{ "item_title" : "Geometric Science of Information", "item_author" : [" Frank Nielsen", "Frédéric Barbaresco "], "item_description" : "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-Wasserstein", "item_img_path" : "https://covers4.booksamillion.com/covers/bam/3/03/026/979/3030269795_b.jpg", "price_data" : { "retail_price" : "109.99", "online_price" : "109.99", "our_price" : "109.99", "club_price" : "109.99", "savings_pct" : "0", "savings_amt" : "0.00", "club_savings_pct" : "0", "club_savings_amt" : "0.00", "discount_pct" : "10", "store_price" : "" } }

Overview

Customers Also Bought

Details