Geometric Theory of Information

Editors:

ISBN: 978-3-319-05316-5 (Print) 978-3-319-05317-2 (Online)

Table of contents (13 chapters)

  1. Front Matter

    Pages i-xii

  2. No Access

    Book Chapter

    Pages 1-30

    Divergence Functions and Geometric Structures They Induce on a Manifold

  3. No Access

    Book Chapter

    Pages 31-55

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

  4. No Access

    Book Chapter

    Pages 57-80

    Hessian Structures and Divergence Functions on Deformed Exponential Families

  5. No Access

    Book Chapter

    Pages 81-96

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

  6. No Access

    Book Chapter

    Pages 97-117

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

  7. No Access

    Book Chapter

    Pages 119-140

    Computational Algebraic Methods in Efficient Estimation

  8. No Access

    Book Chapter

    Pages 141-217

    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

  9. No Access

    Book Chapter

    Pages 219-242

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

  10. No Access

    Book Chapter

    Pages 243-271

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

  11. No Access

    Book Chapter

    Pages 273-299

    Diffeomorphic Iterative Centroid Methods for Template Estimation on Large Datasets

  12. No Access

    Book Chapter

    Pages 301-330

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

  13. No Access

    Book Chapter

    Pages 331-366

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

  14. No Access

    Book Chapter

    Pages 367-388

    Dimensionality Reduction for Classification of Stochastic Texture Images

  15. Back Matter

    Pages 389-392