Geometric Science of Information
Springer International Publishing (Verlag)
978-3-030-26979-1 (ISBN)
The 79 full papers presented in this volume were carefully reviewed and selected from 105 submissions. They cover all the main topics and highlights in the domain of geometric science of information, including information geometry manifolds of structured data/information and their advanced applications.
Part I: Shape Space.- On geometric properties of the textile set and strict textile set.- Inexact elastic shape matching in the square root normal field framework.- Signatures in Shape Analysis: an Efficient Approach to Motion Identification.- Dilation operator approach for time/Doppler spectra characterization on SU(n).- Selective metamorphosis for growth modelling with applications to landmarks.- Part II: Geometric Mechanics.- Intrinsic Incremental Mechanics.- -Multi-symplectic Extension of Lie Group Thermodynamics for Covariant Field Theories.- Euler-Poincare equation for Lie groups with non null symplectic cohomology. Application to the Mechanics.- Geometric numerical methods for mechanics.- Souriau Exponential Map Algorithm for Machine Learning on Matrix Lie Groups.- Part 3: Geometry of Tensor-Valued Data.- R-Complex Finsler Information Geometry Applied to Manifolds of Systems.- Minkowski Sum of Ellipsoids and Means of Covariance Matrices.- Hyperquaternions: An Efficient Mathematical Formalism for Geometry.- Alpha-power sums on symmetric cones.- Packing Bounds for Outer Products with Applications to Compressive Sensing.- Part 4: Lie Group Machine Learning.- On a method to construct exponential families by representation theory.- Lie Group Machine Learning & Gibbs Density on Poincare Unit Disk from Souriau Lie Groups Thermodynamics and SU(1,1) Coadjoint Orbits.- Irreversible Langevin MCMC on Lie Groups.- Predicting Bending Moments with Machine Learning.- The exponential of nilpotent supergroups in the theory of Harish-Chandra representations.- Part 5: Geometric structures in thermodynamics and statistical physics.- Dirac structures in open thermodynamics.- From variational to single and double bracket formulations in nonequilibrium thermodynamics of simple systems.- A omological Approach to Belief Propagation and Bethe Approximations.- - About some systems-theoretic properties of Port Thermodynamic systems.- Expectation variables on a para-contact metric manifold exactly derived from master equations.- Part 6: Monotone embedding and affine immersion of probability models.- Doubly autoparallel structure and its applications.- Toeplitz Hermitian Positive Definite Matrix Machine Learning based on Fisher metric.- Deformed exponential and the behavior of the normalizing function.- Normalization problems for deformed exponential families.- New Geometry of parametric statistical Models.- Part 7: Divergence Geometry.- The Bregman chord divergence.- Testing the number and nature of components in a mixture distribution.- Robust etsimation by means of scaled Bregman power distances. Part I: Non-homogeneous data.- Robust estimation by means of scaled Bregman power distances. Part II: Extreme values.- Part 8: Computational Information Geometry.- Topological methods for unsupervised learning.- Geometry and fixed-rate quantization in Riemannian metric spaces induced by separable Bregman divergences.- The statistical Minkowski distances: Closed-form formula for Gaussian Mixture Models.- Parameter estimation with generalized empirical localization.- Properties of the cross entropy of ARMA processes.- Part 9: Statistical Manifold & Hessian Information Geometry.- Inequalities for Statistical Submanifolds in Hessian Manifolds of Constant Hessian curvature.- Inequalities for statistical submanifolds in sasakian statistical manifolds.- Generalized Wintgen Inequality for Legendrian Submanifolds in Sasakian statistical manifolds.- Logarithmic divergence: geometry and interpretation of curvature.- Hessian Curvature and Optimal Transport.- Part 10: Non-parametric Information Geometry.- Divergence functions in Information Geometry.- Sobolev Statistical Manifolds and Exponential Models.- Minimization of the Kullback-Leibler divergence over a log-normal exponential arc.- Riemannian distance and diameter of the space of probability measures and the parametrix.- Part 11: Statistics on non-linear data.- A unified formulation for the Bures-Wassersteina
| Erscheinungsdatum | 04.08.2019 |
|---|---|
| Reihe/Serie | Image Processing, Computer Vision, Pattern Recognition, and Graphics | Lecture Notes in Computer Science |
| Zusatzinfo | XIX, 770 p. 317 illus., 53 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 1193 g |
| Themenwelt | Informatik ► Grafik / Design ► Digitale Bildverarbeitung |
| Informatik ► Theorie / Studium ► Künstliche Intelligenz / Robotik | |
| Schlagworte | Adaptive Control Systems • Applications • Artificial Intelligence • Clustering • clustering algorithms • Computational Geometry • Computer Science • conference proceedings • image coding • Image Processing • image reconstruction • Informatics • machine learning • Motion Estimation • Neural networks • Numerical Methods • optical flows • Probability • Probability Distribution • random variables • Research • Robotics • Signal Processing • variational methods • vector quantization |
| ISBN-10 | 3-030-26979-5 / 3030269795 |
| ISBN-13 | 978-3-030-26979-1 / 9783030269791 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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