Springer, 2021. — 282 p. — (Signals and Communication Technology). — ISBN 978-3-030-65458-0.
This book focuses on information-geometric manifolds of structured data andmodels and related applied mathematics. It features new and fruitful interactions between several branches of science: Advanced Signal/Image/Video Processing, Complex Data Modeling and Analysis, Statistics on Manifolds, Topology/Machine/Deep Learning and Artificial Intelligence. The selection of applications makes the book a substantial information source, not only for academic scientist but it is also highly relevant for industry.
The book project was initiated following discussions at the international conference GSI'2019 - Geometric Science of Information that was held at ENAC, Toulouse (France).
Information Geometry of Smooth Densities on the Gaussian Space: Poincaré Inequalities
On Normalization Functions and $$ \varphi $$-Families of Probability Distributions
Affine Connections with Torsion in (Para-)complexified Structures
Contact Hamiltonian Systems for Probability Distribution Functions and Expectation Variables: A Study Based on a Class of Master Equations
Invariant Koszul Form of Homogeneous Bounded Domains and Information Geometry Structures
Gauge Freedom of Entropies on q-Gaussian Measures
On Geodesic Triangles with Right Angles in a Dually Flat Space
Chain Rule Optimal Transport
Towards the “Shape” of Cosmological Observables and the String Theory Landscape with Topological Data Analysis
A Review of Two Decades of Correlations, Hierarchies, Networks and Clustering in Financial Markets