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Full Description
This book focuses on information-geometric manifolds of structured data and models 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).
Contents
Information Geometry of smooth densities on the Gaussian space: Poincare inequalities.- On Normalization Functions and ϕ-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.
