Algorithmic advances in Riemannian geometry and applications : for machine learning, computer vision, statistics, and optimization /: for machine learning, computer vision, statistics, and optimization. ([2016])

• Record Type: Book
• Further Information: Note: Ha Quang Minh, Vittorio Murino, editors.
• Editors: Minh, Hà Quang; Murino, Vittorio
• Contents: Preface; Overview and Goals; Acknowledgments; Contents; Contributors; Introduction; Themes of the Volume; Organization of the Volume; 1 Bayesian Statistical Shape Analysis on the Manifold of Diffeomorphisms; 1.1 Introduction; 1.2 Mathematical Background; 1.2.1 Space of Diffeomorphisms; 1.2.2 Metrics on Diffeomorphisms; 1.2.3 Diffeomorphic Atlas Building with LDDMM; 1.3 A Bayesian Model for Atlas Building; 1.4 Estimation of Model Parameters; 1.4.1 Hamiltonian Monte Carlo (HMC) Sampling; 1.4.2 The Maximization Step; 1.5 Bayesian Principal Geodesic Analysis; 1.5.1 Probability Model. 1.5.2 Inference1.6 Results; References; 2 Sampling Constrained Probability Distributions Using Spherical Augmentation; 2.1 Introduction; 2.2 Preliminaries; 2.2.1 Hamiltonian Monte Carlo; 2.2.2 Lagrangian Monte Carlo; 2.3 Spherical Augmentation; 2.3.1 Ball Type Constraints; 2.3.2 Box-Type Constraints; 2.3.3 General q-Norm Constraints; 2.3.4 Functional Constraints; 2.4 Monte Carlo with Spherical Augmentation; 2.4.1 Common Settings; 2.4.2 Spherical Hamiltonian Monte Carlo; 2.4.3 Spherical LMC on Probability Simplex; 2.5 Experimental Results; 2.5.1 Truncated Multivariate Gaussian. 2.5.2 Bayesian Lasso2.5.3 Bridge Regression; 2.5.4 Reconstruction of Quantized Stationary Gaussian Process; 2.5.5 Latent Dirichlet Allocation on Wikipedia Corpus; 2.6 Discussion; References; 3 Geometric Optimization in Machine Learning; 3.1 Introduction; 3.2 Manifolds and Geodesic Convexity; 3.3 Beyond g-Convexity: Thompson Nonexpansivity; 3.3.1 Why Thompson Nonexpansivity?; 3.4 Manifold Optimization; 3.5 Applications; 3.5.1 Gaussian Mixture Models; 3.5.2 MLE for Elliptically Contoured Distributions; 3.5.3 Other Applications; References. 4 Positive Definite Matrices: Data Representation and Applications to Computer Vision4.1 Introduction; 4.1.1 Covariance Descriptors and Example Applications; 4.1.2 Geometry of SPD Matrices; 4.2 Application to Sparse Coding and Dictionary Learning; 4.2.1 Dictionary Learning with SPD Atoms; 4.2.2 Riemannian Dictionary Learning and Sparse Coding; 4.3 Applications of Sparse Coding; 4.3.1 Nearest Neighbors on Covariance Descriptors; 4.3.2 GDL Experiments; 4.3.3 Riemannian Dictionary Learning Experiments; 4.3.4 GDL Versus Riemannian Sparse Coding; 4.4 Conclusion and Future Work; References. 5 From Covariance Matrices to Covariance Operators: Data Representation from Finite to Infinite-Dimensional Settings5.1 Introduction; 5.2 Covariance Matrices for Data Representation; 5.3 Infinite-Dimensional Covariance Operators; 5.3.1 Positive Definite Kernels, Reproducing Kernel Hilbert Spaces, and Feature Maps; 5.3.2 Covariance Operators in RKHS and Data Representation; 5.4 Distances Between RKHS Covariance Operators; 5.4.1 Hilbert -- Schmidt Distance; 5.4.2 Riemannian Distances Between Covariance Operators; 5.4.3 The Affine-Invariant Distance.
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2016
• Extent: 1 online resource, illustrations
• Subjects: 516.373; Computer science; Geometry, Riemannian; Riemannian manifolds; Machine learning; Computer vision; Statistics; optimization; Optical pattern recognition; Engineering; Mathematical statistics; Artificial intelligence; MATHEMATICS -- Geometry -- General; Computer vision; Geometry, Riemannian; Machine learning; Riemannian manifolds; Statistics; Computers -- Intelligence (AI) & Semantics; Computers -- Mathematical & Statistical Software; Mathematics -- Applied; Artificial intelligence; Mathematical & statistical software; Mathematical modelling; Maths for computer scientists; Computers -- Computer Vision & Pattern Recognition; Pattern recognition; Computer Science; Pattern Recognition; Computational Intelligence; Statistics and Computing/Statistics Programs; Mathematical Applications in Computer Science; Artificial Intelligence (incl. Robotics); Probability and Statistics in Computer Science; Electronic books
• Languages: English
• ISBNs: 9783319450261; 3319450263
• Related ISBNs: 9783319450254; 3319450255
• Notes: Note: Includes bibliographical references and index.; Note: Print version record.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.