Geometric Science of Information: Third International Conference, GSI 2017, Paris, France, November 7-9, 2017, Proceedings

Front Matter ....Pages I-XXV
Front Matter ....Pages 1-1
 Stochastic Development Regression Using Method of Moments  (Line Kühnel, Stefan Sommer)....Pages 3-11
 Bootstrapping Descriptors for Non-Euclidean Data  (Benjamin Eltzner, Stephan Huckemann)....Pages 12-19
 Sample-Limited \(L_p\) Barycentric Subspace Analysis on Constant Curvature Spaces  (Xavier Pennec)....Pages 20-28
 Parallel Transport in Shape Analysis: A Scalable Numerical Scheme  (Maxime Louis, Alexandre Bône, Benjamin Charlier, Stanley Durrleman, The Alzheimer’s Disease Neuroimaging Initiative)....Pages 29-37
 Maximum Likelihood Estimation of Riemannian Metrics from Euclidean Data  (Georgios Arvanitidis, Lars Kai Hansen, Søren Hauberg)....Pages 38-46
Front Matter ....Pages 47-47
 Shape Analysis on Lie Groups and Homogeneous Spaces  (Elena Celledoni, Sølve Eidnes, Markus Eslitzbichler, Alexander Schmeding)....Pages 49-56
 Optimal Matching Between Curves in a Manifold  (Alice Le Brigant, Marc Arnaudon, Frédéric Barbaresco)....Pages 57-64
 Optimization in the Space of Smooth Shapes  (Kathrin Welker)....Pages 65-72
 Surface Matching Using Normal Cycles  (Pierre Roussillon, Joan Alexis Glaunès)....Pages 73-80
Front Matter ....Pages 81-81
 Regularized Barycenters in the Wasserstein Space  (Elsa Cazelles, Jérémie Bigot, Nicolas Papadakis)....Pages 83-90
 Extremal Curves in Wasserstein Space  (Giovanni Conforti, Michele Pavon)....Pages 91-99
 Semi-discrete Optimal Transport in Patch Space for Enriching Gaussian Textures  (Bruno Galerne, Arthur Leclaire, Julien Rabin)....Pages 100-108
 Analysis of Optimal Transport Related Misfit Functions in Seismic Imaging  (Yunan Yang, Björn Engquist)....Pages 109-116
Front Matter ....Pages 117-117
 Information Geometry of Wasserstein Divergence  (Ryo Karakida, Shun-ichi Amari)....Pages 119-126
 Anomaly Detection in Network Traffic with a Relationnal Clustering Criterion  (Damien Nogues)....Pages 127-134
 Diffeomorphic Random Sampling Using Optimal Information Transport  (Martin Bauer, Sarang Joshi, Klas Modin)....Pages 135-142
 Optimal Transport to Rényi Entropies  (Olivier Rioul)....Pages 143-150
Front Matter ....Pages 151-151
 Statistical Manifolds Admitting Torsion, Pre-contrast Functions and Estimating Functions  (Masayuki Henmi)....Pages 153-161
 Generalized Wintegen Type Inequality for Lagrangian Submanifolds in Holomorphic Statistical Space Forms  (Michel Nguiffo Boyom, Mohd. Aquib, Mohammad Hasan Shahid, Mohammed Jamali)....Pages 162-169
 Amari Functors and Dynamics in Gauge Structures  (Michel Nguiffo Boyom, Ahmed Zeglaoui)....Pages 170-178
 Sasakian Statistical Manifolds II  (Hitoshi Furuhata)....Pages 179-185
 (Para-)Holomorphic Connections for Information Geometry  (Sergey Grigorian, Jun Zhang)....Pages 186-194
 Matrix Realization of a Homogeneous Hessian Domain  (Hideyuki Ishi)....Pages 195-202
Front Matter ....Pages 203-203
 Information Geometry Under Monotone Embedding. Part I: Divergence Functions  (Jun Zhang, Jan Naudts)....Pages 205-214
 Information Geometry Under Monotone Embedding. Part II: Geometry  (Jan Naudts, Jun Zhang)....Pages 215-222
 A Sequential Structure of Statistical Manifolds on Deformed Exponential Family  (Hiroshi Matsuzoe, Antonio M. Scarfone, Tatsuaki Wada)....Pages 223-230
 Normalization and \(\varphi \)-function: Definition and Consequences  (Luiza H. F. de Andrade, Rui F. Vigelis, Francisca L. J. Vieira, Charles C. Cavalcante)....Pages 231-238
 Deformed Exponential Bundle: The Linear Growth Case  (Luigi Montrucchio, Giovanni Pistone)....Pages 239-246
 On Affine Immersions of the Probability Simplex and Their Conformal Flattening  (Atsumi Ohara)....Pages 247-254
Front Matter ....Pages 255-255
 Pairwise Ising Model Analysis of Human Cortical Neuron Recordings  (Trang-Anh Nghiem, Olivier Marre, Alain Destexhe, Ulisse Ferrari)....Pages 257-264
 Prevalence and Recoverability of Syntactic Parameters in Sparse Distributed Memories  (Jeong Joon Park, Ronnel Boettcher, Andrew Zhao, Alex Mun, Kevin Yuh, Vibhor Kumar et al.)....Pages 265-272
 Multi-scale Activity Estimation with Spatial Abstractions  (Majd Hawasly, Florian T. Pokorny, Subramanian Ramamoorthy)....Pages 273-281
 Geometry of Policy Improvement  (Guido Montúfar, Johannes Rauh)....Pages 282-290
 Joint Geometric and Photometric Visual Tracking Based on Lie Group  (Chenxi Li, Zelin Shi, Yunpeng Liu, Tianci Liu)....Pages 291-298
Front Matter ....Pages 299-299
 Drone Tracking Using an Innovative UKF  (Marion Pilté, Silvère Bonnabel, Frédéric Barbaresco)....Pages 301-309
 Particle Observers for Contracting Dynamical Systems  (Silvère Bonnabel, Jean-Jacques Slotine)....Pages 310-317
 Sigma Point Kalman Filtering on Matrix Lie Groups Applied to the SLAM Problem  (James Richard Forbes, David Evan Zlotnik)....Pages 318-328
 A Topological View on Forced Oscillations and Control of an Inverted Pendulum  (Ivan Polekhin)....Pages 329-335
 Uniform Observability of Linear Time-Varying Systems and Application to Robotics Problems  (Pascal Morin, Alexandre Eudes, Glauco Scandaroli)....Pages 336-344
 Global Exponential Attitude and Gyro Bias Estimation from Vector Measurements  (Philippe Martin, Ioannis Sarras)....Pages 345-351
Front Matter ....Pages 353-353
 Geometric Degree of Non Conservativeness  (Jean Lerbet, Noël Challamel, François Nicot, Félix Darve)....Pages 355-358
 A Symplectic Minimum Variational Principle for Dissipative Dynamical Systems  (Abdelbacet Oueslati, An Danh Nguyen, Géry de Saxcé)....Pages 359-366
 Torsional Newton-Cartan Geometry  (Eric Bergshoeff, Athanasios Chatzistavrakidis, Luca Romano, Jan Rosseel)....Pages 367-374
 Self-oscillations of a Vocal Apparatus: A Port-Hamiltonian Formulation  (Thomas Hélie, Fabrice Silva)....Pages 375-383
 Non Linear Propagation in Reissner Beams: An Integrable System?  (Frédéric Hélein, Joël Bensoam, Pierre Carré)....Pages 384-392
 Quantum Harmonic Analysis and the Positivity of Trace Class Operators; Applications to Quantum Mechanics  (Elena Nicola, Maurice de Gosson, Fabio Nicola)....Pages 393-398
Front Matter ....Pages 399-399
 A Variational Formulation for Fluid Dynamics with Irreversible Processes  (François Gay-Balmaz, Hiroaki Yoshimura)....Pages 401-409
 Dirac Structures in Nonequilbrium Thermodynamics  (Hiroaki Yoshimura, François Gay-Balmaz)....Pages 410-417
 About the Definition of Port Variables for Contact Hamiltonian Systems  (Bernhard Maschke, Arjan van der Schaft)....Pages 418-424
 Method of Orbits of Co-Associated Representation in Thermodynamics of the Lie Non-compact Groups  (Vitaly Mikheev)....Pages 425-431
 Poly-symplectic Model of Higher Order Souriau Lie Groups Thermodynamics for Small Data Analytics  (Frederic Barbaresco)....Pages 432-441
 Thermodynamic Equilibrium and Relativity: Killing Vectors and Lie Derivatives  (F. Becattini)....Pages 442-447
Front Matter ....Pages 449-449
 Natural Langevin Dynamics for Neural Networks  (Gaétan Marceau-Caron, Yann Ollivier)....Pages 451-459
 3D Insights to Some Divergences for Robust Statistics and Machine Learning  (Birgit Roensch, Wolfgang Stummer)....Pages 460-469
 A Stochastic Look at Geodesics on the Sphere  (Marc Arnaudon, Jean-Claude Zambrini)....Pages 470-476
 Constructing Universal, Non-asymptotic Confidence Sets for Intrinsic Means on the Circle  (Matthias Glock, Thomas Hotz)....Pages 477-485
 Noncommutative Geometry and Stochastic Processes  (Marco Frasca)....Pages 486-494
 Hamilton-Jacobi Theory and Information Geometry  (Florio M. Ciaglia, Fabio Di Cosmo, Giuseppe Marmo)....Pages 495-502
Front Matter ....Pages 503-503
 Log-Determinant Divergences Between Positive Definite Hilbert-Schmidt Operators  (Hà Quang Minh)....Pages 505-513
 Some New Flexibilizations of Bregman Divergences and Their Asymptotics  (Wolfgang Stummer, Anna-Lena Kißlinger)....Pages 514-522
 Quantification of Model Risk: Data Uncertainty  (Z. Krajčovičová, P. P. Pérez-Velasco, C. Vázquez)....Pages 523-531
 Process Comparison Combining Signal Power Ratio and Jeffrey’s Divergence Between Unit-Power Signals  (Eric Grivel, Leo Legrand)....Pages 532-540
Front Matter ....Pages 541-541
 Itô Stochastic Differential Equations as 2-Jets  (John Armstrong, Damiano Brigo)....Pages 543-551
 The Cramér-Rao Inequality on Singular Statistical Models  (Hông Vân Lê, Jürgen Jost, Lorenz Schwachhöfer)....Pages 552-560
 Information Geometry of Predictor Functions in a Regression Model  (Shinto Eguchi, Katsuhiro Omae)....Pages 561-568
 Translations in the Exponential Orlicz Space with Gaussian Weight  (Giovanni Pistone)....Pages 569-576
 On Mixture and Exponential Connection by Open Arcs  (Marina Santacroce, Paola Siri, Barbara Trivellato)....Pages 577-584
Front Matter ....Pages 585-585
 Applying Backward Nested Subspace Inference to Tori and Polyspheres  (Benjamin Eltzner, Stephan Huckemann)....Pages 587-594
 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 \(\mathbb {S}^2\)?  (Pierre-Yves Gousenbourger, Laurent Jacques, P.-A. Absil)....Pages 595-603
 Nonlocal Inpainting of Manifold-Valued Data on Finite Weighted Graphs  (Ronny Bergmann, Daniel Tenbrinck)....Pages 604-612
 Affine-Invariant Orders on the Set of Positive-Definite Matrices  (Cyrus Mostajeran, Rodolphe Sepulchre)....Pages 613-620
 Geodesic Least Squares Regression on the Gaussian Manifold with an Application in Astrophysics  (Geert Verdoolaege)....Pages 621-628
Front Matter ....Pages 629-629
 Warped Metrics for Location-Scale Models  (Salem Said, Yannick Berthoumieu)....Pages 631-638
 Bregman Divergences from Comparative Convexity  (Frank Nielsen, Richard Nock)....Pages 639-647
 Weighted Closed Form Expressions Based on Escort Distributions for Rényi Entropy Rates of Markov Chains  (Philippe Regnault, Valérie Girardin, Loïck Lhote)....Pages 648-656
 On the Error Exponent of a Random Tensor with Orthonormal Factor Matrices  (Rémy Boyer, Frank Nielsen)....Pages 657-664
 Coordinate-Wise Transformation and Stein-Type Densities  (Tomonari Sei)....Pages 665-672
Front Matter ....Pages 673-673
 Riemannian Online Algorithms for Estimating Mixture Model Parameters  (Paolo Zanini, Salem Said, Yannick Berthoumieu, Marco Congedo, Christian Jutten)....Pages 675-683
 Density Estimation for Compound Cox Processes on Hyperspheres  (Florent Chatelain, Nicolas Le Bihan, Jonathan H. Manton)....Pages 684-691
 Maximum Likelihood Estimators on Manifolds  (Hatem Hajri, Salem Said, Yannick Berthoumieu)....Pages 692-700
 Von Mises-Like Probability Density Functions on Surfaces  (Florence Nicol, Stéphane Puechmorel)....Pages 701-708
 Riemannian Gaussian Distributions on the Space of Positive-Definite Quaternion Matrices  (Salem Said, Nicolas Le Bihan, Jonathan H. Manton)....Pages 709-716
 A Family of Anisotropic Distributions on the Hyperbolic Plane  (Emmanuel Chevallier)....Pages 717-724
Front Matter ....Pages 725-725
 A Riemanian Approach to Blob Detection in Manifold-Valued Images  (Aleksei Shestov, Mikhail Kumskov)....Pages 727-735
 Co-occurrence Matrix of Covariance Matrices: A Novel Coding Model for the Classification of Texture Images  (Ioana Ilea, Lionel Bombrun, Salem Said, Yannick Berthoumieu)....Pages 736-744
 Positive Signal Spaces and the Mehler-Fock Transform  (Reiner Lenz)....Pages 745-753
 Bounding the Convergence Time of Local Probabilistic Evolution  (Simon Apers, Alain Sarlette, Francesco Ticozzi)....Pages 754-762
 Inductive Means and Sequences Applied to Online Classification of EEG  (Estelle M. Massart, Sylvain Chevallier)....Pages 763-770
Front Matter ....Pages 771-771
 Vessel Tracking via Sub-Riemannian Geodesics on the Projective Line Bundle  (Erik J. Bekkers, Remco Duits, Alexey Mashtakov, Yuri Sachkov)....Pages 773-781
 Anisotropic Edge-Based Balloon Eikonal Active Contours  (Da Chen, Laurent D. Cohen)....Pages 782-790
 Automatic Differentiation of Non-holonomic Fast Marching for Computing Most Threatening Trajectories Under Sensors Surveillance  (Jean-Marie Mirebeau, Johann Dreo)....Pages 791-800
 On the Existence of Paths Connecting Probability Distributions  (Rui F. Vigelis, Luiza H. F. de Andrade, Charles C. Cavalcante)....Pages 801-808
 Classification of Totally Umbilical CR-Statistical Submanifolds in Holomorphic Statistical Manifolds with Constant Holomorphic Curvature  (Michel Nguiffo Boyom, Aliya Naaz Siddiqui, Wan Ainun Mior Othman, Mohammad Hasan Shahid)....Pages 809-817
Front Matter ....Pages 819-819
 An Approach to Dynamical Distance Geometry  (Antonio Mucherino, Douglas S. Gonçalves)....Pages 821-829
 Distance Geometry in Linearizable Norms  (Claudia D’Ambrosio, Leo Liberti)....Pages 830-837
 Self-similar Geometry for Ad-Hoc Wireless Networks: Hyperfractals   (Philippe Jacquet, Dalia Popescu)....Pages 838-846
 Information Distances in Stochastic Resolution Analysis  (Radmila Pribić)....Pages 847-855
 k-Means Clustering with Hölder Divergences  (Frank Nielsen, Ke Sun, Stéphane Marchand-Maillet)....Pages 856-863
 Real Hypersurfaces in the Complex Quadric with Certain Condition of Normal Jacobi Operator  (Imsoon Jeong, Gyu Jong Kim, Young Jin Suh)....Pages 864-871
Back Matter ....Pages 873-877