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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 Stochastic Development Regression Using Method of Moments
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    Chapter 2 Bootstrapping Descriptors for Non-Euclidean Data
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    Chapter 3 Sample-Limited $$L_p$$ Barycentric Subspace Analysis on Constant Curvature Spaces
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    Chapter 4 Parallel Transport in Shape Analysis: A Scalable Numerical Scheme
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    Chapter 5 Maximum Likelihood Estimation of Riemannian Metrics from Euclidean Data
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    Chapter 6 Shape Analysis on Lie Groups and Homogeneous Spaces
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    Chapter 7 Optimal Matching Between Curves in a Manifold
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    Chapter 8 Optimization in the Space of Smooth Shapes
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    Chapter 9 Surface Matching Using Normal Cycles
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    Chapter 10 Regularized Barycenters in the Wasserstein Space
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    Chapter 11 Extremal Curves in Wasserstein Space
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    Chapter 12 Semi-discrete Optimal Transport in Patch Space for Enriching Gaussian Textures
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    Chapter 13 Analysis of Optimal Transport Related Misfit Functions in Seismic Imaging
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    Chapter 14 Information Geometry of Wasserstein Divergence
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    Chapter 15 Anomaly Detection in Network Traffic with a Relationnal Clustering Criterion
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    Chapter 16 Diffeomorphic Random Sampling Using Optimal Information Transport
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    Chapter 17 Optimal Transport to Rényi Entropies
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    Chapter 18 Statistical Manifolds Admitting Torsion, Pre-contrast Functions and Estimating Functions
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    Chapter 19 Generalized Wintegen Type Inequality for Lagrangian Submanifolds in Holomorphic Statistical Space Forms
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    Chapter 20 Amari Functors and Dynamics in Gauge Structures
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    Chapter 21 Sasakian Statistical Manifolds II
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    Chapter 22 (Para-)Holomorphic Connections for Information Geometry
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    Chapter 23 Matrix Realization of a Homogeneous Hessian Domain
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    Chapter 24 Information Geometry Under Monotone Embedding. Part I: Divergence Functions
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    Chapter 25 Information Geometry Under Monotone Embedding. Part II: Geometry
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    Chapter 26 A Sequential Structure of Statistical Manifolds on Deformed Exponential Family
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    Chapter 27 Normalization and $$\varphi $$ -function: Definition and Consequences
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    Chapter 28 Deformed Exponential Bundle: The Linear Growth Case
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    Chapter 29 On Affine Immersions of the Probability Simplex and Their Conformal Flattening
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    Chapter 30 Pairwise Ising Model Analysis of Human Cortical Neuron Recordings
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    Chapter 31 Prevalence and Recoverability of Syntactic Parameters in Sparse Distributed Memories
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    Chapter 32 Multi-scale Activity Estimation with Spatial Abstractions
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    Chapter 33 Geometry of Policy Improvement
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    Chapter 34 Joint Geometric and Photometric Visual Tracking Based on Lie Group
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    Chapter 35 Drone Tracking Using an Innovative UKF
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    Chapter 36 Particle Observers for Contracting Dynamical Systems
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    Chapter 37 Sigma Point Kalman Filtering on Matrix Lie Groups Applied to the SLAM Problem
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    Chapter 38 A Topological View on Forced Oscillations and Control of an Inverted Pendulum
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    Chapter 39 Uniform Observability of Linear Time-Varying Systems and Application to Robotics Problems
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    Chapter 40 Global Exponential Attitude and Gyro Bias Estimation from Vector Measurements
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    Chapter 41 Geometric Degree of Non Conservativeness
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    Chapter 42 A Symplectic Minimum Variational Principle for Dissipative Dynamical Systems
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    Chapter 43 Torsional Newton-Cartan Geometry
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    Chapter 44 Self-oscillations of a Vocal Apparatus: A Port-Hamiltonian Formulation
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    Chapter 45 Non Linear Propagation in Reissner Beams: An Integrable System?
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    Chapter 46 Quantum Harmonic Analysis and the Positivity of Trace Class Operators; Applications to Quantum Mechanics
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    Chapter 47 A Variational Formulation for Fluid Dynamics with Irreversible Processes
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    Chapter 48 Dirac Structures in Nonequilbrium Thermodynamics
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    Chapter 49 About the Definition of Port Variables for Contact Hamiltonian Systems
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    Chapter 50 Method of Orbits of Co-Associated Representation in Thermodynamics of the Lie Non-compact Groups
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    Chapter 51 Poly-symplectic Model of Higher Order Souriau Lie Groups Thermodynamics for Small Data Analytics
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    Chapter 52 Thermodynamic Equilibrium and Relativity: Killing Vectors and Lie Derivatives
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    Chapter 53 Natural Langevin Dynamics for Neural Networks
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    Chapter 54 3D Insights to Some Divergences for Robust Statistics and Machine Learning
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    Chapter 55 A Stochastic Look at Geodesics on the Sphere
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    Chapter 56 Constructing Universal, Non-asymptotic Confidence Sets for Intrinsic Means on the Circle
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    Chapter 57 Noncommutative Geometry and Stochastic Processes
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    Chapter 58 Hamilton-Jacobi Theory and Information Geometry
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    Chapter 59 Log-Determinant Divergences Between Positive Definite Hilbert-Schmidt Operators
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    Chapter 60 Some New Flexibilizations of Bregman Divergences and Their Asymptotics
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    Chapter 61 Quantification of Model Risk: Data Uncertainty
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    Chapter 62 Process Comparison Combining Signal Power Ratio and Jeffrey’s Divergence Between Unit-Power Signals
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    Chapter 63 Itô Stochastic Differential Equations as 2-Jets
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    Chapter 64 The Cramér-Rao Inequality on Singular Statistical Models
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    Chapter 65 Information Geometry of Predictor Functions in a Regression Model
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    Chapter 66 Translations in the Exponential Orlicz Space with Gaussian Weight
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    Chapter 67 On Mixture and Exponential Connection by Open Arcs
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    Chapter 68 Applying Backward Nested Subspace Inference to Tori and Polyspheres
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    Chapter 69 Fast Method to Fit a $$\mathcal {C}^1$$ Piecewise-Bézier Function to Manifold-Valued Data Points: How Suboptimal is the Curve Obtained on the Sphere $$\mathbb {S}^2$$ ?
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    Chapter 70 Nonlocal Inpainting of Manifold-Valued Data on Finite Weighted Graphs
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    Chapter 71 Affine-Invariant Orders on the Set of Positive-Definite Matrices
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    Chapter 72 Geodesic Least Squares Regression on the Gaussian Manifold with an Application in Astrophysics
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    Chapter 73 Warped Metrics for Location-Scale Models
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    Chapter 74 Bregman Divergences from Comparative Convexity
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    Chapter 75 Weighted Closed Form Expressions Based on Escort Distributions for Rényi Entropy Rates of Markov Chains
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    Chapter 76 On the Error Exponent of a Random Tensor with Orthonormal Factor Matrices
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    Chapter 77 Coordinate-Wise Transformation and Stein-Type Densities
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    Chapter 78 Riemannian Online Algorithms for Estimating Mixture Model Parameters
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    Chapter 79 Density Estimation for Compound Cox Processes on Hyperspheres
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    Chapter 80 Maximum Likelihood Estimators on Manifolds
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    Chapter 81 Von Mises-Like Probability Density Functions on Surfaces
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    Chapter 82 Riemannian Gaussian Distributions on the Space of Positive-Definite Quaternion Matrices
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    Chapter 83 A Family of Anisotropic Distributions on the Hyperbolic Plane
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    Chapter 84 A Riemanian Approach to Blob Detection in Manifold-Valued Images
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    Chapter 85 Co-occurrence Matrix of Covariance Matrices: A Novel Coding Model for the Classification of Texture Images
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    Chapter 86 Positive Signal Spaces and the Mehler-Fock Transform
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    Chapter 87 Bounding the Convergence Time of Local Probabilistic Evolution
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    Chapter 88 Inductive Means and Sequences Applied to Online Classification of EEG
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    Chapter 89 Vessel Tracking via Sub-Riemannian Geodesics on the Projective Line Bundle
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    Chapter 90 Anisotropic Edge-Based Balloon Eikonal Active Contours
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    Chapter 91 Automatic Differentiation of Non-holonomic Fast Marching for Computing Most Threatening Trajectories Under Sensors Surveillance
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    Chapter 92 On the Existence of Paths Connecting Probability Distributions
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    Chapter 93 Classification of Totally Umbilical CR-Statistical Submanifolds in Holomorphic Statistical Manifolds with Constant Holomorphic Curvature
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    Chapter 94 An Approach to Dynamical Distance Geometry
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    Chapter 95 Distance Geometry in Linearizable Norms
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    Chapter 96 Self-similar Geometry for Ad-Hoc Wireless Networks: Hyperfractals
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    Chapter 97 Information Distances in Stochastic Resolution Analysis
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    Chapter 98 k-Means Clustering with Hölder Divergences
  100. Altmetric Badge
    Chapter 99 Real Hypersurfaces in the Complex Quadric with Certain Condition of Normal Jacobi Operator
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 (91st percentile)
  • High Attention Score compared to outputs of the same age and source (96th percentile)

Mentioned by

twitter
32 X users
peer_reviews
1 peer review site
facebook
1 Facebook page
googleplus
1 Google+ user
q&a
1 Q&A thread

Citations

dimensions_citation
6 Dimensions

Readers on

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5 Mendeley
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Title
Geometric Science of Information
Published by
arXiv, January 2017
DOI 10.1007/978-3-319-68445-1
ISBNs
978-3-31-968444-4, 978-3-31-968445-1
Authors

Aleksei Shestov, Mikhail Kumskov

Editors

Frank Nielsen, Frédéric Barbaresco

X Demographics

X Demographics

The data shown below were collected from the profiles of 32 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 5 Mendeley readers of this research output. Click here to see the associated Mendeley record.

Geographical breakdown

Country Count As %
Unknown 5 100%

Demographic breakdown

Readers by professional status Count As %
Researcher 2 40%
Unknown 3 60%
Readers by discipline Count As %
Agricultural and Biological Sciences 1 20%
Engineering 1 20%
Unknown 3 60%
Attention Score in Context

Attention Score in Context

This research output has an Altmetric Attention Score of 19. 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 20 April 2022.
All research outputs
#1,906,528
of 24,953,268 outputs
Outputs from arXiv
#31,148
of 1,016,439 outputs
Outputs of similar age
#38,737
of 432,242 outputs
Outputs of similar age from arXiv
#528
of 14,661 outputs
Altmetric has tracked 24,953,268 research outputs across all sources so far. Compared to these this one has done particularly well and is in the 92nd percentile: it's in the top 10% of all research outputs ever tracked by Altmetric.
So far Altmetric has tracked 1,016,439 research outputs from this source. They receive a mean Attention Score of 4.1. This one has done particularly well, scoring higher than 96% 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 432,242 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 91% of its contemporaries.
We're also able to compare this research output to 14,661 others from the same source and published within six weeks on either side of this one. This one has done particularly well, scoring higher than 96% of its contemporaries.