Geometric Science of Information: First International Conference, GSI 2013, Paris, France, August 28-30, 2013. Proceedings

Front Matter....Pages -
Front Matter....Pages 1-1
Information Geometry and Its Applications: Survey....Pages 3-3
Information-Geometric Optimization: The Interest of Information Theory for Discrete and Continuous Optimization....Pages 4-4
Nonparametric Information Geometry....Pages 5-36
Geometry of Hessian Structures....Pages 37-55
Front Matter....Pages 57-57
Bi-invariant Means on Lie Groups with Cartan-Schouten Connections....Pages 59-67
Parallel Transport with Pole Ladder: Application to Deformations of Time Series of Images....Pages 68-75
Horizontal Dimensionality Reduction and Iterated Frame Bundle Development....Pages 76-83
A Subspace Learning of Dynamics on a Shape Manifold: A Generative Modeling Approach....Pages 84-91
Front Matter....Pages 93-93
Geodesic Image Regression with a Sparse Parameterization of Diffeomorphisms....Pages 95-102
Template Estimation for Large Database: A Diffeomorphic Iterative Centroid Method Using Currents....Pages 103-111
On the Geometry and the Deformation of Shapes Represented by Piecewise Continuous Bézier Curves with Application to Shape Optimization....Pages 112-119
Random Spatial Structure of Geometric Deformations and Bayesian Nonparametrics....Pages 120-127
Front Matter....Pages 129-129
A Riemannian Fourier Transform via Spin Representations....Pages 131-139
K-Centroids-Based Supervised Classification of Texture Images Using the SIRV Modeling....Pages 140-148
Bayesian Atlas Estimation from High Angular Resolution Diffusion Imaging (HARDI)....Pages 149-157
Dimensionality Reduction for Classification of Stochastic Fibre Radiographs....Pages 158-165
Front Matter....Pages 167-167
Optimal Transport and Minimal Trade Problem, Impacts on Relational Metrics and Applications to Large Graphs and Networks Modularity....Pages 169-179
Comparing Different Modularization Criteria Using Relational Metric....Pages 180-187
A General Framework for Comparing Heterogeneous Binary Relations....Pages 188-195
On Prime-Valent Symmetric Bicirculants and Cayley Snarks....Pages 196-203
Front Matter....Pages 205-205
Studying New Classes of Graph Metrics....Pages 207-214
Tessellabilities, Reversibilities, and Decomposabilities of Polytopes....Pages 215-223
Counting the Number of Solutions of K DMDGP Instances....Pages 224-230
On the Identification of Discretization Orders for Distance Geometry with Intervals....Pages 231-238
Front Matter....Pages 239-239
Hypothesis Testing, Information Divergence and Computational Geometry....Pages 241-248
A New Implementation of k -MLE for Mixture Modeling of Wishart Distributions....Pages 249-256
Variational Problem in Euclidean Space with Density....Pages 257-264
The Exponential Family in Abstract Information Theory....Pages 265-272
Front Matter....Pages 273-273
Hessian Structures on Deformed Exponential Families....Pages 275-282
Foliations on Affinely Flat Manifolds: Information Geometry....Pages 283-292
Hypersurfaces with Isometric Reeb Flow in Hermitian Symmetric Spaces of Rank 2....Pages 293-301
Generalized Minimizers of Convex Integral Functionals and Pythagorean Identities....Pages 302-307
Front Matter....Pages 309-309
Computational Information Geometry in Statistics: Foundations....Pages 311-318
Computational Information Geometry in Statistics: Mixture Modelling....Pages 319-326
A General Metric for Riemannian Manifold Hamiltonian Monte Carlo....Pages 327-334
Visualizing Projective Shape Space....Pages 335-342
Front Matter....Pages 343-343
Interpolation and Regression of Rotation Matrices....Pages 345-352
A Geometric Framework for Non-Unitary Joint Diagonalization of Complex Symmetric Matrices....Pages 353-360
An Extrinsic Look at the Riemannian Hessian....Pages 361-368
Law of Cosines and Shannon-Pythagorean Theorem for Quantum Information....Pages 369-376
Front Matter....Pages 343-343
A Note on the Intrinsic Cramer-Rao Bound....Pages 377-386
Front Matter....Pages 387-387
A Comparison of Two Dual Methods for Discrete Optimal Transport....Pages 389-396
The Tangent Earth Mover’s Distance....Pages 397-404
A Geometric Study of Wasserstein Spaces: An Addendum on the Boundary....Pages 405-412
A Primal-Dual Approach for a Total Variation Wasserstein Flow....Pages 413-421
Front Matter....Pages 423-423
Group Action Induced Distances on Spaces of High-Dimensional Linear Stochastic Processes....Pages 425-432
Extrinsic vs Intrinsic Means on the Circle....Pages 433-440
Nonlinear Modeling and Processing Using Empirical Intrinsic Geometry with Application to Biomedical Imaging....Pages 441-448
Integral Geometry of Linearly Combined Gaussian and Student- t , and Skew Student’s t Random Fields....Pages 449-456
Front Matter....Pages 457-457
Estimation and Tests Under L-Moment Condition Models....Pages 459-466
Weighted Sampling, Maximum Likelihood and Minimum Divergence Estimators....Pages 467-478
Some Decision Procedures Based on Scaled Bregman Distance Surfaces....Pages 479-486
Some Results on a χ -divergence, an Extended Fisher Information and Generalized Cramér-Rao Inequalities....Pages 487-494
Front Matter....Pages 495-495
The Stochastic Flow Theorem for an Operator of Order Four....Pages 497-501
Geometry and Shannon Capacity....Pages 502-512
A Metric for Quantum States Issued from von Neumann’s Entropy....Pages 513-518
Continuity of f-projections on Discrete Spaces....Pages 519-524
Front Matter....Pages 525-525
Frames for Tensor Field Morphology....Pages 527-534
Complete Lattice Structure of Poincaré Upper-Half Plane and Mathematical Morphology for Hyperbolic-Valued Images....Pages 535-542
Supervised Morphology for Structure Tensor-Valued Images Based on Symmetric Divergence Kernels....Pages 543-550
Front Matter....Pages 525-525
Using the Bhattacharyya Mean for the Filtering and Clustering of Positive-Definite Matrices....Pages 551-558
Front Matter....Pages 559-559
Deconvolution for the Wasserstein Metric and Geometric Inference....Pages 561-568
On Directional-Search Procedures for Orbifolds: Connections with the Manifold Framework....Pages 569-577
Adaptation of Multiscale Function Extension to Inexact Matching: Application to the Mapping of Individuals to a Learnt Manifold....Pages 578-586
Interleaved Filtrations: Theory and Applications in Point Cloud Data Analysis....Pages 587-592
Front Matter....Pages 593-593
Symplectic and Kähler Structures on Statistical Manifolds Induced from Divergence Functions....Pages 595-603
Information/Contact Geometries and Koszul Entropy....Pages 604-611
Geometric Quantization of Complex Monge-Ampère Operator for Certain Diffusion Flows....Pages 612-620
Geometry on Positive Definite Matrices Induced from V-Potential Function....Pages 621-629
Front Matter....Pages 631-631
Online Change Detection in Exponential Families with Unknown Parameters....Pages 633-640
Differential Geometry Applied to Acoustics: Non Linear Propagation in Reissner Beams....Pages 641-649
Predictive Information in Gaussian Processes with Application to Music Analysis....Pages 650-657
Characterizing Time Series Variability and Predictability from Information Geometry Dynamics....Pages 658-665
Front Matter....Pages 667-667
Variational Bayesian Approximation for Linear Inverse Problems with a Hierarchical Prior Models....Pages 669-676
Learning General Gaussian Kernel Hyperparameters for SVR....Pages 677-684
Stochastic Filtering by Projection: The Example of the Quadratic Sensor....Pages 685-692
A Probabilistic Solution to the AX=XB Problem: Sensor Calibration without Correspondence....Pages 693-701
Random Clouds on Matrix Lie Groups....Pages 702-709
Front Matter....Pages 711-711
Infinite-Dimensional Manifolds of Finite-Entropy Probability Measures....Pages 713-720
Asymptotically Efficient Estimators for Algebraic Statistical Manifolds....Pages 721-728
Front Matter....Pages 711-711
The Δ 2 -Condition and ϕ -Families of Probability Distributions....Pages 729-736
A Riemannian Geometry in the q -Exponential Banach Manifold Induced by q -Divergences....Pages 737-742
Front Matter....Pages 743-743
Harmonic Maps Relative to α -Connections on Hessian Domains....Pages 745-750
A Kernel View on Manifold Sub-sampling Based on Karcher Variance Optimization....Pages 751-758
Maximal Information Divergence from Statistical Models Defined by Neural Networks....Pages 759-766
Neighborhood Random Classification....Pages 767-774
Front Matter....Pages 775-775
Information Geometry and Interior-Point Algorithms....Pages 777-784
Geometric Mean Algorithms Based on Harmonic and Arithmetic Iterations....Pages 785-793
Multiscale Covariance Fields, Local Scales, and Shape Transforms....Pages 794-801
Deterministic Walks and Quasi-Subgradient Methods for the Karcher Mean on NPC Spaces....Pages 802-809
Front Matter....Pages 811-811
Fast Polynomial Spline Approximation for Large Scattered Data Sets via L 1 Minimization....Pages 813-820
Target Detection of Non-stationary Radar Signal and Riemannian Geometry....Pages 821-828
High-Dimensional Range Profile Geometrical Visualization and Performance Estimation of Radar Target Classification via a Gaussian Mixture Model....Pages 829-836
Visual Point Set Processing with Lattice Structures: Application to Parsimonious Representations of Digital Histopathology Images....Pages 837-844
Activity Video Analysis via Operator-Based Local Embedding....Pages 845-852
Multivariate Texture Discrimination Based on Geodesics to Class Centroids on a Generalized Gaussian Manifold....Pages 853-860
Robust Estimation of Natural Gradient in Optimization by Regularized Linear Regression....Pages 861-867
To the Homogeneous Symplectic Manifold toward the Geometry of information....Pages 868-876
Back Matter....Pages -