| Description |
1 online resource (xx, 879 pages) : illustrations |
| Series |
Lecture notes in computer science, 0302-9743 ; 8085 |
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LNCS sublibrary. SL 6, Image processing, computer vision, pattern recognition, and graphics |
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Lecture notes in computer science ; 8085.
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LNCS sublibrary. SL 6, Image processing, computer vision, pattern recognition, and graphics.
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| Contents |
Invited Keynote papers. Information Geometry and Its Applications: Survey -- Information-Geometric Optimization: The Interest of Information Theory for Discrete and Continuous Optimization -- Nonparametric Information Geometry -- Geometry of Hessian Structures -- Geometric Statistics on Manifolds and Lie Groups. Bi-invariant Means on Lie Groups with Cartan-Schouten Connections -- Parallel Transport with Pole Ladder: Application to Deformations of Time Series of Images -- Horizontal Dimensionality Reduction and Iterated Frame Bundle Development -- A Subspace Learning of Dynamics on a Shape Manifold: A Generative Modeling Approach -- Deformations in Shape Spaces. Geodesic Image Regression with a Sparse Parameterization of Diffeomorphisms -- Template Estimation for Large Database: A Diffeomorphic Iterative Centroid Method Using Currents -- On the Geometry and the Deformation of Shapes Represented by Piecewise Continuous Bézier Curves with Application to Shape Optimization -- Random Spatial Structure of Geometric Deformations and Bayesian Nonparametrics |
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Differential Geometry in Signal Processing. A Riemannian Fourier Transform via Spin Representations -- K-Centroids-Based Supervised Classification of Texture Images Using the SIRV Modeling -- Bayesian Atlas Estimation from High Angular Resolution Diffusion Imaging (HARDI) -- Dimensionality Reduction for Classification of Stochastic Fibre Radiographs -- Relational Metric. Optimal Transport and Minimal Trade Problem, Impacts on Relational Metrics and Applications to Large Graphs and Networks Modularity -- Comparing Different Modularization Criteria Using Relational Metric -- A General Framework for Comparing Heterogeneous Binary Relations -- On Prime-Valent Symmetric Bicirculants and Cayley Snarks -- Discrete Metric Spaces. Studying New Classes of Graph Metrics -- Tessellabilities, Reversibilities, and Decomposabilities of Polytopes -- Counting the Number of Solutions of KDMDGP Instances -- On the Identification of Discretization Orders for Distance Geometry with Intervals |
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Computational Information Geometry. Hypothesis Testing, Information Divergence and Computational Geometry -- A New Implementation of k-MLE for Mixture Modeling of Wishart Distributions -- Variational Problem in Euclidean Space with Density -- The Exponential Family in Abstract Information Theory -- Hessian Information Geometry I. Hessian Structures on Deformed Exponential Families -- Foliations on Affinely Flat Manifolds: Information Geometry -- Hypersurfaces with Isometric Reeb Flow in Hermitian Symmetric Spaces of Rank 2 -- Generalized Minimizers of Convex Integral Functionals and Pythagorean Identities -- Computational Aspects of Information Geometry in Statistics. Computational Information Geometry in Statistics: Foundations -- Computational Information Geometry in Statistics: Mixture Modelling -- A General Metric for Riemannian Manifold Hamiltonian Monte Carlo -- Visualizing Projective Shape Space |
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Optimization on Matrix Manifolds. Interpolation and Regression of Rotation Matrices -- A Geometric Framework for Non-Unitary Joint Diagonalization of Complex Symmetric Matrices -- An Extrinsic Look at the Riemannian Hessian -- Law of Cosines and Shannon-Pythagorean Theorem for Quantum Information -- A Note on the Intrinsic Cramer-Rao Bound -- Optimal Transport Theory. A Comparison of Two Dual Methods for Discrete Optimal Transport -- The Tangent Earth Mover's Distance -- A Geometric Study of Wasserstein Spaces: An Addendum on the Boundary -- A Primal-Dual Approach for a Total Variation Wasserstein Flow -- Probability on Manifolds. Group Action Induced Distances on Spaces of High-Dimensional Linear Stochastic Processes -- Extrinsic vs Intrinsic Means on the Circle -- Nonlinear Modeling and Processing Using Empirical Intrinsic Geometry with Application to Biomedical Imaging -- Integral Geometry of Linearly Combined Gaussian and Student-t, and Skew Student's t Random Fields |
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880-01 Machine/Manifold/Topology Learning. Deconvolution for the Wasserstein Metric and Geometric Inference -- On Directional-Search Procedures for Orbifolds: Connections with the Manifold Framework -- Adaptation of Multiscale Function Extension to Inexact Matching: Application to the Mapping of Individuals to a Learnt Manifold -- Interleaved Filtrations: Theory and Applications in Point Cloud Data Analysis -- Hessian Information Geometry II. Symplectic and Kähler Structures on Statistical Manifolds Induced from Divergence Functions -- Information/Contact Geometries and Koszul Entropy -- Geometric Quantization of Complex Monge-Ampère Operator for Certain Diffusion Flows -- Geometry on Positive Definite Matrices Induced from V-Potential Function -- Geometry of Audio Processing. Online Change Detection in Exponential Families with Unknown Parameters -- Differential Geometry Applied to Acoustics: Non Linear Propagation in Reissner Beams -- Predictive Information in Gaussian Processes with Application to Music Analysis -- Characterizing Time Series Variability and Predictability from Information Geometry Dynamics |
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880-01/(S Divergence Geometry and Ancillarity. Estimation and Tests Under L-Moment Condition Models -- Weighted Sampling, Maximum Likelihood and Minimum Divergence Estimators -- Some Decision Procedures Based on Scaled Bregman Distance Surfaces -- Some Results on a χ-divergence, an Extended Fisher Information and Generalized Cramér-Rao Inequalities -- Entropic Geometry. The Stochastic Flow Theorem for an Operator of Order Four -- Geometry and Shannon Capacity -- A Metric for Quantum States Issued from von Neumann's Entropy -- Continuity of f-projections on Discrete Spaces -- Tensor-Valued Mathematical Morphology. Frames for Tensor Field Morphology -- Complete Lattice Structure of Poincaré Upper-Half Plane and Mathematical Morphology for Hyperbolic-Valued Images -- Supervised Morphology for Structure Tensor-Valued Images Based on Symmetric Divergence Kernels -- Using the Bhattacharyya Mean for the Filtering and Clustering of Positive-Definite Matrices |
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880-02 Algorithms on Manifolds. Information Geometry and Interior-Point Algorithms -- Geometric Mean Algorithms Based on Harmonic and Arithmetic Iterations -- Multiscale Covariance Fields, Local Scales, and Shape Transforms -- Deterministic Walks and Quasi-Subgradient Methods for the Karcher Mean on NPC Spaces -- Papers Presented at the Poster Session. Fast Polynomial Spline Approximation for Large Scattered Data Sets via L 1 Minimization -- Target Detection of Non-stationary Radar Signal and Riemannian Geometry -- High-Dimensional Range Profile Geometrical Visualization and Performance Estimation of Radar Target Classification via a Gaussian Mixture Model -- Visual Point Set Processing with Lattice Structures: Application to Parsimonious Representations of Digital Histopathology Images -- Activity Video Analysis via Operator-Based Local Embedding -- Multivariate Texture Discrimination Based on Geodesics to Class Centroids on a Generalized Gaussian Manifold -- Robust Estimation of Natural Gradient in Optimization by Regularized Linear Regression -- To the Homogeneous Symplectic Manifold toward the Geometry of information |
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880-02/(S Geometry of Inverse Problems. Variational Bayesian Approximation for Linear Inverse Problems with a Hierarchical Prior Models -- Learning General Gaussian Kernel Hyperparameters for SVR -- Stochastic Filtering by Projection: The Example of the Quadratic Sensor -- A Probabilistic Solution to the AX=XB Problem: Sensor Calibration without Correspondence -- Random Clouds on Matrix Lie Groups -- Algebraic/Infinite Dimensionnal/Banach Information Manifolds. Infinite-Dimensional Manifolds of Finite-Entropy Probability Measures -- Asymptotically Efficient Estimators for Algebraic Statistical Manifolds -- The Δ2-Condition and φ-Families of Probability Distributions -- A Riemannian Geometry in the q-Exponential Banach Manifold Induced by q-Divergences -- Information Geometry Manifolds -- Harmonic Maps Relative to α-Connections on Hessian Domains -- A Kernel View on Manifold Sub-sampling Based on Karcher Variance Optimization -- Maximal Information Divergence from Statistical Models Defined by Neural Networks -- Neighborhood Random Classification |
| Summary |
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 |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Online resource; title from PDF title page (SpringerLink, viewed October 2, 2013) |
| Subject |
Geometry -- Congresses
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Information science -- Congresses
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Mathematics.
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Information Science
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Mathematics
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Mathematics
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Geometry
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Information science
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| Genre/Form |
proceedings (reports)
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Conference papers and proceedings
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Conference papers and proceedings.
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Actes de congrès.
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| Form |
Electronic book
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| Author |
Nielsen, Frank, editor
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Barbaresco, Frédéric, editor
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| ISBN |
9783642400209 |
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3642400205 |
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3642400191 |
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9783642400193 |
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