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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 On Geometric Properties of the Textile Set and Strict Textile Set
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    Chapter 2 Inexact Elastic Shape Matching in the Square Root Normal Field Framework
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    Chapter 3 Signatures in Shape Analysis: An Efficient Approach to Motion Identification
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    Chapter 4 Dilation Operator Approach and Square Root Velocity Transform for Time/Doppler Spectra Characterization on SU(n)
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    Chapter 5 Selective Metamorphosis for Growth Modelling with Applications to Landmarks
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    Chapter 6 Intrinsic Incremental Mechanics
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    Chapter 7 Multi-symplectic Lie Group Thermodynamics for Covariant Field Theories
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    Chapter 8 Euler-Poincaré Equation for Lie Groups with Non Null Symplectic Cohomology. Application to the Mechanics
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    Chapter 9 Geometric Numerical Methods with Lie Groups
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    Chapter 10 Souriau Exponential Map Algorithm for Machine Learning on Matrix Lie Groups
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    Chapter 11 $$\mathbb {R}$$ R -Complex Finsler Information Geometry Applied to Manifolds of Systems
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    Chapter 12 Minkowski Sum of Ellipsoids and Means of Covariance Matrices
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    Chapter 13 Hyperquaternions: An Efficient Mathematical Formalism for Geometry
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    Chapter 14 $$\alpha $$ α -power Sums on Symmetric Cones
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    Chapter 15 Packing Bounds for Outer Products with Applications to Compressive Sensing
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    Chapter 16 On a Method to Construct Exponential Families by Representation Theory
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    Chapter 17 Lie Group Machine Learning and Gibbs Density on Poincaré Unit Disk from Souriau Lie Groups Thermodynamics and SU(1,1) Coadjoint Orbits
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    Chapter 18 Irreversible Langevin MCMC on Lie Groups
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    Chapter 19 Predicting Bending Moments with Machine Learning
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    Chapter 20 The Exponential of Nilpotent Supergroups in the Theory of Harish-Chandra Representations
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    Chapter 21 Dirac Structures in Open Thermodynamics
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    Chapter 22 From Variational to Bracket Formulations in Nonequilibrium Thermodynamics of Simple Systems
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    Chapter 23 A Homological Approach to Belief Propagation and Bethe Approximations
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    Chapter 24 About Some System-Theoretic Properties of Port-Thermodynamic Systems
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    Chapter 25 Expectation Variables on a Para-Contact Metric Manifold Exactly Derived from Master Equations
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    Chapter 26 Doubly Autoparallel Structure on Positive Definite Matrices and Its Applications
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    Chapter 27 Toeplitz Hermitian Positive Definite Matrix Machine Learning Based on Fisher Metric
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    Chapter 28 Deformed Exponential and the Behavior of the Normalizing Function
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    Chapter 29 Normalization Problems for Deformed Exponential Families
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    Chapter 30 New Geometry of Parametric Statistical Models
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    Chapter 31 The Bregman Chord Divergence
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    Chapter 32 Testing the Number and the Nature of the Components in a Mixture Distribution
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    Chapter 33 Robust Estimation by Means of Scaled Bregman Power Distances. Part I. Non-homogeneous Data
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    Chapter 34 Robust Estimation by Means of Scaled Bregman Power Distances. Part II. Extreme Values
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    Chapter 35 Topological Methods for Unsupervised Learning
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    Chapter 36 Geometry and Fixed-Rate Quantization in Riemannian Metric Spaces Induced by Separable Bregman Divergences
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    Chapter 37 The Statistical Minkowski Distances: Closed-Form Formula for Gaussian Mixture Models
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    Chapter 38 Parameter Estimation with Generalized Empirical Localization
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    Chapter 39 Properties of the Cross Entropy Between ARMA Processes
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    Chapter 40 Inequalities for Statistical Submanifolds in Hessian Manifolds of Constant Hessian Curvature
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    Chapter 41 B. Y. Chen Inequalities for Statistical Submanifolds in Sasakian Statistical Manifolds
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    Chapter 42 Generalized Wintgen Inquality for Legendrian Submanifolds in Sasakian Statistical Manifolds
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    Chapter 43 Logarithmic Divergences: Geometry and Interpretation of Curvature
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    Chapter 44 Hessian Curvature and Optimal Transport
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    Chapter 45 Divergence Functions in Information Geometry
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    Chapter 46 Sobolev Statistical Manifolds and Exponential Models
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    Chapter 47 Minimization of the Kullback-Leibler Divergence over a Log-Normal Exponential Arc
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    Chapter 48 Riemannian Distance and Diameter of the Space of Probability Measures and the Parametrix
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    Chapter 49 A Unified Formulation for the Bures-Wasserstein and Log-Euclidean/Log-Hilbert-Schmidt Distances between Positive Definite Operators
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    Chapter 50 Exploration of Balanced Metrics on Symmetric Positive Definite Matrices
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    Chapter 51 Affine-Invariant Midrange Statistics
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    Chapter 52 Is Affine-Invariance Well Defined on SPD Matrices? A Principled Continuum of Metrics
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    Chapter 53 Shape Part Transfer via Semantic Latent Space Factorization
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    Chapter 54 Variational Discretization Framework for Geophysical Flow Models
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    Chapter 55 Finite Element Methods for Geometric Evolution Equations
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    Chapter 56 Local Truncation Error of Low-Order Fractional Variational Integrators
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    Chapter 57 A Partitioned Finite Element Method for the Structure-Preserving Discretization of Damped Infinite-Dimensional Port-Hamiltonian Systems with Boundary Control
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    Chapter 58 Geometry, Energy, and Entropy Compatible (GEEC) Variational Approaches to Various Numerical Schemes for Fluid Dynamics
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    Chapter 59 Canonical Moments for Optimal Uncertainty Quantification on a Variety
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    Chapter 60 Computational Investigations of an Obstacle-Type Shape Optimization Problem in the Space of Smooth Shapes
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    Chapter 61 Bézier Curves and $$C^{2}$$ C 2 Interpolation in Riemannian Symmetric Spaces
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    Chapter 62 A Formalization of the Natural Gradient Method for General Similarity Measures
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    Chapter 63 The Frenet-Serret Framework for Aligning Geometric Curves
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    Chapter 64 When Geometry Meets Psycho-Physics and Quantum Mechanics: Modern Perspectives on the Space of Perceived Colors
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    Chapter 65 Quantum Statistical Manifolds: The Finite-Dimensional Case
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    Chapter 66 Generalized Gibbs Ensembles in Discrete Quantum Gravity
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    Chapter 67 On the Notion of Composite System
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    Chapter 68 The Riemannian Barycentre as a Proxy for Global Optimisation
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    Chapter 69 Hamiltonian Monte Carlo on Lie Groups and Constrained Mechanics on Homogeneous Manifolds
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    Chapter 70 On the Fisher-Rao Information Metric in the Space of Normal Distributions
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    Chapter 71 Simulation of Conditioned Diffusions on the Flat Torus
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    Chapter 72 Towards Parametric Bi-Invariant Density Estimation on SE(2)
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    Chapter 73 Affine Natural Proximal Learning
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    Chapter 74 Parametric Fokker-Planck equation
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    Chapter 74 Parametric Fokker-Planck Equation
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    Chapter 75 Multi-marginal Schrödinger Bridges
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    Chapter 76 Hopf–Cole Transformation and Schrödinger Problems
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    Chapter 77 Curvature of the Manifold of Fixed-Rank Positive-Semidefinite Matrices Endowed with the Bures–Wasserstein Metric
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    Chapter 78 Second-Order Networks in PyTorch
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    Chapter 79 Symmetric Algorithmic Components for Shape Analysis with Diffeomorphisms
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 (84th percentile)
  • High Attention Score compared to outputs of the same age and source (93rd percentile)

Mentioned by

twitter
18 X users
wikipedia
1 Wikipedia page

Citations

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7 Dimensions

Readers on

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Title
Geometric Science of Information
Published by
arXiv, January 2019
DOI 10.1007/978-3-030-26980-7
ISBNs
978-3-03-026979-1, 978-3-03-026980-7
Authors

Goffredo Chirco, Isha Kotecha

Editors

Frank Nielsen, Frédéric Barbaresco

X Demographics

X Demographics

The data shown below were collected from the profiles of 18 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 %
Student > Bachelor 1 20%
Unknown 4 80%
Readers by discipline Count As %
Linguistics 1 20%
Unknown 4 80%
Attention Score in Context

Attention Score in Context

This research output has an Altmetric Attention Score of 11. 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 26 October 2022.
All research outputs
#3,179,313
of 25,626,416 outputs
Outputs from arXiv
#52,378
of 932,671 outputs
Outputs of similar age
#69,588
of 448,418 outputs
Outputs of similar age from arXiv
#1,203
of 19,204 outputs
Altmetric has tracked 25,626,416 research outputs across all sources so far. Compared to these this one has done well and is in the 87th percentile: it's in the top 25% of all research outputs ever tracked by Altmetric.
So far Altmetric has tracked 932,671 research outputs from this source. They receive a mean Attention Score of 4.3. 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 448,418 tracked outputs that were published within six weeks on either side of this one in any source. This one has done well, scoring higher than 84% of its contemporaries.
We're also able to compare this research output to 19,204 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 93% of its contemporaries.