Geometric Science Of Information: First International Conference, Gsi 2013, Paris, France, August 28-30, 2013, Proceedings (lecture Notes In Computer Science)

This Book Constitutes The Refereed Proceedings Of The First International Conference On Geometric Science Of Information, Gsi 2013, Held In Paris, France, In August 2013. The Nearly 100 Papers Presented Were Carefully Reviewed And Selected From Numerous Submissions And Are Organized Into The Following Thematic Sessions: Geometric Statistics On Manifolds And Lie Groups, Deformations In Shape Spaces, Differential Geometry In Signal Processing, Relational Metric, Discrete Metric Spaces, Computational Information Geometry, Hessian Information Geometry I And Ii, Computational Aspects Of Information Geometry In Statistics, Optimization On Matrix Manifolds, Optimal Transport Theory, Probability On Manifolds, Divergence Geometry And Ancillarity, Entropic Geometry, Tensor-valued Mathematical Morphology, Machine/manifold/topology Learning, Geometry Of Audio Processing, Geometry Of Inverse Problems, Algebraic/infinite Dimensionnal/banach Information Manifolds, Information Geometry Manifolds,and Algorithms On Manifolds. Geometric Statistics On Manifolds And Lie Groups -- Deformations In Shape Spaces -- Differential Geometry In Signal Processing -- Relational Metric -- Discrete Metric Spaces -- Computational Information Geometry -- Computational Aspects Of Information Geometry In Statistics -- Optimization On Matrix Manifolds -- Optimal Transport Theory -- Probability On Manifolds -- Divergence Geometry And Ancillarity -- Entropic Geometry -- Tensor-valued Mathematical Morphology -- Machine/manifold/topology Learning -- Hessian Information Geometry -- Geometry Of Audio Processing -- Geometry Of Inverse Problems -- Algebraic/infinite Dimensional/banach Information Manifolds -- Information Geometry Manifolds -- Algorithms On Manifolds. Edited By Frank Nielsen, Frédéric Barbaresco. 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 - This book is an outcome of the Indo-French Workshop on Matrix Information Geometries (MIG): Applications in Sensor and Cognitive Systems Engineering, which was held in Ecole Polytechnique and Thales Research and Technology Center, Palaiseau, France, in February 23-25, 2011. The workshop was generously funded by the Indo-French Centre for the Promotion of Advanced Research (IFCPAR). During the event, 22 renowned invited french or indian speakers gave lectures on their areas of expertise within the field of matrix analysis or processing. From these talks, a total of 17 original contribution or state-of-the-art chapters have been assembled in this volume. All articles were thoroughly peer-reviewed and improved, according to the suggestions of the international referees. The 17 contributions presented are organized in three parts: (1) State-of-the-art surveys & original matrix theory work, (2) Advanced matrix theory for radar processing, and (3) Matrix-based signal processing applications This book presents advances in matrix and tensor data processing in the domain of signal, image and information processing. The theoretical mathematical approaches are discusses in the context of potential applications in sensor and cognitive systems engineering. The topics and application include Information Geometry, Differential Geometry of structured Matrix, Positive Definite Matrix, Covariance Matrix, Sensors (Electromagnetic Fields, Acoustic sensors) and Applications in Cognitive systems, in particular Data Mining.