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速递书局
| 封面: |
 |
| 题名: |
Geometric Science of Information |
| 作者: |
Gerhard Goos, Juris Hartmanis, and Jan van Leeuwen |
| 出版社: |
Springer |
| 出版日期: |
2013-08-28 |
| ISBN: |
0302-9743 |
| 附属页: |
齐全 |
| 书签: |
有 |
| 格式: |
清晰PDF |
| 内容简介: |
Table of Contents
Invited Keynote Papers
Information Geometry and Its Applications: Survey . . . . . . . . . . . . . . . . . . 3
Shun-ichi Amari
Information-Geometric Optimization: The Interest of Information
Theory for Discrete and Continuous Optimization . . . . . . . . . . . . . . . . . . . . 4
Yann Ollivier
Nonparametric Information Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Giovanni Pistone
Geometry of Hessian Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Hirohiko Shima
Geometric Statistics on Manifolds and Lie Groups
Bi-invariant Means on Lie Groups with Cartan-Schouten
Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
Xavier Pennec
Parallel Transport with Pole Ladder: Application to Deformations of
Time Series of Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
Marco Lorenzi and Xavier Pennec
Horizontal Dimensionality Reduction and Iterated Frame Bundle
Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
Stefan Sommer
A Subspace Learning of Dynamics on a Shape Manifold: A Generative
Modeling Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
Sheng Yi and Hamid Krim
Deformations in Shape Spaces
Geodesic Image Regression with a Sparse Parameterization of
Diffeomorphisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
James Fishbaugh, Marcel Prastawa, Guido Gerig, and
Stanley Durrleman
Template Estimation for Large Database: A Diffeomorphic Iterative
Centroid Method Using Currents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
Claire Cury, Joan A. Glaun`es, and Olivier Colliot
XII Table of Contents
On the Geometry and the Deformation of Shapes Represented by
Piecewise Continuous B´ezier Curves with Application to Shape
Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
Olivier Ruatta
Random Spatial Structure of Geometric Deformations and Bayesian
Nonparametrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
Christof Seiler, Xavier Pennec, and Susan Holmes
Differential Geometry in Signal Processing
A Riemannian Fourier Transform via Spin Representations . . . . . . . . . . . . 131
T. Batard and M. Berthier
K-Centroids-Based Supervised Classification of Texture Images Using
the SIRV Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
Aur´elien Schutz, Lionel Bombrun, and Yannick Berthoumieu
Bayesian Atlas Estimation from High Angular Resolution Diffusion
Imaging (HARDI) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
Jia Du, Alvina Goh, and Anqi Qiu
Dimensionality Reduction for Classification of Stochastic Fibre
Radiographs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
C.T.J. Dodson and W.W. Sampson
Relational Metric
Optimal Transport and Minimal Trade Problem, Impacts on Relational
Metrics and Applications to Large Graphs and Networks Modularity . . . 169
F. Marcotorchino and P. Conde C´espedes
Comparing Different Modularization Criteria Using Relational
Metric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
P. Conde C´espedes and J.F. Marcotorchino
A General Framework for Comparing Heterogeneous Binary
Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
Julien Ah-Pine
On Prime-Valent Symmetric Bicirculants and Cayley Snarks. . . . . . . . . . . 196
Ademir Hujdurovi´c, Klavdija Kutnar, and Dragan Maruˇsiˇc
Discrete Metric Spaces
Studying New Classes of Graph Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
Pavel Chebotarev
Table of Contents XIII
Tessellabilities, Reversibilities, and Decomposabilities of Polytopes
(A Survey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
Jin Akiyama, Ikuro Sato, and Hyunwoo Seong
Counting the Number of Solutions of KDMDGP Instances . . . . . . . . . . . . 224
Leo Liberti, Carlile Lavor, Jorge Alencar, and Germano Abud
On the Identification of Discretization Orders for Distance Geometry
with Intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
Antonio Mucherino
Computational Information Geometry
Hypothesis Testing, Information Divergence and Computational
Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
Frank Nielsen
A New Implementation of k-MLE for Mixture Modeling of Wishart
Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
Christophe Saint-Jean and Frank Nielsen
Variational Problem in Euclidean Space with Density . . . . . . . . . . . . . . . . . 257
Lakehal Belarbi and Mohamed Belkhelfa
The Exponential Family in Abstract Information Theory . . . . . . . . . . . . . . 265
Jan Naudts and Ben Anthonis
Hessian Information Geometry I
Hessian Structures on Deformed Exponential Families . . . . . . . . . . . . . . . . 275
Hiroshi Matsuzoe and Masayuki Henmi
Foliations on Affinely Flat Manifolds: Information Geometry . . . . . . . . . . 283
Michel Nguiffo Boyom and Robert Wolak
Hypersurfaces with Isometric Reeb Flow in Hermitian Symmetric
Spaces of Rank 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
Young Jin Suh
Generalized Minimizers of Convex Integral Functionals and
Pythagorean Identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302
Imre Csisz´ar and Frantiˇsek Mat´uˇs
XIV Table of Contents
Computational Aspects of Information Geometry in
Statistics
Computational Information Geometry in Statistics: Foundations . . . . . . . 311
Karim Anaya-Izquierdo, Frank Critchley, Paul Marriott, and
Paul Vos
Computational Information Geometry in Statistics: Mixture
Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319
Karim Anaya-Izquierdo, Frank Critchley, Paul Marriott, and
Paul Vos
A General Metric for Riemannian Manifold Hamiltonian Monte
Carlo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
Michael Betancourt
Visualizing Projective Shape Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335
John T. Kent
Optimization on Matrix Manifolds
Interpolation and Regression of Rotation Matrices . . . . . . . . . . . . . . . . . . . 345
Nicolas Boumal
A Geometric Framework for Non-Unitary Joint Diagonalization of
Complex Symmetric Matrices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353
Martin Kleinsteuber and Hao Shen
An Extrinsic Look at the Riemannian Hessian . . . . . . . . . . . . . . . . . . . . . . . 361
P.-A. Absil, Robert Mahony, and Jochen Trumpf
Law of Cosines and Shannon-Pythagorean Theorem for Quantum
Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369
Roman V. Belavkin
A Note on the Intrinsic Cramer-Rao Bound . . . . . . . . . . . . . . . . . . . . . . . . . 377
Axel Barrau and Silv`ere Bonnabel
Optimal Transport Theory
A Comparison of Two Dual Methods for Discrete Optimal Transport . . . 389
Quentin M´erigot
The Tangent Earth Mover’s Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397
Ofir Pele and Ben Taskar
A Geometric Study of Wasserstein Spaces: An Addendum on the
Boundary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405
J´erˆome Bertrand and Benoˆıt R. Kloeckner
Table of Contents XV
A Primal-Dual Approach for a Total Variation Wasserstein Flow . . . . . . . 413
Martin Benning, Luca Calatroni, Bertram D¨uring, and
Carola-Bibiane Sch¨onlieb
Probability on Manifolds
Group Action Induced Distances on Spaces of High-Dimensional Linear
Stochastic Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425
Bijan Afsari and Ren´e Vidal
Extrinsic vs Intrinsic Means on the Circle . . . . . . . . . . . . . . . . . . . . . . . . . . . 433
Thomas Hotz
Nonlinear Modeling and Processing Using Empirical Intrinsic Geometry
with Application to Biomedical Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441
Ronen Talmon, Yoel Shkolnisky, and Ronald R. Coifman
Integral Geometry of Linearly Combined Gaussian and Student-t, and
Skew Student’s t Random Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449
Yann Gavet, Ola Suleiman Ahmad, and Jean-Charles Pinoli
Divergence Geometry and Ancillarity
Estimation and Tests Under L-Moment Condition Models . . . . . . . . . . . . . 459
Alexis Decurninge
Weighted Sampling, Maximum Likelihood and Minimum Divergence
Estimators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467
Michel Broniatowski
Some Decision Procedures Based on Scaled Bregman Distance
Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479
Anna-Lena Kißlinger and Wolfgang Stummer
Some Results on a χ-divergence, an Extended Fisher Information and
Generalized Cramer-Rao Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487
Jean-Fran¸cois Bercher
Entropic Geometry
The Stochastic Flow Theorem for an Operator of Order Four . . . . . . . . . . 497
R´emi L´eandre
Geometry and Shannon Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 502
Philippe Jacquet
A Metric for Quantum States Issued from von Neumann’s Entropy . . . . . 513
Roger Balian
XVI Table of Contents
Continuity of f-projections on Discrete Spaces . . . . . . . . . . . . . . . . . . . . . . . 519
Christoph Gietl and Fabian P. Reffel
Tensor-Valued Mathematical Morphology
Frames for Tensor Field Morphology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527
Jasper J. van de Gronde and Jos B.T.M. Roerdink
Complete Lattice Structure of Poincar´e Upper-Half Plane and
Mathematical Morphology for Hyperbolic-Valued Images . . . . . . . . . . . . . . 535
Jes´us Angulo and Santiago Velasco-Forero
Supervised Morphology for Structure Tensor-Valued Images Based
on Symmetric Divergence Kernels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543
Santiago Velasco-Forero and Jes´us Angulo
Using the Bhattacharyya Mean for the Filtering and Clustering of
Positive-Definite Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 551
Malek Charfi, Zeineb Chebbi, Maher Moakher, and Baba C. Vemuri
Machine/Manifold/Topology Learning
Deconvolution for the Wasserstein Metric and Geometric Inference . . . . . 561
Claire Caillerie, Fr´ed´eric Chazal, J´erˆome Dedecker, and
Bertrand Michel
On Directional-Search Procedures for Orbifolds: Connections with the
Manifold Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 569
Fabian Lim
Adaptation of Multiscale Function Extension to Inexact Matching:
Application to the Mapping of Individuals to a Learnt Manifold . . . . . . . 578
Nicolas Duchateau, Mathieu De Craene, Marta Sitges, and
Vicent Caselles
Interleaved Filtrations: Theory and Applications in Point Cloud Data
Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 587
Fr´ed´eric Chazal and Steve Y. Oudot
Hessian Information Geometry II
Symplectic and K¨ahler Structures on Statistical Manifolds Induced
from Divergence Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595
Jun Zhang and Fubo Li
Information/Contact Geometries and Koszul Entropy. . . . . . . . . . . . . . . . . 604
Fr´ed´eric Barbaresco
Table of Contents XVII
Geometric Quantization of Complex Monge-Amp´ere Operator
for Certain Diffusion Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 612
Julien Keller
Geometry on Positive Definite Matrices Induced from V-Potential
Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 621
Atsumi Ohara and Shinto Eguchi
Geometry of Audio Processing
Online Change Detection in Exponential Families with Unknown
Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633
Arnaud Dessein and Arshia Cont
Differential Geometry Applied to Acoustics: Non Linear Propagation
in Reissner Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 641
Joel Bensoam
Predictive Information in Gaussian Processes with Application to
Music Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 650
Samer Abdallah and Mark Plumbley
Characterizing Time Series Variability and Predictability from
Information Geometry Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 658
Shlomo Dubnov
Geometry of Inverse Problems
Variational Bayesian Approximation for Linear Inverse Problems with
a Hierarchical Prior Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 669
Ali Mohammad-Djafari
Learning General Gaussian Kernel Hyperparameters for SVR . . . . . . . . . . 677
F. Abdallah, Hichem Snoussi, H. Laanaya, and R. Lengell´e
Stochastic Filtering by Projection: The Example of the Quadratic
Sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685
John Armstrong and Damiano Brigo
A Probabilistic Solution to the AX=XB Problem: Sensor Calibration
without Correspondence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 693
M. Kendal Ackerman and Gregory S. Chirikjian
Random Clouds on Matrix Lie Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 702
Simone Fiori
XVIII Table of Contents
Algebraic/Infinite Dimensionnal/Banach Information
Mani-Folds
Infinite-Dimensional Manifolds of Finite-Entropy Probability
Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 713
Nigel J. Newton
Asymptotically Efficient Estimators for Algebraic Statistical
Manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 721
Kei Kobayashi and Henry P. Wynn
The Δ2-Condition and ϕ-Families of Probability Distributions . . . . . . . . . 729
Rui F. Vigelis and Charles C. Cavalcante
A Riemannian Geometry in the q-Exponential Banach Manifold
Induced by q-Divergences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 737
G. Loaiza and H.R. Quiceno
Information Geometry Manifolds
Harmonic Maps Relative to α-Connections on Hessian Domains . . . . . . . . 745
Keiko Uohashi
A Kernel View on Manifold Sub-sampling Based on Karcher Variance
Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 751
Nicolas Courty and Thomas Burger
Maximal Information Divergence from Statistical Models Defined by
Neural Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 759
Guido Mont´ufar, Johannes Rauh, and Nihat Ay
Neighborhood Random Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 767
Djamel A. Zighed, Diala Ezzeddine, and Fabien Rico
Algorithms on Manifolds
Information Geometry and Interior-Point Algorithms . . . . . . . . . . . . . . . . . 777
Satoshi Kakihara, Atsumi Ohara, and Takashi Tsuchiya
Geometric Mean Algorithms Based on Harmonic and Arithmetic
Iterations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 785
Ben Jeuris and Raf Vandebril
Multiscale Covariance Fields, Local Scales, and Shape Transforms . . . . . . 794
Diego H. Diaz Martinez, Facundo M´emoli, and Washington Mio
Deterministic Walks and Quasi-Subgradient Methods for the Karcher
Mean on NPC Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 802
Mikl´os P´alfia
Table of Contents XIX
Papers Presented at the Poster Session
Fast Polynomial Spline Approximation for Large Scattered Data Sets
via L1 Minimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 813
Laurent Gajny, ´ Eric Nyiri, and Olivier Gibaru
Target Detection of Non-stationary Radar Signal and Riemannian
Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 821
Haiyan Fan, Yongmei Jiang, and Gangyao Kuang
High-Dimensional Range Profile Geometrical Visualization and
Performance Estimation of Radar Target Classification via a Gaussian
Mixture Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 829
Thomas Boulay, Ali Mohammad-Djafari, Nicolas Gac, and
Julien Lagoutte
Visual Point Set Processing with Lattice Structures: Application
to Parsimonious Representations of Digital Histopathology Images . . . . . 837
Nicolas Lom´enie
Activity Video Analysis via Operator-Based Local Embedding . . . . . . . . . 845
Xiao Bian and Hamid Krim
Multivariate Texture Discrimination Based on Geodesics to Class
Centroids on a Generalized Gaussian Manifold . . . . . . . . . . . . . . . . . . . . . . . 853
A. Shabbir, G. Verdoolaege, and G. Van Oost
Robust Estimation of Natural Gradient in Optimization by Regularized
Linear Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 861
Luigi Malag`o and Matteo Matteucci
To the Homogeneous Symplectic Manifold toward the Geometry of
Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 868
F. Mouna, T.B. Bouetou, and M.B. Nguiffo
Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 877 |
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