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Geometric Science of Information

Overview of attention for book
Cover of 'Geometric Science of Information'

Table of Contents

  1. Altmetric Badge
    Book Overview
  2. Altmetric Badge
    Chapter 1 Evolution Equations with Anisotropic Distributions and Diffusion PCA
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    Chapter 2 Barycentric Subspaces and Affine Spans in Manifolds
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    Chapter 3 Dimension Reduction on Polyspheres with Application to Skeletal Representations
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    Chapter 4 Affine-Invariant Riemannian Distance Between Infinite-Dimensional Covariance Operators
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    Chapter 5 A Sub-Riemannian Modular Approach for Diffeomorphic Deformations
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    Chapter 6 The Nonlinear Bernstein-Schrödinger Equation in Economics
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    Chapter 7 Some Geometric Consequences of the Schrödinger Problem
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    Chapter 8 Optimal Transport, Independance Versus Indetermination Duality, Impact on a New Copula Design
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    Chapter 9 Optimal Mass Transport over Bridges
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    Chapter 10 Non-convex Relaxation of Optimal Transport for Color Transfer Between Images
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    Chapter 11 Generalized Pareto Distributions, Image Statistics and Autofocusing in Automated Microscopy
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    Chapter 12 Barycenter in Wasserstein Spaces: Existence and Consistency
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    Chapter 13 Multivariate L-Moments Based on Transports
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    Chapter 14 Spherical Parameterization for Genus Zero Surfaces Using Laplace-Beltrami Eigenfunctions
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    Chapter 15 Biased Estimators on Quotient Spaces
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    Chapter 16 Reparameterization Invariant Metric on the Space of Curves
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    Chapter 17 Invariant Geometric Structures on Statistical Models
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    Chapter 18 The Abstract Setting for Shape Deformation Analysis and LDDMM Methods
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    Chapter 19 The Extremal Index for a Random Tessellation
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    Chapter 20 A Two-Color Interacting Random Balls Model for Co-localization Analysis of Proteins
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    Chapter 21 Asymptotics of Superposition of Point Processes
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    Chapter 22 Asymptotic Properties of Random Polytopes
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    Chapter 23 Asymmetric Topologies on Statistical Manifolds
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    Chapter 24 Hessian Structures and Non-invariant (F, G)-Geometry on a Deformed Exponential Family
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    Chapter 25 New Metric and Connections in Statistical Manifolds
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    Chapter 26 Curvatures of Statistical Structures
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    Chapter 27 The Pontryagin Forms of Hessian Manifolds
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    Chapter 28 Matrix Realization of a Homogeneous Cone
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    Chapter 29 Multiply CR-Warped Product Statistical Submanifolds of a Holomorphic Statistical Space Form
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    Chapter 30 Information Algebras and Their Applications
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    Chapter 31 Finite Polylogarithms, Their Multiple Analogues and the Shannon Entropy
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    Chapter 32 Heights of Toric Varieties, Entropy and Integration over Polytopes
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    Chapter 33 Characterization and Estimation of the Variations of a Random Convex Set by Its Mean n-Variogram: Application to the Boolean Model
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    Chapter 34 Laplace’s Rule of Succession in Information Geometry
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    Chapter 35 Standard Divergence in Manifold of Dual Affine Connections
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    Chapter 36 Transformations and Coupling Relations for Affine Connections
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    Chapter 37 Online k-MLE for Mixture Modeling with Exponential Families
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    Chapter 38 Second-Order Optimization over the Multivariate Gaussian Distribution
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    Chapter 39 The Information Geometry of Mirror Descent
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    Chapter 40 Texture Classification Using Rao’s Distance on the Space of Covariance Matrices
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    Chapter 41 Color Texture Discrimination Using the Principal Geodesic Distance on a Multivariate Generalized Gaussian Manifold
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    Chapter 42 Bag-of-Components: An Online Algorithm for Batch Learning of Mixture Models
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    Chapter 43 Statistical Gaussian Model of Image Regions in Stochastic Watershed Segmentation
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    Chapter 44 Quantization of Hyperspectral Image Manifold Using Probabilistic Distances
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    Chapter 45 Generalized EM Algorithms for Minimum Divergence Estimation
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    Chapter 46 Extension of Information Geometry to Non-statistical Systems: Some Examples
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    Chapter 47 An Information Geometry Problem in Mathematical Finance
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    Chapter 48 Multivariate Divergences with Application in Multisample Density Ratio Models
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    Chapter 49 Generalized Mutual-Information Based Independence Tests
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    Chapter 50 Riemannian Trust Regions with Finite-Difference Hessian Approximations are Globally Convergent
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    Chapter 51 Block-Jacobi Methods with Newton-Steps and Non-unitary Joint Matrix Diagonalization
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    Chapter 52 Weakly Correlated Sparse Components with Nearly Orthonormal Loadings
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    Chapter 53 Fitting Smooth Paths on Riemannian Manifolds: Endometrial Surface Reconstruction and Preoperative MRI-Based Navigation
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    Chapter 54 PDE Constrained Shape Optimization as Optimization on Shape Manifolds
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    Chapter 55 Poincaré Equations for Cosserat Shells: Application to Cephalopod Locomotion
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    Chapter 56 Entropy and Structure of the Thermodynamical Systems
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    Chapter 57 Symplectic Structure of Information Geometry: Fisher Metric and Euler-Poincaré Equation of Souriau Lie Group Thermodynamics
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    Chapter 58 Pontryagin Calculus in Riemannian Geometry
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    Chapter 59 Rolling Symmetric Spaces
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    Chapter 60 Enlargement, Geodesics, and Collectives
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    Chapter 61 Geometry of Goodness-of-Fit Testing in High Dimensional Low Sample Size Modelling
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    Chapter 62 Computing Boundaries in Local Mixture Models
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    Chapter 63 Approximating Covering and Minimum Enclosing Balls in Hyperbolic Geometry
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    Chapter 64 From Euclidean to Riemannian Means: Information Geometry for SSVEP Classification
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    Chapter 65 Group Theoretical Study on Geodesics for the Elliptical Models
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    Chapter 66 Path Connectedness on a Space of Probability Density Functions
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    Chapter 67 Image Processing in the Semidiscrete Group of Rototranslations
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    Chapter 68 Universal, Non-asymptotic Confidence Sets for Circular Means
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    Chapter 69 A Methodology for Deblurring and Recovering Conformational States of Biomolecular Complexes from Single Particle Electron Microscopy
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    Chapter 70 Nonlinear Operators on Graphs via Stacks
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    Chapter 71 An Intrinsic Cramér-Rao Bound on Lie Groups
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    Chapter 72 Clustering Random Walk Time Series
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    Chapter 73 A Common Symmetrization Framework for Iterative (Linear) Maps
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    Chapter 74 New Model Search for Nonlinear Recursive Models, Regressions and Autoregressions
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    Chapter 75 Random Pairwise Gossip on \(CAT(\kappa )\) Metric Spaces
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    Chapter 76 Stochastic PDE Projection on Manifolds: Assumed-Density and Galerkin Filters
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    Chapter 77 Variational Bayesian Approximation Method for Classification and Clustering with a Mixture of Student-t Model
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    Chapter 78 Geometric Properties of Textile Plot
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    Chapter 79 A Generalization of Independence and Multivariate Student’s t-distributions
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    Chapter 80 Probability Density Estimation on the Hyperbolic Space Applied to Radar Processing
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    Chapter 81 Histograms of Images Valued in the Manifold of Colours Endowed with Perceptual Metrics
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    Chapter 82 Entropy Minimizing Curves with Application to Automated Flight Path Design
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    Chapter 83 Kernel Density Estimation on Symmetric Spaces
Overall attention for this book and its chapters
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About this Attention Score

  • In the top 25% of all research outputs scored by Altmetric
  • High Attention Score compared to outputs of the same age (90th percentile)
  • High Attention Score compared to outputs of the same age and source (85th percentile)

Mentioned by

news
1 news outlet
twitter
7 X users
googleplus
1 Google+ user

Citations

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7 Dimensions

Readers on

mendeley
18 Mendeley
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Title
Geometric Science of Information
Published by
Lecture notes in computer science, January 2015
DOI 10.1007/978-3-319-25040-3
ISBNs
978-3-31-925039-7, 978-3-31-925040-3
Authors

Verdoolaege, Geert, Shabbir, Aqsa

Editors

Frank Nielsen, Frederic Barbaresco

X Demographics

X Demographics

The data shown below were collected from the profiles of 7 X users who shared this research output. Click here to find out more about how the information was compiled.
Mendeley readers

Mendeley readers

The data shown below were compiled from readership statistics for 18 Mendeley readers of this research output. Click here to see the associated Mendeley record.

Geographical breakdown

Country Count As %
Unknown 18 100%

Demographic breakdown

Readers by professional status Count As %
Student > Doctoral Student 1 6%
Student > Bachelor 1 6%
Researcher 1 6%
Student > Master 1 6%
Unknown 14 78%
Readers by discipline Count As %
Engineering 2 11%
Computer Science 1 6%
Environmental Science 1 6%
Unknown 14 78%
Attention Score in Context

Attention Score in Context

This research output has an Altmetric Attention Score of 14. This is our high-level measure of the quality and quantity of online attention that it has received. This Attention Score, as well as the ranking and number of research outputs shown below, was calculated when the research output was last mentioned on 27 January 2020.
All research outputs
#2,175,907
of 22,844,985 outputs
Outputs from Lecture notes in computer science
#428
of 8,126 outputs
Outputs of similar age
#32,167
of 353,225 outputs
Outputs of similar age from Lecture notes in computer science
#36
of 257 outputs
Altmetric has tracked 22,844,985 research outputs across all sources so far. Compared to these this one has done particularly well and is in the 90th percentile: it's in the top 10% of all research outputs ever tracked by Altmetric.
So far Altmetric has tracked 8,126 research outputs from this source. They receive a mean Attention Score of 5.0. This one has done particularly well, scoring higher than 94% of its peers.
Older research outputs will score higher simply because they've had more time to accumulate mentions. To account for age we can compare this Altmetric Attention Score to the 353,225 tracked outputs that were published within six weeks on either side of this one in any source. This one has done particularly well, scoring higher than 90% of its contemporaries.
We're also able to compare this research output to 257 others from the same source and published within six weeks on either side of this one. This one has done well, scoring higher than 85% of its contemporaries.