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The Resource Handbook of Variational Methods for Nonlinear Geometric Data, edited by Philipp Grohs, Martin Holler, Andreas Weinmann, (electronic resource)

Handbook of Variational Methods for Nonlinear Geometric Data, edited by Philipp Grohs, Martin Holler, Andreas Weinmann, (electronic resource)

Editor
Contributor
Summary
This book explains how variational methods have evolved to being amongst the most powerful tools for applied mathematics. They involve techniques from various branches of mathematics such as statistics, modeling, optimization, numerical mathematics and analysis. The vast majority of research on variational methods, however, is focused on data in linear spaces. Variational methods for non-linear data is currently an emerging research topic. As a result, and since such methods involve various branches of mathematics, there is a plethora of different, recent approaches dealing with different aspects of variational methods for nonlinear geometric data. Research results are rather scattered and appear in journals of different mathematical communities. The main purpose of the book is to account for that by providing, for the first time, a comprehensive collection of different research directions and existing approaches in this context. It is organized in a way that leading researchers from the different fields provide an introductory overview of recent research directions in their respective discipline. As such, the book is a unique reference work for both newcomers in the field of variational methods for non-linear geometric data, as well as for established experts that aim at to exploit new research directions or collaborations. Chapter 9 of this book is available open access under a CC BY 4.0 license at link.springer.com.--
Language
eng
Work
Publication
Edition
1st ed. 2020.
Extent
1 online resource (XXVI, 701 pages)
Contents
  • 1. Geometric Finite Elements
  • 2. Non-smooth variational regularization for processing manifold-valued data
  • 3. Lifting methods for manifold-valued variational problems
  • 4. Geometric subdivision and multiscale transforms
  • 5. Variational Methods for Discrete Geometric Functionals
  • 6 Variational methods for fluid-structure interactions
  • 7. Convex lifting-type methods for curvature regularization
  • 8. Assignment Flows
  • 9. Geometric methods on low-rank matrix and tensor manifolds
  • 10. Statistical Methods Generalizing Principal Component Analysis to Non-Euclidean Spaces
  • 11. Advances in Geometric Statistics for manifold dimension reduction
  • 12. Deep Variational Inference.­­- 13. Shape Analysis of Functional Data
  • 14. Statistical Analysis of Trajectories of Multi-Modality Data
  • 15. Geometric Metrics for Topological Representations
  • 16. On Geometric Invariants, Learning, and Recognition of Shapes and Forms
  • 17. Sub-Riemannian Methods in Shape Analysis
  • 18. First order methods for optimization on Riemannian manifolds
  • 19. Recent Advances in Stochastic Riemannian Optimization
  • 20. Averaging symmetric positive-definite matrices
  • 21. Rolling Maps and Nonlinear Data
  • 22. Manifold-valued Data in Medical Imaging Applications
  • 23. The Riemannian and Affine Geometry of Facial Expression and Action Recognition
  • 24. Biomedical Applications of Geometric Functional Data Analysis
Isbn
9783030313517
Link
https://eui.idm.oclc.org/login?url=https://doi.org/10.1007/978-3-030-31351-7
Instance
Label
Handbook of Variational Methods for Nonlinear Geometric Data
Title
Handbook of Variational Methods for Nonlinear Geometric Data
Statement of responsibility
edited by Philipp Grohs, Martin Holler, Andreas Weinmann
Contributor
Editor
Subject
Language
eng
Summary
This book explains how variational methods have evolved to being amongst the most powerful tools for applied mathematics. They involve techniques from various branches of mathematics such as statistics, modeling, optimization, numerical mathematics and analysis. The vast majority of research on variational methods, however, is focused on data in linear spaces. Variational methods for non-linear data is currently an emerging research topic. As a result, and since such methods involve various branches of mathematics, there is a plethora of different, recent approaches dealing with different aspects of variational methods for nonlinear geometric data. Research results are rather scattered and appear in journals of different mathematical communities. The main purpose of the book is to account for that by providing, for the first time, a comprehensive collection of different research directions and existing approaches in this context. It is organized in a way that leading researchers from the different fields provide an introductory overview of recent research directions in their respective discipline. As such, the book is a unique reference work for both newcomers in the field of variational methods for non-linear geometric data, as well as for established experts that aim at to exploit new research directions or collaborations. Chapter 9 of this book is available open access under a CC BY 4.0 license at link.springer.com.--
Assigning source
Provided by publisher
Image bit depth
0
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
  • Grohs, Philipp
  • Holler, Martin
  • Weinmann, Andreas
Series statement
  • Springer eBooks.
  • Springer eBooks.
http://library.link/vocab/subjectName
  • Computer mathematics
  • Computer science—Mathematics
  • Optical data processing
Label
Handbook of Variational Methods for Nonlinear Geometric Data, edited by Philipp Grohs, Martin Holler, Andreas Weinmann, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=https://doi.org/10.1007/978-3-030-31351-7
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
1. Geometric Finite Elements -- 2. Non-smooth variational regularization for processing manifold-valued data -- 3. Lifting methods for manifold-valued variational problems -- 4. Geometric subdivision and multiscale transforms -- 5. Variational Methods for Discrete Geometric Functionals -- 6 Variational methods for fluid-structure interactions -- 7. Convex lifting-type methods for curvature regularization -- 8. Assignment Flows -- 9. Geometric methods on low-rank matrix and tensor manifolds -- 10. Statistical Methods Generalizing Principal Component Analysis to Non-Euclidean Spaces -- 11. Advances in Geometric Statistics for manifold dimension reduction -- 12. Deep Variational Inference.­­- 13. Shape Analysis of Functional Data -- 14. Statistical Analysis of Trajectories of Multi-Modality Data -- 15. Geometric Metrics for Topological Representations -- 16. On Geometric Invariants, Learning, and Recognition of Shapes and Forms -- 17. Sub-Riemannian Methods in Shape Analysis -- 18. First order methods for optimization on Riemannian manifolds -- 19. Recent Advances in Stochastic Riemannian Optimization -- 20. Averaging symmetric positive-definite matrices -- 21. Rolling Maps and Nonlinear Data -- 22. Manifold-valued Data in Medical Imaging Applications -- 23. The Riemannian and Affine Geometry of Facial Expression and Action Recognition -- 24. Biomedical Applications of Geometric Functional Data Analysis
Control code
978-3-030-31351-7
Dimensions
unknown
Edition
1st ed. 2020.
Extent
1 online resource (XXVI, 701 pages)
File format
multiple file formats
Form of item
  • online
  • electronic
Isbn
9783030313517
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
159 illustrations, 125 illustrations in color.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1150167241
Label
Handbook of Variational Methods for Nonlinear Geometric Data, edited by Philipp Grohs, Martin Holler, Andreas Weinmann, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=https://doi.org/10.1007/978-3-030-31351-7
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
1. Geometric Finite Elements -- 2. Non-smooth variational regularization for processing manifold-valued data -- 3. Lifting methods for manifold-valued variational problems -- 4. Geometric subdivision and multiscale transforms -- 5. Variational Methods for Discrete Geometric Functionals -- 6 Variational methods for fluid-structure interactions -- 7. Convex lifting-type methods for curvature regularization -- 8. Assignment Flows -- 9. Geometric methods on low-rank matrix and tensor manifolds -- 10. Statistical Methods Generalizing Principal Component Analysis to Non-Euclidean Spaces -- 11. Advances in Geometric Statistics for manifold dimension reduction -- 12. Deep Variational Inference.­­- 13. Shape Analysis of Functional Data -- 14. Statistical Analysis of Trajectories of Multi-Modality Data -- 15. Geometric Metrics for Topological Representations -- 16. On Geometric Invariants, Learning, and Recognition of Shapes and Forms -- 17. Sub-Riemannian Methods in Shape Analysis -- 18. First order methods for optimization on Riemannian manifolds -- 19. Recent Advances in Stochastic Riemannian Optimization -- 20. Averaging symmetric positive-definite matrices -- 21. Rolling Maps and Nonlinear Data -- 22. Manifold-valued Data in Medical Imaging Applications -- 23. The Riemannian and Affine Geometry of Facial Expression and Action Recognition -- 24. Biomedical Applications of Geometric Functional Data Analysis
Control code
978-3-030-31351-7
Dimensions
unknown
Edition
1st ed. 2020.
Extent
1 online resource (XXVI, 701 pages)
File format
multiple file formats
Form of item
  • online
  • electronic
Isbn
9783030313517
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
159 illustrations, 125 illustrations in color.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1150167241

Subject

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