Geometric Theory of Information

Front Matter....Pages i-xii
Divergence Functions and Geometric Structures They Induce on a Manifold....Pages 1-30
Geometry on Positive Definite Matrices Deformed by V-Potentials and Its Submanifold Structure....Pages 31-55
Hessian Structures and Divergence Functions on Deformed Exponential Families....Pages 57-80
Harmonic Maps Relative to $$\alpha $$ α -Connections....Pages 81-96
A Riemannian Geometry in the $$q$$ q -Exponential Banach Manifold Induced by $$q$$ q -Divergences....Pages 97-117
Computational Algebraic Methods in Efficient Estimation....Pages 119-140
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....Pages 141-217
Distances on Spaces of High-Dimensional Linear Stochastic Processes: A Survey....Pages 219-242
Discrete Ladders for Parallel Transport in Transformation Groups with an Affine Connection Structure....Pages 243-271
Diffeomorphic Iterative Centroid Methods for Template Estimation on Large Datasets....Pages 273-299
Hartigan’s Method for $$k$$ k -MLE: Mixture Modeling with Wishart Distributions and Its Application to Motion Retrieval....Pages 301-330
Morphological Processing of Univariate Gaussian Distribution-Valued Images Based on Poincaré Upper-Half Plane Representation....Pages 331-366
Dimensionality Reduction for Classification of Stochastic Texture Images....Pages 367-388
Back Matter....Pages 389-392