The Resource The structure and stability of persistence modules, Frédéric Chazal, Vin de Silva, Marc Glisse, Steve Oudot
The structure and stability of persistence modules, Frédéric Chazal, Vin de Silva, Marc Glisse, Steve Oudot
Resource Information
The item The structure and stability of persistence modules, Frédéric Chazal, Vin de Silva, Marc Glisse, Steve Oudot represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.This item is available to borrow from 1 library branch.
Resource Information
The item The structure and stability of persistence modules, Frédéric Chazal, Vin de Silva, Marc Glisse, Steve Oudot represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.
This item is available to borrow from 1 library branch.
- Summary
- This book is a comprehensive treatment of the theory of persistence modules over the real line. It presents a set of mathematical tools to analyse the structure and to establish the stability of such modules, providing a sound mathematical framework for the study of persistence diagrams. Completely self-contained, this brief introduces the notion of persistence measure and makes extensive use of a new calculus of quiver representations to facilitate explicit computations. Appealing to both beginners and experts in the subject, The Structure and Stability of Persistence Modules provides a purely algebraic presentation of persistence, and thus complements the existing literature, which focuses mainly on topological and algorithmic aspects
- Language
- eng
- Extent
- 1 online resource
- Contents
-
- Preface; Acknowledgments; Contents; 1 Introduction; 1.1 A Brief History of Persistence; 1.2 Main Contributions; 1.3 Application: Stable Descriptors for Metric Spaces; 1.4 Application: Stable Clustering Using Persistence; 1.5 Recommended Reading; 1.6 Organisation; 1.7 Multisets; 2 Persistence Modules; 2.1 Persistence Modules Over a Real Parameter; 2.2 Index Posets; 2.3 Module Categories; 2.4 Interval Modules; 2.5 Interval Decomposition; 2.6 The Decomposition Persistence Diagram; 2.7 Quiver Calculations; 3 Rectangle Measures; 3.1 The Persistence Measure; 3.2 The Persistence Measure (Continued)
- 3.3 Abstract r-Measures3.4 Equivalence of Measures and Diagrams; 3.5 Non-finite Measures; 3.6 Measures and Diagrams in the Extended Plane; 3.7 The Measure Persistence Diagram; 3.8 Tameness; 3.9 Tameness (Continued); 3.10 Vanishing Lemmas; 3.11 Vanishing Lemmas (Continued); 3.12 Finite Approximations; 4 Interleaving; 4.1 Shifted Homomorphisms; 4.2 Interleaving; 4.3 Interleaving (Continued); 4.4 The Interpolation Lemma; 4.5 The Interpolation Lemma (Continued); 5 The Isometry Theorem; 5.1 The Interleaving Distance; 5.2 The Bottleneck Distance; 5.3 The Bottleneck Distance (Continued)
- 5.4 The Isometry Theorem5.5 The Converse Stability Theorem; 5.6 The Stability Theorem; 5.7 The Measure Stability Theorem; 5.8 The Measure Stability Theorem (Continued); 6 Variations; 6.1 Partial Interleavings; 6.2 Extended Persistence; References; Index
- Isbn
- 9783319425450
- Label
- The structure and stability of persistence modules
- Title
- The structure and stability of persistence modules
- Statement of responsibility
- Frédéric Chazal, Vin de Silva, Marc Glisse, Steve Oudot
- Language
- eng
- Summary
- This book is a comprehensive treatment of the theory of persistence modules over the real line. It presents a set of mathematical tools to analyse the structure and to establish the stability of such modules, providing a sound mathematical framework for the study of persistence diagrams. Completely self-contained, this brief introduces the notion of persistence measure and makes extensive use of a new calculus of quiver representations to facilitate explicit computations. Appealing to both beginners and experts in the subject, The Structure and Stability of Persistence Modules provides a purely algebraic presentation of persistence, and thus complements the existing literature, which focuses mainly on topological and algorithmic aspects
- Cataloging source
- N$T
- Dewey number
- 512/.42
- Illustrations
- illustrations
- Index
- index present
- LC call number
- QA247
- Literary form
- non fiction
- Nature of contents
-
- dictionaries
- bibliography
- http://library.link/vocab/relatedWorkOrContributorDate
-
- 1971-
- 1971-
- 1979-
- http://library.link/vocab/relatedWorkOrContributorName
-
- Chazal, Frédéric
- De Silva, Vin
- Glisse, Marc
- Oudot, Steve Y.
- Series statement
- SpringerBriefs in mathematics,
- http://library.link/vocab/subjectName
- Modules (Algebra)
- Label
- The structure and stability of persistence modules, Frédéric Chazal, Vin de Silva, Marc Glisse, Steve Oudot
- Antecedent source
- unknown
- Bibliography note
- Includes bibliographical references and index
- Carrier category
- online resource
- Carrier category code
-
- cr
- Carrier MARC source
- rdacarrier
- Color
- multicolored
- Content category
- text
- Content type code
-
- txt
- Content type MARC source
- rdacontent
- Contents
-
- Preface; Acknowledgments; Contents; 1 Introduction; 1.1 A Brief History of Persistence; 1.2 Main Contributions; 1.3 Application: Stable Descriptors for Metric Spaces; 1.4 Application: Stable Clustering Using Persistence; 1.5 Recommended Reading; 1.6 Organisation; 1.7 Multisets; 2 Persistence Modules; 2.1 Persistence Modules Over a Real Parameter; 2.2 Index Posets; 2.3 Module Categories; 2.4 Interval Modules; 2.5 Interval Decomposition; 2.6 The Decomposition Persistence Diagram; 2.7 Quiver Calculations; 3 Rectangle Measures; 3.1 The Persistence Measure; 3.2 The Persistence Measure (Continued)
- 3.3 Abstract r-Measures3.4 Equivalence of Measures and Diagrams; 3.5 Non-finite Measures; 3.6 Measures and Diagrams in the Extended Plane; 3.7 The Measure Persistence Diagram; 3.8 Tameness; 3.9 Tameness (Continued); 3.10 Vanishing Lemmas; 3.11 Vanishing Lemmas (Continued); 3.12 Finite Approximations; 4 Interleaving; 4.1 Shifted Homomorphisms; 4.2 Interleaving; 4.3 Interleaving (Continued); 4.4 The Interpolation Lemma; 4.5 The Interpolation Lemma (Continued); 5 The Isometry Theorem; 5.1 The Interleaving Distance; 5.2 The Bottleneck Distance; 5.3 The Bottleneck Distance (Continued)
- 5.4 The Isometry Theorem5.5 The Converse Stability Theorem; 5.6 The Stability Theorem; 5.7 The Measure Stability Theorem; 5.8 The Measure Stability Theorem (Continued); 6 Variations; 6.1 Partial Interleavings; 6.2 Extended Persistence; References; Index
- Dimensions
- unknown
- Extent
- 1 online resource
- File format
- unknown
- Form of item
- online
- Isbn
- 9783319425450
- Level of compression
- unknown
- Media category
- computer
- Media MARC source
- rdamedia
- Media type code
-
- c
- Other physical details
- illustrations.
- Quality assurance targets
- not applicable
- Reformatting quality
- unknown
- Sound
- unknown sound
- Specific material designation
- remote
- System control number
-
- SPR960458101
- ocn960458101
- Label
- The structure and stability of persistence modules, Frédéric Chazal, Vin de Silva, Marc Glisse, Steve Oudot
- Antecedent source
- unknown
- Bibliography note
- Includes bibliographical references and index
- Carrier category
- online resource
- Carrier category code
-
- cr
- Carrier MARC source
- rdacarrier
- Color
- multicolored
- Content category
- text
- Content type code
-
- txt
- Content type MARC source
- rdacontent
- Contents
-
- Preface; Acknowledgments; Contents; 1 Introduction; 1.1 A Brief History of Persistence; 1.2 Main Contributions; 1.3 Application: Stable Descriptors for Metric Spaces; 1.4 Application: Stable Clustering Using Persistence; 1.5 Recommended Reading; 1.6 Organisation; 1.7 Multisets; 2 Persistence Modules; 2.1 Persistence Modules Over a Real Parameter; 2.2 Index Posets; 2.3 Module Categories; 2.4 Interval Modules; 2.5 Interval Decomposition; 2.6 The Decomposition Persistence Diagram; 2.7 Quiver Calculations; 3 Rectangle Measures; 3.1 The Persistence Measure; 3.2 The Persistence Measure (Continued)
- 3.3 Abstract r-Measures3.4 Equivalence of Measures and Diagrams; 3.5 Non-finite Measures; 3.6 Measures and Diagrams in the Extended Plane; 3.7 The Measure Persistence Diagram; 3.8 Tameness; 3.9 Tameness (Continued); 3.10 Vanishing Lemmas; 3.11 Vanishing Lemmas (Continued); 3.12 Finite Approximations; 4 Interleaving; 4.1 Shifted Homomorphisms; 4.2 Interleaving; 4.3 Interleaving (Continued); 4.4 The Interpolation Lemma; 4.5 The Interpolation Lemma (Continued); 5 The Isometry Theorem; 5.1 The Interleaving Distance; 5.2 The Bottleneck Distance; 5.3 The Bottleneck Distance (Continued)
- 5.4 The Isometry Theorem5.5 The Converse Stability Theorem; 5.6 The Stability Theorem; 5.7 The Measure Stability Theorem; 5.8 The Measure Stability Theorem (Continued); 6 Variations; 6.1 Partial Interleavings; 6.2 Extended Persistence; References; Index
- Dimensions
- unknown
- Extent
- 1 online resource
- File format
- unknown
- Form of item
- online
- Isbn
- 9783319425450
- Level of compression
- unknown
- Media category
- computer
- Media MARC source
- rdamedia
- Media type code
-
- c
- Other physical details
- illustrations.
- Quality assurance targets
- not applicable
- Reformatting quality
- unknown
- Sound
- unknown sound
- Specific material designation
- remote
- System control number
-
- SPR960458101
- ocn960458101
Library Links
Embed
Settings
Select options that apply then copy and paste the RDF/HTML data fragment to include in your application
Embed this data in a secure (HTTPS) page:
Layout options:
Include data citation:
<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.liverpool.ac.uk/portal/The-structure-and-stability-of-persistence/OBKZb8jk7cg/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.liverpool.ac.uk/portal/The-structure-and-stability-of-persistence/OBKZb8jk7cg/">The structure and stability of persistence modules, Frédéric Chazal, Vin de Silva, Marc Glisse, Steve Oudot</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.liverpool.ac.uk/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.liverpool.ac.uk/">University of Liverpool</a></span></span></span></span></div>
Note: Adjust the width and height settings defined in the RDF/HTML code fragment to best match your requirements
Preview
Cite Data - Experimental
Data Citation of the Item The structure and stability of persistence modules, Frédéric Chazal, Vin de Silva, Marc Glisse, Steve Oudot
Copy and paste the following RDF/HTML data fragment to cite this resource
<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.liverpool.ac.uk/portal/The-structure-and-stability-of-persistence/OBKZb8jk7cg/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.liverpool.ac.uk/portal/The-structure-and-stability-of-persistence/OBKZb8jk7cg/">The structure and stability of persistence modules, Frédéric Chazal, Vin de Silva, Marc Glisse, Steve Oudot</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.liverpool.ac.uk/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.liverpool.ac.uk/">University of Liverpool</a></span></span></span></span></div>
