The Resource Algorithmic advances in Riemannian geometry and applications : for machine learning, computer vision, statistics, and optimization, Ha Quang Minh, Vittorio Murino, editors
Algorithmic advances in Riemannian geometry and applications : for machine learning, computer vision, statistics, and optimization, Ha Quang Minh, Vittorio Murino, editors
Resource Information
The item Algorithmic advances in Riemannian geometry and applications : for machine learning, computer vision, statistics, and optimization, Ha Quang Minh, Vittorio Murino, editors represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Massey University Library, University of New Zealand.This item is available to borrow from 1 library branch.
Resource Information
The item Algorithmic advances in Riemannian geometry and applications : for machine learning, computer vision, statistics, and optimization, Ha Quang Minh, Vittorio Murino, editors represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Massey University Library, University of New Zealand.
This item is available to borrow from 1 library branch.
 Summary
 This book presents a selection of the most recent algorithmic advances in Riemannian geometry in the context of machine learning, statistics, optimization, computer vision, and related fields. The unifying theme of the different chapters in the book is the exploitation of the geometry of data using the mathematical machinery of Riemannian geometry. As demonstrated by all the chapters in the book, when the data is intrinsically nonEuclidean, the utilization of this geometrical information can lead to better algorithms that can capture more accurately the structures inherent in the data, leading ultimately to better empirical performance. This book is not intended to be an encyclopedic compilation of the applications of Riemannian geometry. Instead, it focuses on several important research directions that are currently actively pursued by researchers in the field. These include statistical modeling and analysis on manifolds,optimization on manifolds, Riemannian manifolds and kernel methods, and dictionary learning and sparse coding on manifolds. Examples of applications include novel algorithms for Monte Carlo sampling and Gaussian Mixture Model fitting, 3D brain image analysis,image classification, action recognition, and motion tracking
 Language
 eng
 Extent
 1 online resource
 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 BoxType Constraints; 2.3.3 General qNorm 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 gConvexity: 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 InfiniteDimensional Settings5.1 Introduction; 5.2 Covariance Matrices for Data Representation; 5.3 InfiniteDimensional 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 AffineInvariant Distance
 Isbn
 9783319450261
 Label
 Algorithmic advances in Riemannian geometry and applications : for machine learning, computer vision, statistics, and optimization
 Title
 Algorithmic advances in Riemannian geometry and applications
 Title remainder
 for machine learning, computer vision, statistics, and optimization
 Statement of responsibility
 Ha Quang Minh, Vittorio Murino, editors
 Language
 eng
 Summary
 This book presents a selection of the most recent algorithmic advances in Riemannian geometry in the context of machine learning, statistics, optimization, computer vision, and related fields. The unifying theme of the different chapters in the book is the exploitation of the geometry of data using the mathematical machinery of Riemannian geometry. As demonstrated by all the chapters in the book, when the data is intrinsically nonEuclidean, the utilization of this geometrical information can lead to better algorithms that can capture more accurately the structures inherent in the data, leading ultimately to better empirical performance. This book is not intended to be an encyclopedic compilation of the applications of Riemannian geometry. Instead, it focuses on several important research directions that are currently actively pursued by researchers in the field. These include statistical modeling and analysis on manifolds,optimization on manifolds, Riemannian manifolds and kernel methods, and dictionary learning and sparse coding on manifolds. Examples of applications include novel algorithms for Monte Carlo sampling and Gaussian Mixture Model fitting, 3D brain image analysis,image classification, action recognition, and motion tracking
 Dewey number
 516.373
 Illustrations
 illustrations
 Index
 index present
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 http://library.link/vocab/relatedWorkOrContributorName

 Minh, Ha Quang,
 Murino, Vittorio,
 Series statement
 Advances in computer vision and pattern recognition
 http://library.link/vocab/subjectName

 Geometry, Riemannian
 Riemannian manifolds
 Machine learning
 Computer vision
 Statistics
 optimization
 Label
 Algorithmic advances in Riemannian geometry and applications : for machine learning, computer vision, statistics, and optimization, Ha Quang Minh, Vittorio Murino, editors
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references and index
 Color
 multicolored
 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 BoxType Constraints; 2.3.3 General qNorm 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 gConvexity: 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 InfiniteDimensional Settings5.1 Introduction; 5.2 Covariance Matrices for Data Representation; 5.3 InfiniteDimensional 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 AffineInvariant Distance
 Control code
 ocn960048865
 Dimensions
 unknown
 Extent
 1 online resource
 File format
 unknown
 Form of item
 online
 Isbn
 9783319450261
 Level of compression
 unknown
 Other physical details
 illustrations
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number
 (OCoLC)960048865
 Label
 Algorithmic advances in Riemannian geometry and applications : for machine learning, computer vision, statistics, and optimization, Ha Quang Minh, Vittorio Murino, editors
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references and index
 Color
 multicolored
 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 BoxType Constraints; 2.3.3 General qNorm 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 gConvexity: 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 InfiniteDimensional Settings5.1 Introduction; 5.2 Covariance Matrices for Data Representation; 5.3 InfiniteDimensional 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 AffineInvariant Distance
 Control code
 ocn960048865
 Dimensions
 unknown
 Extent
 1 online resource
 File format
 unknown
 Form of item
 online
 Isbn
 9783319450261
 Level of compression
 unknown
 Other physical details
 illustrations
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number
 (OCoLC)960048865
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