Geometric Theory of Information

Chapter 1 Divergence Functions and Geometric Structures They Induce on a Manifold

Chapter 2 Geometry on Positive Definite Matrices Deformed by V-Potentials and Its Submanifold Structure

Chapter 3 Hessian Structures and Divergence Functions on Deformed Exponential Families

Chapter 4 Harmonic Maps Relative to $$\alpha $$ α -Connections

Chapter 5 A Riemannian Geometry in the $$q$$ q -Exponential Banach Manifold Induced by $$q$$ q -Divergences

Chapter 6 Computational Algebraic Methods in Efficient Estimation

Chapter 7 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

Chapter 8 Distances on Spaces of High-Dimensional Linear Stochastic Processes: A Survey

Chapter 9 Discrete Ladders for Parallel Transport in Transformation Groups with an Affine Connection Structure

Chapter 10 Diffeomorphic Iterative Centroid Methods for Template Estimation on Large Datasets

Chapter 11 Hartigan’s Method for $$k$$ k -MLE: Mixture Modeling with Wishart Distributions and Its Application to Motion Retrieval

Chapter 12 Morphological Processing of Univariate Gaussian Distribution-Valued Images Based on Poincaré Upper-Half Plane Representation

Chapter 13 Dimensionality Reduction for Classification of Stochastic Texture Images