Geometric Science of Information : 4th International Conference, GSI 2019, Toulouse, France, August 27-29, 2019, Proceedings / edited by Frank Nielsen, Frédéric Barbaresco.

Format:

Book

Contributor:

Nielsen, Frank, Editor.

Barbaresco, Frédéric, Editor.

SpringerLink (Online service)

Series:

Computer Science (SpringerNature-11645)

LNCS sublibrary. Image processing, computer vision, pattern recognition, and graphics ; SL 6, 11712

Image Processing, Computer Vision, Pattern Recognition, and Graphics ; 11712

Language:

English

Subjects (All):

Computer science-Mathematics.

Artificial intelligence.

Computer vision.

Data mining.

Mathematics of Computing.

Artificial Intelligence.

Computer Vision.

Data Mining and Knowledge Discovery.

Local Subjects:

Mathematics of Computing.

Artificial Intelligence.

Computer Vision.

Data Mining and Knowledge Discovery.

Physical Description:

1 online resource (XIX, 770 pages) : 317 illustrations, 53 illustrations in color.

Edition:

1st ed. 2019.

Contained In:

Springer Nature eBook

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2019.

System Details:

text file PDF

Summary:

This book constitutes the proceedings of the 4th International Conference on Geometric Science of Information, GSI 2019, held in Toulouse, France, in August 2019. The 79 full papers presented in this volume were carefully reviewed and selected from 105 submissions. They cover all the main topics and highlights in the domain of geometric science of information, including information geometry manifolds of structured data/information and their advanced applications.

Contents:

Part I: Shape Space

On geometric properties of the textile set and strict textile set

Inexact elastic shape matching in the square root normal field framework

Signatures in Shape Analysis: an Efficient Approach to Motion Identification

Dilation operator approach for time/Doppler spectra characterization on SU(n)

Selective metamorphosis for growth modelling with applications to landmarks

Part II: Geometric Mechanics

Intrinsic Incremental Mechanics

-Multi-symplectic Extension of Lie Group Thermodynamics for Covariant Field Theories

Euler-Poincare equation for Lie groups with non null symplectic cohomology. Application to the Mechanics

Geometric numerical methods for mechanics

Souriau Exponential Map Algorithm for Machine Learning on Matrix Lie Groups

Part 3: Geometry of Tensor-Valued Data

R-Complex Finsler Information Geometry Applied to Manifolds of Systems

Minkowski Sum of Ellipsoids and Means of Covariance Matrices

Hyperquaternions: An Efficient Mathematical Formalism for Geometry

Alpha-power sums on symmetric cones

Packing Bounds for Outer Products with Applications to Compressive Sensing

Part 4: Lie Group Machine Learning

On a method to construct exponential families by representation theory

Lie Group Machine Learning and Gibbs Density on Poincare Unit Disk from Souriau Lie Groups Thermodynamics and SU(1,1) Coadjoint Orbits

Irreversible Langevin MCMC on Lie Groups

Predicting Bending Moments with Machine Learning

The exponential of nilpotent supergroups in the theory of Harish-Chandra representations

Part 5: Geometric structures in thermodynamics and statistical physics

Dirac structures in open thermodynamics

From variational to single and double bracket formulations in nonequilibrium thermodynamics of simple systems

A omological Approach to Belief Propagation and Bethe Approximations

- About some systems-theoretic properties of Port Thermodynamic systems

Expectation variables on a para-contact metric manifold exactly derived from master equations

Part 6: Monotone embedding and affine immersion of probability models

Doubly autoparallel structure and its applications

Toeplitz Hermitian Positive Definite Matrix Machine Learning based on Fisher metric

Deformed exponential and the behavior of the normalizing function

Normalization problems for deformed exponential families

New Geometry of parametric statistical Models

Part 7: Divergence Geometry

The Bregman chord divergence

Testing the number and nature of components in a mixture distribution

Robust etsimation by means of scaled Bregman power distances. Part I: Non-homogeneous data

Robust estimation by means of scaled Bregman power distances. Part II: Extreme values

Part 8: Computational Information Geometry

Topological methods for unsupervised learning

Geometry and fixed-rate quantization in Riemannian metric spaces induced by separable Bregman divergences

The statistical Minkowski distances: Closed-form formula for Gaussian Mixture Models

Parameter estimation with generalized empirical localization

Properties of the cross entropy of ARMA processes

Part 9: Statistical Manifold and Hessian Information Geometry

Inequalities for Statistical Submanifolds in Hessian Manifolds of Constant Hessian curvature

Inequalities for statistical submanifolds in sasakian statistical manifolds

Generalized Wintgen Inequality for Legendrian Submanifolds in Sasakian statistical manifolds

Logarithmic divergence: geometry and interpretation of curvature

Hessian Curvature and Optimal Transport

Part 10: Non-parametric Information Geometry

Divergence functions in Information Geometry

Sobolev Statistical Manifolds and Exponential Models

Minimization of the Kullback-Leibler divergence over a log-normal exponential arc

Riemannian distance and diameter of the space of probability measures and the parametrix

Part 11: Statistics on non-linear data

A unified formulation for the Bures-Wasserstein and Log-Euclidean/Log-Hilbert-Schmidt distances between positive definite operators

Exploration of Balanced Metrics on Symmetric Positive Definite Matrices

Affine-invariant midrange statistics

Is affine-invariance well defined on SPD matrices? A principled continuum of metrics

Shape part transfer via semantic latent space factorization

Part 12: Geometric and structure preserving discretizations

Variational discretization framework for geophysical flows

Finite element methods for geometric evolution equations

Local truncation error of low-order fractional variational integrators

A partitioned finite element method for the structure-preserving discretization of damped in finite-dimensional port-Hamiltonian systems with boundary control

Geometry, Energy, and Entropy Compatible (GEEC) variational approaches to various numerical schemes for fluid dynamics

Part 13: Optimization on Manifold

Canonical Moments for Optimal Uncertainty Quantification on a Variety

Computational investigations of an obstacle-type shape optimization problem in the space of smooth shapes

Bezier curves and C^2 interpolation in Riemannian Symmetric Spaces

A Formalization of The Natural Gradient Method for General Similarity Measures

The Frenet-Serret framework for aligning geometric curves

Part 14: Geometry of Quantum States

When geometry meets psycho-physics and quantum mechanics: Modern perspectives on the space of perceived colors

Quantum statistical manifolds: The finite-dimensional case

Generalized Gibbs Ensembles in Discrete Quantum Gravity

On the notion of composite system, classical and quantum

Part 15: Probability on Riemannian Manifolds

The Riemannian barycentre as a proxy for global optimization

Hamiltonian Monte Carlo on Lie groups and constrained mechanics on homogeneous manifolds

On the Fisher Rao information metric in the space of normal distributions

Simulation of Conditioned Diffusions on the Flat Torus

Towards parametric bi-invariant density estimation on SE(2)

Part 16: Wasserstein Information Geometry / Optimal Transport

Affine Natural Proximal Learning

Parametric Fokker-Planck equation

Multi-marginal Schroedinger bridges

Hopf-Cole transformation and Schrodinger problems

- Curvature of the manifold of fixed-rank positive-semidefinite matrices endowed with the Bures-Wasserstein metric

Part 17: Geometric Science of Information Libraries

Second-order networks in PyTorch

Symmetric Algorithmic Components for Shape Analysis with Dieomorphisms.

Other Format:

Printed edition:

ISBN:

978-3-030-26980-7

9783030269807

Access Restriction:

Restricted for use by site license.