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4th GSI 2019: Toulouse, France
- Frank Nielsen, Frédéric Barbaresco:
Geometric Science of Information - 4th International Conference, GSI 2019, Toulouse, France, August 27-29, 2019, Proceedings. Lecture Notes in Computer Science 11712, Springer 2019, ISBN 978-3-030-26979-1
Shape Space
- Tomonari Sei
, Ushio Tanaka:
On Geometric Properties of the Textile Set and Strict Textile Set. 3-12 - Martin Bauer
Inexact Elastic Shape Matching in the Square Root Normal Field Framework. 13-20 - Elena Celledoni
Signatures in Shape Analysis: An Efficient Approach to Motion Identification. 21-30 - Guillaume Bouleux
Dilation Operator Approach and Square Root Velocity Transform for Time/Doppler Spectra Characterization on SU(n). 31-38 - Andreas Bock, Alexis Arnaudon, Colin J. Cotter
Selective Metamorphosis for Growth Modelling with Applications to Landmarks. 39-48
Geometric Mechanics
- Jean Lerbet
Intrinsic Incremental Mechanics. 51-54 - Goffredo Chirco
Multi-symplectic Lie Group Thermodynamics for Covariant Field Theories. 55-65 - Géry de Saxcé
Euler-Poincaré Equation for Lie Groups with Non Null Symplectic Cohomology. Application to the Mechanics. 66-74 - Joël Bensoam
Geometric Numerical Methods with Lie Groups. 75-84 - Frédéric Barbaresco:
Souriau Exponential Map Algorithm for Machine Learning on Matrix Lie Groups. 85-95
Geometry of Tensor-Valued Data
- Christophe Corbier:
\mathbb R R -Complex Finsler Information Geometry Applied to Manifolds of Systems. 99-106 - Jesús Angulo:
Minkowski Sum of Ellipsoids and Means of Covariance Matrices. 107-115 - Patrick R. Girard
Hyperquaternions: An Efficient Mathematical Formalism for Geometry. 116-125 - Keiko Uohashi:
\alpha α -power Sums on Symmetric Cones. 126-134 - Sebastian Semper, Thomas Hotz:
Packing Bounds for Outer Products with Applications to Compressive Sensing. 135-143
Lie Group Machine Learning
- Koichi Tojo, Taro Yoshino:
On a Method to Construct Exponential Families by Representation Theory. 147-156 - Frédéric Barbaresco:
Lie Group Machine Learning and Gibbs Density on Poincaré Unit Disk from Souriau Lie Groups Thermodynamics and SU(1, 1) Coadjoint Orbits. 157-170 - Alexis Arnaudon
Irreversible Langevin MCMC on Lie Groups. 171-179 - Elena Celledoni
Predicting Bending Moments with Machine Learning. 180-187 - Claudio Carmeli
The Exponential of Nilpotent Supergroups in the Theory of Harish-Chandra Representations. 188-195
Geometric Structures in Thermodynamics and Statistical Physics
- Hiroaki Yoshimura
Dirac Structures in Open Thermodynamics. 199-208 - François Gay-Balmaz
From Variational to Bracket Formulations in Nonequilibrium Thermodynamics of Simple Systems. 209-217 - Olivier Peltre:
A Homological Approach to Belief Propagation and Bethe Approximations. 218-227 - Arjan van der Schaft, Bernhard Maschke:
About Some System-Theoretic Properties of Port-Thermodynamic Systems. 228-238 - Shin-itiro Goto
Expectation Variables on a Para-Contact Metric Manifold Exactly Derived from Master Equations. 239-247
Monotone Embedding and Affine Immersion of Probability Models
- Atsumi Ohara:
Doubly Autoparallel Structure on Positive Definite Matrices and Its Applications. 251-260 - Yann Cabanes, Frédéric Barbaresco, Marc Arnaudon, Jérémie Bigot:
Toeplitz Hermitian Positive Definite Matrix Machine Learning Based on Fisher Metric. 261-270 - Francisca Leidmar Josué Vieira, Rui Facundo Vigelis, Luiza Helena Félix de Andrade, Charles Casimiro Cavalcante
Deformed Exponential and the Behavior of the Normalizing Function. 271-278 - Hiroshi Matsuzoe, Antonio Maria Scarfone, Tatsuaki Wada:
Normalization Problems for Deformed Exponential Families. 279-287 - Jun Zhang, Gabriel Khan:
New Geometry of Parametric Statistical Models. 288-296
Divergence Geometry
- Frank Nielsen
The Bregman Chord Divergence. 299-308 - Michel Broniatowski, Emilie Miranda, Wolfgang Stummer:
Testing the Number and the Nature of the Components in a Mixture Distribution. 309-318 - Birgit Roensch, Wolfgang Stummer:
Robust Estimation by Means of Scaled Bregman Power Distances. Part I. Non-homogeneous Data. 319-330 - Birgit Roensch, Wolfgang Stummer:
Robust Estimation by Means of Scaled Bregman Power Distances. Part II. Extreme Values. 331-340
Computational Information Geometry
- Leland McInnes:
Topological Methods for Unsupervised Learning. 343-350 - Erika Gomes-Gonçalves
Geometry and Fixed-Rate Quantization in Riemannian Metric Spaces Induced by Separable Bregman Divergences. 351-358 - Frank Nielsen
The Statistical Minkowski Distances: Closed-Form Formula for Gaussian Mixture Models. 359-367 - Takashi Takenouchi:
Parameter Estimation with Generalized Empirical Localization. 368-376 - Éric Grivel:
Properties of the Cross Entropy Between ARMA Processes. 377-386
Statistical Manifold and Hessian Information Geometry
- Aliya Naaz Siddiqui
Inequalities for Statistical Submanifolds in Hessian Manifolds of Constant Hessian Curvature. 389-397 - Mohd. Aquib, Michel Nguiffo Boyom, Ali Hussain Alkhaldi, Mohammad Hasan Shahid:
B. Y. Chen Inequalities for Statistical Submanifolds in Sasakian Statistical Manifolds. 398-406 - Michel Nguiffo Boyom, Zamrooda Jabeen, Mehraj Ahmad Lone
Generalized Wintgen Inquality for Legendrian Submanifolds in Sasakian Statistical Manifolds. 407-412 - Ting-Kam Leonard Wong, Jiaowen Yang:
Logarithmic Divergences: Geometry and Interpretation of Curvature. 413-422 - Gabriel Khan, Jun Zhang:
Hessian Curvature and Optimal Transport. 423-430
Non-parametric Information Geometry
- Domenico Felice
Divergence Functions in Information Geometry. 433-442 - Nigel J. Newton:
Sobolev Statistical Manifolds and Exponential Models. 443-452 - Paola Siri, Barbara Trivellato:
Minimization of the Kullback-Leibler Divergence over a Log-Normal Exponential Arc. 453-461 - Mitsuhiro Itoh, Hiroyasu Satoh
Riemannian Distance and Diameter of the Space of Probability Measures and the Parametrix. 462-471
Statistics on Non-linear Data
- Hà Quang Minh
A Unified Formulation for the Bures-Wasserstein and Log-Euclidean/Log-Hilbert-Schmidt Distances between Positive Definite Operators. 475-483 - Yann Thanwerdas, Xavier Pennec
Exploration of Balanced Metrics on Symmetric Positive Definite Matrices. 484-493 - Cyrus Mostajeran, Christian Grussler, Rodolphe Sepulchre:
Affine-Invariant Midrange Statistics. 494-501 - Yann Thanwerdas, Xavier Pennec
Is Affine-Invariance Well Defined on SPD Matrices? A Principled Continuum of Metrics. 502-510 - Raphaël Groscot, Laurent D. Cohen, Leonidas J. Guibas:
Shape Part Transfer via Semantic Latent Space Factorization. 511-519
Geometric and Structure Preserving Discretizations
- Werner Bauer
Variational Discretization Framework for Geophysical Flow Models. 523-531 - Evan S. Gawlik
Finite Element Methods for Geometric Evolution Equations. 532-540 - Fernando Jiménez, Sina Ober-Blöbaum:
Local Truncation Error of Low-Order Fractional Variational Integrators. 541-548 - Anass Serhani, Denis Matignon, Ghislain Haine
A Partitioned Finite Element Method for the Structure-Preserving Discretization of Damped Infinite-Dimensional Port-Hamiltonian Systems with Boundary Control. 549-558 - Antoine Llor
Geometry, Energy, and Entropy Compatible (GEEC) Variational Approaches to Various Numerical Schemes for Fluid Dynamics. 559-567
Optimization on Manifold
- Jérôme Stenger, Fabrice Gamboa, Merlin Keller, Bertrand Iooss
Canonical Moments for Optimal Uncertainty Quantification on a Variety. 571-578 - Daniel Luft, Kathrin Welker:
Computational Investigations of an Obstacle-Type Shape Optimization Problem in the Space of Smooth Shapes. 579-588 - Chafik Samir
Bézier Curves and C^2 C 2 Interpolation in Riemannian Symmetric Spaces. 589-598 - Anton Mallasto, Tom C. J. Dela Haije, Aasa Feragen
A Formalization of the Natural Gradient Method for General Similarity Measures. 599-607 - Nicolas J.-B. Brunel, Juhyun Park:
The Frenet-Serret Framework for Aligning Geometric Curves. 608-617
Geometry of Quantum States
- Michel Berthier
When Geometry Meets Psycho-Physics and Quantum Mechanics: Modern Perspectives on the Space of Perceived Colors. 621-630 - Jan Naudts
Quantum Statistical Manifolds: The Finite-Dimensional Case. 631-637 - Goffredo Chirco
Generalized Gibbs Ensembles in Discrete Quantum Gravity. 638-646 - Florio Maria Ciaglia
On the Notion of Composite System. 647-654
Probability on Riemannian Manifolds
- Salem Said, Jonathan H. Manton:
The Riemannian Barycentre as a Proxy for Global Optimisation. 657-664 - Alessandro Barp:
Hamiltonian Monte Carlo on Lie Groups and Constrained Mechanics on Homogeneous Manifolds. 665-675 - Julianna Pinele
On the Fisher-Rao Information Metric in the Space of Normal Distributions. 676-684 - Mathias Højgaard Jensen
Simulation of Conditioned Diffusions on the Flat Torus. 685-694 - Emmanuel Chevallier:
Towards Parametric Bi-Invariant Density Estimation on SE(2). 695-702
Wasserstein Information Geometry/Optimal Transport
- Wuchen Li, Alex Tong Lin, Guido Montúfar:
Affine Natural Proximal Learning. 705-714 - Wuchen Li, Shu Liu, Hongyuan Zha, Haomin Zhou:
Parametric Fokker-Planck Equation. 715-724 - Yongxin Chen
Multi-marginal Schrödinger Bridges. 725-732 - Flavien Léger, Wuchen Li:
Hopf-Cole Transformation and Schrödinger Problems. 733-738 - Estelle M. Massart
Curvature of the Manifold of Fixed-Rank Positive-Semidefinite Matrices Endowed with the Bures-Wasserstein Metric. 739-748
Geometric Science of Information Libraries
- Daniel A. Brooks, Olivier Schwander, Frédéric Barbaresco, Jean-Yves Schneider, Matthieu Cord:
Second-Order Networks in PyTorch. 751-758 - Nicolas Guigui, Shuman Jia, Maxime Sermesant, Xavier Pennec
Symmetric Algorithmic Components for Shape Analysis with Diffeomorphisms. 759-768
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