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Geometric Science of Information

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Cover of 'Geometric Science of Information'

Table of Contents

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    Book Overview
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    Chapter 1 Information Geometry and Its Applications: Survey
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    Chapter 2 Information-Geometric Optimization: The Interest of Information Theory for Discrete and Continuous Optimization
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    Chapter 3 Nonparametric Information Geometry
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    Chapter 4 Geometry of Hessian Structures
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    Chapter 5 Bi-invariant Means on Lie Groups with Cartan-Schouten Connections
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    Chapter 6 Parallel Transport with Pole Ladder: Application to Deformations of Time Series of Images
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    Chapter 7 Horizontal Dimensionality Reduction and Iterated Frame Bundle Development
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    Chapter 8 A Subspace Learning of Dynamics on a Shape Manifold: A Generative Modeling Approach
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    Chapter 9 Geodesic Image Regression with a Sparse Parameterization of Diffeomorphisms
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    Chapter 10 Template Estimation for Large Database: A Diffeomorphic Iterative Centroid Method Using Currents
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    Chapter 11 On the Geometry and the Deformation of Shapes Represented by Piecewise Continuous Bézier Curves with Application to Shape Optimization
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    Chapter 12 Random Spatial Structure of Geometric Deformations and Bayesian Nonparametrics
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    Chapter 13 A Riemannian Fourier Transform via Spin Representations
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    Chapter 14 K-Centroids-Based Supervised Classification of Texture Images Using the SIRV Modeling
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    Chapter 15 Geometric Science of Information
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    Chapter 16 Geometric Science of Information
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    Chapter 17 Optimal Transport and Minimal Trade Problem, Impacts on Relational Metrics and Applications to Large Graphs and Networks Modularity
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    Chapter 18 Comparing Different Modularization Criteria Using Relational Metric
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    Chapter 19 A General Framework for Comparing Heterogeneous Binary Relations
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    Chapter 20 On Prime-Valent Symmetric Bicirculants and Cayley Snarks
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    Chapter 21 Studying New Classes of Graph Metrics
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    Chapter 22 Tessellabilities, Reversibilities, and Decomposabilities of Polytopes
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    Chapter 23 Counting the Number of Solutions of KDMDGP Instances
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    Chapter 24 On the Identification of Discretization Orders for Distance Geometry with Intervals
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    Chapter 25 Hypothesis Testing, Information Divergence and Computational Geometry
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    Chapter 26 A New Implementation of k-MLE for Mixture Modeling of Wishart Distributions
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    Chapter 27 Variational Problem in Euclidean Space with Density
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    Chapter 28 The Exponential Family in Abstract Information Theory
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    Chapter 29 Hessian Structures on Deformed Exponential Families
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    Chapter 30 Foliations on Affinely Flat Manifolds: Information Geometry
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    Chapter 31 Hypersurfaces with Isometric Reeb Flow in Hermitian Symmetric Spaces of Rank 2
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    Chapter 32 Generalized Minimizers of Convex Integral Functionals and Pythagorean Identities
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    Chapter 33 Computational Information Geometry in Statistics: Foundations
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    Chapter 34 Computational Information Geometry in Statistics: Mixture Modelling
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    Chapter 35 A General Metric for Riemannian Manifold Hamiltonian Monte Carlo
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    Chapter 36 Visualizing Projective Shape Space
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    Chapter 37 Interpolation and Regression of Rotation Matrices
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    Chapter 38 A Geometric Framework for Non-Unitary Joint Diagonalization of Complex Symmetric Matrices
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    Chapter 39 An Extrinsic Look at the Riemannian Hessian
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    Chapter 40 Law of Cosines and Shannon-Pythagorean Theorem for Quantum Information
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    Chapter 41 A Note on the Intrinsic Cramer-Rao Bound
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    Chapter 42 A Comparison of Two Dual Methods for Discrete Optimal Transport
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    Chapter 43 The Tangent Earth Mover’s Distance
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    Chapter 44 A Geometric Study of Wasserstein Spaces: An Addendum on the Boundary
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    Chapter 45 Geometric Science of Information
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    Chapter 46 Group Action Induced Distances on Spaces of High-Dimensional Linear Stochastic Processes
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    Chapter 47 Extrinsic vs Intrinsic Means on the Circle
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    Chapter 48 Nonlinear Modeling and Processing Using Empirical Intrinsic Geometry with Application to Biomedical Imaging
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    Chapter 49 Integral Geometry of Linearly Combined Gaussian and Student-t, and Skew Student’s t Random Fields
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    Chapter 50 Estimation and Tests Under L-Moment Condition Models
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    Chapter 51 Weighted Sampling, Maximum Likelihood and Minimum Divergence Estimators
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    Chapter 52 Some Decision Procedures Based on Scaled Bregman Distance Surfaces
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    Chapter 53 Some Results on a χ-divergence, an Extended Fisher Information and Generalized Cramér-Rao Inequalities
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    Chapter 54 The Stochastic Flow Theorem for an Operator of Order Four
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    Chapter 55 Geometry and Shannon Capacity
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    Chapter 56 A Metric for Quantum States Issued from von Neumann’s Entropy
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    Chapter 57 Continuity of f-projections on Discrete Spaces
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    Chapter 58 Frames for Tensor Field Morphology
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    Chapter 59 Complete Lattice Structure of Poincaré Upper-Half Plane and Mathematical Morphology for Hyperbolic-Valued Images
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    Chapter 60 Supervised Morphology for Structure Tensor-Valued Images Based on Symmetric Divergence Kernels
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    Chapter 61 Using the Bhattacharyya Mean for the Filtering and Clustering of Positive-Definite Matrices
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    Chapter 62 Deconvolution for the Wasserstein Metric and Geometric Inference
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    Chapter 63 On Directional-Search Procedures for Orbifolds: Connections with the Manifold Framework
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    Chapter 64 Adaptation of Multiscale Function Extension to Inexact Matching: Application to the Mapping of Individuals to a Learnt Manifold
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    Chapter 65 Interleaved Filtrations: Theory and Applications in Point Cloud Data Analysis
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    Chapter 66 Symplectic and Kähler Structures on Statistical Manifolds Induced from Divergence Functions
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    Chapter 67 Information/Contact Geometries and Koszul Entropy
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    Chapter 68 Geometric Quantization of Complex Monge-Ampère Operator for Certain Diffusion Flows
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    Chapter 69 Geometry on Positive Definite Matrices Induced from V-Potential Function
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    Chapter 70 Online Change Detection in Exponential Families with Unknown Parameters
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    Chapter 71 Differential Geometry Applied to Acoustics: Non Linear Propagation in Reissner Beams
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    Chapter 72 Predictive Information in Gaussian Processes with Application to Music Analysis
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    Chapter 73 Characterizing Time Series Variability and Predictability from Information Geometry Dynamics
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    Chapter 74 Variational Bayesian Approximation for Linear Inverse Problems with a Hierarchical Prior Models
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    Chapter 75 Learning General Gaussian Kernel Hyperparameters for SVR
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    Chapter 76 Stochastic Filtering by Projection: The Example of the Quadratic Sensor
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    Chapter 77 A Probabilistic Solution to the AX=XB Problem: Sensor Calibration without Correspondence
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    Chapter 78 Random Clouds on Matrix Lie Groups
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    Chapter 79 Infinite-Dimensional Manifolds of Finite-Entropy Probability Measures
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    Chapter 80 Asymptotically Efficient Estimators for Algebraic Statistical Manifolds
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    Chapter 81 The Δ2-Condition and ϕ-Families of Probability Distributions
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    Chapter 82 A Riemannian Geometry in the q-Exponential Banach Manifold Induced by q-Divergences
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    Chapter 83 Harmonic Maps Relative to α-Connections on Hessian Domains
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    Chapter 84 A Kernel View on Manifold Sub-sampling Based on Karcher Variance Optimization
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    Chapter 85 Maximal Information Divergence from Statistical Models Defined by Neural Networks
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    Chapter 86 Neighborhood Random Classification
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    Chapter 87 Information Geometry and Interior-Point Algorithms
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    Chapter 88 Geometric Mean Algorithms Based on Harmonic and Arithmetic Iterations
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    Chapter 89 Multiscale Covariance Fields, Local Scales, and Shape Transforms
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    Chapter 90 Deterministic Walks and Quasi-Subgradient Methods for the Karcher Mean on NPC Spaces
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    Chapter 91 Fast Polynomial Spline Approximation for Large Scattered Data Sets via L 1 Minimization
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    Chapter 92 Target Detection of Non-stationary Radar Signal and Riemannian Geometry
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    Chapter 93 High-Dimensional Range Profile Geometrical Visualization and Performance Estimation of Radar Target Classification via a Gaussian Mixture Model
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    Chapter 94 Visual Point Set Processing with Lattice Structures: Application to Parsimonious Representations of Digital Histopathology Images
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    Chapter 95 Activity Video Analysis via Operator-Based Local Embedding
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    Chapter 96 Multivariate Texture Discrimination Based on Geodesics to Class Centroids on a Generalized Gaussian Manifold
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    Chapter 97 Robust Estimation of Natural Gradient in Optimization by Regularized Linear Regression
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    Chapter 98 To the Homogeneous Symplectic Manifold toward the Geometry of information
Attention for Chapter 85: Maximal Information Divergence from Statistical Models Defined by Neural Networks
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Chapter title
Maximal Information Divergence from Statistical Models Defined by Neural Networks
Chapter number 85
Book title
Geometric Science of Information
Published in
Lecture notes in computer science, January 2013
DOI 10.1007/978-3-642-40020-9_85
Book ISBNs
978-3-64-240019-3, 978-3-64-240020-9

Guido Montúfar, Johannes Rauh, Nihat Ay, Guido Montufar


Frank Nielsen, Frédéric Barbaresco

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Mendeley readers

Mendeley readers

The data shown below were compiled from readership statistics for 11 Mendeley readers of this research output. Click here to see the associated Mendeley record.

Geographical breakdown

Country Count As %
United Kingdom 1 9%
Germany 1 9%
Vietnam 1 9%
Unknown 8 73%

Demographic breakdown

Readers by professional status Count As %
Student > Ph. D. Student 5 45%
Researcher 3 27%
Professor 2 18%
Professor > Associate Professor 1 9%
Readers by discipline Count As %
Mathematics 5 45%
Computer Science 2 18%
Physics and Astronomy 2 18%
Economics, Econometrics and Finance 1 9%
Engineering 1 9%
Other 0 0%
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