Series 
Lecture notes in computer science, 03029743 ; 8085 

LNCS sublibrary. SL 6, Image processing, computer vision, pattern recognition, and graphics 

Lecture notes in computer science ;
8085.


LNCS sublibrary. SL 6, Image processing, computer vision, pattern recognition, and graphics.

Subject 
Geometry  Congresses.


Information science  Congresses.


Information Science.


Mathematics.

Alt Name 
Nielsen, Frank,


Barbaresco, Frédéric,

Description 
1 online resource (xx, 879 pages) : illustrations. 
Bibliography Note 
Includes bibliographical references and index. 
Contents 
Invited Keynote papers. Information Geometry and Its Applications: Survey  InformationGeometric Optimization: The Interest of Information Theory for Discrete and Continuous Optimization  Nonparametric Information Geometry  Geometry of Hessian Structures  Geometric Statistics on Manifolds and Lie Groups. Biinvariant Means on Lie Groups with CartanSchouten Connections  Parallel Transport with Pole Ladder: Application to Deformations of Time Series of Images  Horizontal Dimensionality Reduction and Iterated Frame Bundle Development  A Subspace Learning of Dynamics on a Shape Manifold: A Generative Modeling Approach  Deformations in Shape Spaces. Geodesic Image Regression with a Sparse Parameterization of Diffeomorphisms  Template Estimation for Large Database: A Diffeomorphic Iterative Centroid Method Using Currents  On the Geometry and the Deformation of Shapes Represented by Piecewise Continuous Bezier Curves with Application to Shape Optimization  Random Spatial Structure of Geometric Deformations and Bayesian Nonparametrics. 

Differential Geometry in Signal Processing. A Riemannian Fourier Transform via Spin Representations  KCentroidsBased Supervised Classification of Texture Images Using the SIRV Modeling  Bayesian Atlas Estimation from High Angular Resolution Diffusion Imaging (HARDI)  Dimensionality Reduction for Classification of Stochastic Fibre Radiographs  Relational Metric. Optimal Transport and Minimal Trade Problem, Impacts on Relational Metrics and Applications to Large Graphs and Networks Modularity  Comparing Different Modularization Criteria Using Relational Metric  A General Framework for Comparing Heterogeneous Binary Relations  On PrimeValent Symmetric Bicirculants and Cayley Snarks  Discrete Metric Spaces. Studying New Classes of Graph Metrics  Tessellabilities, Reversibilities, and Decomposabilities of Polytopes  Counting the Number of Solutions of KDMDGP Instances  On the Identification of Discretization Orders for Distance Geometry with Intervals. 

Computational Information Geometry. Hypothesis Testing, Information Divergence and Computational Geometry  A New Implementation of kMLE for Mixture Modeling of Wishart Distributions  Variational Problem in Euclidean Space with Density  The Exponential Family in Abstract Information Theory  Hessian Information Geometry I. Hessian Structures on Deformed Exponential Families  Foliations on Affinely Flat Manifolds: Information Geometry  Hypersurfaces with Isometric Reeb Flow in Hermitian Symmetric Spaces of Rank 2  Generalized Minimizers of Convex Integral Functionals and Pythagorean Identities  Computational Aspects of Information Geometry in Statistics. Computational Information Geometry in Statistics: Foundations  Computational Information Geometry in Statistics: Mixture Modelling  A General Metric for Riemannian Manifold Hamiltonian Monte Carlo  Visualizing Projective Shape Space. 

Optimization on Matrix Manifolds. Interpolation and Regression of Rotation Matrices  A Geometric Framework for NonUnitary Joint Diagonalization of Complex Symmetric Matrices  An Extrinsic Look at the Riemannian Hessian  Law of Cosines and ShannonPythagorean Theorem for Quantum Information  A Note on the Intrinsic CramerRao Bound  Optimal Transport Theory. A Comparison of Two Dual Methods for Discrete Optimal Transport  The Tangent Earth Mover's Distance  A Geometric Study of Wasserstein Spaces: An Addendum on the Boundary  A PrimalDual Approach for a Total Variation Wasserstein Flow  Probability on Manifolds. Group Action Induced Distances on Spaces of HighDimensional Linear Stochastic Processes  Extrinsic vs Intrinsic Means on the Circle  Nonlinear Modeling and Processing Using Empirical Intrinsic Geometry with Application to Biomedical Imaging  Integral Geometry of Linearly Combined Gaussian and Studentt, and Skew Student's t Random Fields. 

Machine/Manifold/Topology Learning. Deconvolution for the Wasserstein Metric and Geometric Inference  On DirectionalSearch Procedures for Orbifolds: Connections with the Manifold Framework  Adaptation of Multiscale Function Extension to Inexact Matching: Application to the Mapping of Individuals to a Learnt Manifold  Interleaved Filtrations: Theory and Applications in Point Cloud Data Analysis  Hessian Information Geometry II. Symplectic and Kahler Structures on Statistical Manifolds Induced from Divergence Functions  Information/Contact Geometries and Koszul Entropy  Geometric Quantization of Complex MongeAmpere Operator for Certain Diffusion Flows  Geometry on Positive Definite Matrices Induced from VPotential Function  Geometry of Audio Processing. Online Change Detection in Exponential Families with Unknown Parameters  Differential Geometry Applied to Acoustics: Non Linear Propagation in Reissner Beams  Predictive Information in Gaussian Processes with Application to Music Analysis  Characterizing Time Series Variability and Predictability from Information Geometry Dynamics. 

Divergence Geometry and Ancillarity. Estimation and Tests Under LMoment Condition Models  Weighted Sampling, Maximum Likelihood and Minimum Divergence Estimators  Some Decision Procedures Based on Scaled Bregman Distance Surfaces  Some Results on a χdivergence, an Extended Fisher Information and Generalized CramerRao Inequalities  Entropic Geometry. The Stochastic Flow Theorem for an Operator of Order Four  Geometry and Shannon Capacity  A Metric for Quantum States Issued from von Neumann's Entropy  Continuity of fprojections on Discrete Spaces  TensorValued Mathematical Morphology. Frames for Tensor Field Morphology  Complete Lattice Structure of Poincare UpperHalf Plane and Mathematical Morphology for HyperbolicValued Images  Supervised Morphology for Structure TensorValued Images Based on Symmetric Divergence Kernels  Using the Bhattacharyya Mean for the Filtering and Clustering of PositiveDefinite Matrices. 

Algorithms on Manifolds. Information Geometry and InteriorPoint Algorithms  Geometric Mean Algorithms Based on Harmonic and Arithmetic Iterations  Multiscale Covariance Fields, Local Scales, and Shape Transforms  Deterministic Walks and QuasiSubgradient Methods for the Karcher Mean on NPC Spaces  Papers Presented at the Poster Session. Fast Polynomial Spline Approximation for Large Scattered Data Sets via L 1 Minimization  Target Detection of Nonstationary Radar Signal and Riemannian Geometry  HighDimensional Range Profile Geometrical Visualization and Performance Estimation of Radar Target Classification via a Gaussian Mixture Model  Visual Point Set Processing with Lattice Structures: Application to Parsimonious Representations of Digital Histopathology Images  Activity Video Analysis via OperatorBased Local Embedding  Multivariate Texture Discrimination Based on Geodesics to Class Centroids on a Generalized Gaussian Manifold  Robust Estimation of Natural Gradient in Optimization by Regularized Linear Regression  To the Homogeneous Symplectic Manifold toward the Geometry of information. 

Geometry of Inverse Problems. Variational Bayesian Approximation for Linear Inverse Problems with a Hierarchical Prior Models  Learning General Gaussian Kernel Hyperparameters for SVR  Stochastic Filtering by Projection: The Example of the Quadratic Sensor  A Probabilistic Solution to the AX=XB Problem: Sensor Calibration without Correspondence  Random Clouds on Matrix Lie Groups  Algebraic/Infinite Dimensionnal/Banach Information Manifolds. InfiniteDimensional Manifolds of FiniteEntropy Probability Measures  Asymptotically Efficient Estimators for Algebraic Statistical Manifolds  The Δ2Condition and φFamilies of Probability Distributions  A Riemannian Geometry in the qExponential Banach Manifold Induced by qDivergences  Information Geometry Manifolds  Harmonic Maps Relative to αConnections on Hessian Domains  A Kernel View on Manifold Subsampling Based on Karcher Variance Optimization  Maximal Information Divergence from Statistical Models Defined by Neural Networks  Neighborhood Random Classification. 
Summary 
This book constitutes the refereed proceedings of the First International Conference on Geometric Science of Information, GSI 2013, held in Paris, France, in August 2013. The nearly 100 papers presented were carefully reviewed and selected from numerous submissions and are organized into the following thematic sessions: Geometric Statistics on Manifolds and Lie Groups, Deformations in Shape Spaces, Differential Geometry in Signal Processing, Relational Metric, Discrete Metric Spaces, Computational Information Geometry, Hessian Information Geometry I and II, Computational Aspects of Information Geometry in Statistics, Optimization on Matrix Manifolds, Optimal Transport Theory, Probability on Manifolds, Divergence Geometry and Ancillarity, Entropic Geometry, TensorValued Mathematical Morphology, Machine/Manifold/Topology Learning, Geometry of Audio Processing, Geometry of Inverse Problems, Algebraic/Infinite dimensionnal/Banach Information Manifolds, Information Geometry Manifolds, and Algorithms on Manifolds. 
Note 
Online resource; title from PDF title page (SpringerLink, viewed October 2, 2013). 
ISBN 
9783642400209 (electronic bk.) 

3642400205 (electronic bk.) 

3642400191 

9783642400193 

9783642400193 
ISBN/ISSN 
10.1007/9783642400209 
OCLC # 
859259594 
Additional Format 
Printed edition: 9783642400193 
