Geometric Science of Information: Second International Conference, GSI 2015, Palaiseau, France, October 28–30, 2015, Proceedings

Front Matter....Pages -
Front Matter....Pages 1-1
Evolution Equations with Anisotropic Distributions and Diffusion PCA....Pages 3-11
Barycentric Subspaces and Affine Spans in Manifolds....Pages 12-21
Dimension Reduction on Polyspheres with Application to Skeletal Representations....Pages 22-29
Affine-Invariant Riemannian Distance Between Infinite-Dimensional Covariance Operators....Pages 30-38
A Sub-Riemannian Modular Approach for Diffeomorphic Deformations....Pages 39-47
Front Matter....Pages 49-49
The Nonlinear Bernstein-Schrödinger Equation in Economics....Pages 51-59
Some Geometric Consequences of the Schrödinger Problem....Pages 60-68
Optimal Transport, Independance Versus Indetermination Duality, Impact on a New Copula Design....Pages 69-76
Optimal Mass Transport over Bridges....Pages 77-84
Front Matter....Pages 85-85
Non-convex Relaxation of Optimal Transport for Color Transfer Between Images....Pages 87-95
Generalized Pareto Distributions, Image Statistics and Autofocusing in Automated Microscopy....Pages 96-103
Barycenter in Wasserstein Spaces: Existence and Consistency....Pages 104-108
Multivariate L-Moments Based on Transports....Pages 109-117
Front Matter....Pages 119-119
Spherical Parameterization for Genus Zero Surfaces Using Laplace-Beltrami Eigenfunctions....Pages 121-129
Biased Estimators on Quotient Spaces....Pages 130-139
Reparameterization Invariant Metric on the Space of Curves....Pages 140-149
Invariant Geometric Structures on Statistical Models....Pages 150-158
The Abstract Setting for Shape Deformation Analysis and LDDMM Methods....Pages 159-167
Front Matter....Pages 169-169
The Extremal Index for a Random Tessellation....Pages 171-178
A Two-Color Interacting Random Balls Model for Co-localization Analysis of Proteins....Pages 179-186
Front Matter....Pages 169-169
Asymptotics of Superposition of Point Processes....Pages 187-194
Asymptotic Properties of Random Polytopes....Pages 195-202
Asymmetric Topologies on Statistical Manifolds....Pages 203-210
Front Matter....Pages 211-211
Hessian Structures and Non-invariant (F,G)-Geometry on a Deformed Exponential Family....Pages 213-221
New Metric and Connections in Statistical Manifolds....Pages 222-229
Curvatures of Statistical Structures....Pages 230-239
The Pontryagin Forms of Hessian Manifolds....Pages 240-247
Matrix Realization of a Homogeneous Cone....Pages 248-256
Multiply CR-Warped Product Statistical Submanifolds of a Holomorphic Statistical Space Form....Pages 257-268
Front Matter....Pages 269-269
Information Algebras and Their Applications....Pages 271-276
Finite Polylogarithms, Their Multiple Analogues and the Shannon Entropy....Pages 277-285
Heights of Toric Varieties, Entropy and Integration over Polytopes....Pages 286-295
Characterization and Estimation of the Variations of a Random Convex Set by Its Mean n-Variogram: Application to the Boolean Model....Pages 296-308
Front Matter....Pages 309-309
Laplace’s Rule of Succession in Information Geometry....Pages 311-319
Standard Divergence in Manifold of Dual Affine Connections....Pages 320-325
Transformations and Coupling Relations for Affine Connections....Pages 326-339
Online k-MLE for Mixture Modeling with Exponential Families....Pages 340-348
Second-Order Optimization over the Multivariate Gaussian Distribution....Pages 349-358
The Information Geometry of Mirror Descent....Pages 359-368
Front Matter....Pages 369-369
Texture Classification Using Rao’s Distance on the Space of Covariance Matrices....Pages 371-378
Front Matter....Pages 369-369
Color Texture Discrimination Using the Principal Geodesic Distance on a Multivariate Generalized Gaussian Manifold....Pages 379-386
Bag-of-Components: An Online Algorithm for Batch Learning of Mixture Models....Pages 387-395
Statistical Gaussian Model of Image Regions in Stochastic Watershed Segmentation....Pages 396-405
Quantization of Hyperspectral Image Manifold Using Probabilistic Distances....Pages 406-414
Front Matter....Pages 415-415
Generalized EM Algorithms for Minimum Divergence Estimation....Pages 417-426
Extension of Information Geometry to Non-statistical Systems: Some Examples....Pages 427-434
An Information Geometry Problem in Mathematical Finance....Pages 435-443
Multivariate Divergences with Application in Multisample Density Ratio Models....Pages 444-453
Generalized Mutual-Information Based Independence Tests....Pages 454-463
Front Matter....Pages 465-465
Riemannian Trust Regions with Finite-Difference Hessian Approximations are Globally Convergent....Pages 467-475
Block-Jacobi Methods with Newton-Steps and Non-unitary Joint Matrix Diagonalization....Pages 476-483
Weakly Correlated Sparse Components with Nearly Orthonormal Loadings....Pages 484-490
Fitting Smooth Paths on Riemannian Manifolds: Endometrial Surface Reconstruction and Preoperative MRI-Based Navigation....Pages 491-498
PDE Constrained Shape Optimization as Optimization on Shape Manifolds....Pages 499-508
Front Matter....Pages 509-509
Poincaré Equations for Cosserat Shells: Application to Cephalopod Locomotion....Pages 511-518
Entropy and Structure of the Thermodynamical Systems....Pages 519-528
Symplectic Structure of Information Geometry: Fisher Metric and Euler-Poincaré Equation of Souriau Lie Group Thermodynamics....Pages 529-540
Pontryagin Calculus in Riemannian Geometry....Pages 541-549
Rolling Symmetric Spaces....Pages 550-557
Enlargement, Geodesics, and Collectives....Pages 558-565
Front Matter....Pages 567-567
Geometry of Goodness-of-Fit Testing in High Dimensional Low Sample Size Modelling....Pages 569-576
Computing Boundaries in Local Mixture Models....Pages 577-585
Approximating Covering and Minimum Enclosing Balls in Hyperbolic Geometry....Pages 586-594
From Euclidean to Riemannian Means: Information Geometry for SSVEP Classification....Pages 595-604
Group Theoretical Study on Geodesics for the Elliptical Models....Pages 605-614
Path Connectedness on a Space of Probability Density Functions....Pages 615-624
Front Matter....Pages 625-625
Image Processing in the Semidiscrete Group of Rototranslations....Pages 627-634
Universal, Non-asymptotic Confidence Sets for Circular Means....Pages 635-642
A Methodology for Deblurring and Recovering Conformational States of Biomolecular Complexes from Single Particle Electron Microscopy....Pages 643-653
Nonlinear Operators on Graphs via Stacks....Pages 654-663
An Intrinsic Cramér-Rao Bound on Lie Groups....Pages 664-672
Front Matter....Pages 673-673
Clustering Random Walk Time Series....Pages 675-684
A Common Symmetrization Framework for Iterative (Linear) Maps....Pages 685-692
New Model Search for Nonlinear Recursive Models, Regressions and Autoregressions....Pages 693-701
Random Pairwise Gossip on CAT(k) Metric Spaces....Pages 702-709
Front Matter....Pages 711-711
Stochastic PDE Projection on Manifolds: Assumed-Density and Galerkin Filters....Pages 713-722
Variational Bayesian Approximation Method for Classification and Clustering with a Mixture of Student-t Model....Pages 723-731
Geometric Properties of Textile Plot....Pages 732-739
A Generalization of Independence and Multivariate Student’s t-distributions....Pages 740-749
Front Matter....Pages 751-751
Probability Density Estimation on the Hyperbolic Space Applied to Radar Processing....Pages 753-761
Front Matter....Pages 751-751
Histograms of Images Valued in the Manifold of Colours Endowed with Perceptual Metrics....Pages 762-769
Entropy Minimizing Curves with Application to Automated Flight Path Design....Pages 770-778
Kernel Density Estimation on Symmetric Spaces....Pages 779-787
Back Matter....Pages -