Estimation on Large Datasets

    • Claire Cury, Joan Alexis Glaunès, Olivier Colliot

    Pages 273-299

12. Hartigan’s Method for \(k\)-MLE: Mixture Modeling with Wishart Distributions and Its Application to Motion Retrieval

    • Christophe Saint-Jean, Frank Nielsen

    Pages 301-330

13. Morphological Processing of Univariate Gaussian Distribution-Valued Images Based on Poincaré Upper-Half Plane Representation

    • Jesús Angulo, Santiago Velasco-Forero

    Pages 331-366

14. Dimensionality Reduction for Classification of Stochastic Texture Images

    • C. T. J. Dodson, W. W. Sampson

    Pages 367-388

15. Back Matter

    Pages 389-392

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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.

• Banach Information Manifolds
• Computational Information Geometry
• GSI’2013 - Geometric Science of Information
• Information Analysis
• Information Ranking
• Shape Spaces
• Shape Variability
• remote sensing/photogrammetry

• Laboratoire d'Informatique (LIX), Polytechnique School, Palaiseau Cedex, France

  Frank Nielsen

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