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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 87: Information Geometry and Interior-Point Algorithms
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Chapter title
Information Geometry and Interior-Point Algorithms
Chapter number 87
Book title
Geometric Science of Information
Published in
Lecture notes in computer science, January 2013
DOI 10.1007/978-3-642-40020-9_87
Book ISBNs
978-3-64-240019-3, 978-3-64-240020-9
Authors

Satoshi Kakihara, Atsumi Ohara, Takashi Tsuchiya

Editors

Frank Nielsen, Frédéric Barbaresco

Mendeley readers

Mendeley readers

The data shown below were compiled from readership statistics for 5 Mendeley readers of this research output. Click here to see the associated Mendeley record.

Geographical breakdown

Country Count As %
New Zealand 1 20%
Unknown 4 80%

Demographic breakdown

Readers by professional status Count As %
Researcher 2 40%
Student > Ph. D. Student 1 20%
Professor > Associate Professor 1 20%
Lecturer 1 20%
Readers by discipline Count As %
Mathematics 1 20%
Computer Science 1 20%
Engineering 1 20%
Unknown 2 40%