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Persistence Theory: From Quiver Representations to Data Analysis

Steve Y. Oudot Inria Saclay, Palaiseau, France
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Softcover ISBN: 978-1-4704-3443-4
Product Code: SURV/209.S
List Price: $69.00 MAA Member Price:$62.10
AMS Member Price: $55.20 Electronic ISBN: 978-1-4704-2795-5 Product Code: SURV/209.E List Price:$65.00
MAA Member Price: $58.50 AMS Member Price:$52.00
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List Price: $103.50 MAA Member Price:$93.15
AMS Member Price: $82.80 Click above image for expanded view Persistence Theory: From Quiver Representations to Data Analysis Steve Y. Oudot Inria Saclay, Palaiseau, France Available Formats:  Softcover ISBN: 978-1-4704-3443-4 Product Code: SURV/209.S  List Price:$69.00 MAA Member Price: $62.10 AMS Member Price:$55.20
 Electronic ISBN: 978-1-4704-2795-5 Product Code: SURV/209.E
 List Price: $65.00 MAA Member Price:$58.50 AMS Member Price: $52.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$103.50 MAA Member Price: $93.15 AMS Member Price:$82.80
• Book Details

Mathematical Surveys and Monographs
Volume: 2092015; 218 pp
MSC: Primary 62; 55; 16; 68;

Persistence theory emerged in the early 2000s as a new theory in the area of applied and computational topology. This book provides a broad and modern view of the subject, including its algebraic, topological, and algorithmic aspects. It also elaborates on applications in data analysis. The level of detail of the exposition has been set so as to keep a survey style, while providing sufficient insights into the proofs so the reader can understand the mechanisms at work.

The book is organized into three parts. The first part is dedicated to the foundations of persistence and emphasizes its connection to quiver representation theory. The second part focuses on its connection to applications through a few selected topics. The third part provides perspectives for both the theory and its applications. The book can be used as a text for a course on applied topology or data analysis.

Graduate students and researchers interested in algebraic topology and applications to data analysis.

• Chapters
• Introduction
• Part 1. Theoretical foundations
• Chapter 1. Algebraic persistence
• Chapter 2. Topological persistence
• Chapter 3. Stability
• Part 2. Applications
• Chapter 4. Topological inference
• Chapter 5. Topological inference 2.0
• Chapter 6. Clustering
• Chapter 7. Signatures for metric spaces
• Part 3. Perspectives
• Chapter 8. New trends in topological data analysis
• Chapter 9. Further prospects on the theory
• Appendix A. Introduction to quiver theory with a view toward persistence

• Requests

Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 2092015; 218 pp
MSC: Primary 62; 55; 16; 68;

Persistence theory emerged in the early 2000s as a new theory in the area of applied and computational topology. This book provides a broad and modern view of the subject, including its algebraic, topological, and algorithmic aspects. It also elaborates on applications in data analysis. The level of detail of the exposition has been set so as to keep a survey style, while providing sufficient insights into the proofs so the reader can understand the mechanisms at work.

The book is organized into three parts. The first part is dedicated to the foundations of persistence and emphasizes its connection to quiver representation theory. The second part focuses on its connection to applications through a few selected topics. The third part provides perspectives for both the theory and its applications. The book can be used as a text for a course on applied topology or data analysis.

Graduate students and researchers interested in algebraic topology and applications to data analysis.

• Chapters
• Introduction
• Part 1. Theoretical foundations
• Chapter 1. Algebraic persistence
• Chapter 2. Topological persistence
• Chapter 3. Stability
• Part 2. Applications
• Chapter 4. Topological inference
• Chapter 5. Topological inference 2.0
• Chapter 6. Clustering
• Chapter 7. Signatures for metric spaces
• Part 3. Perspectives
• Chapter 8. New trends in topological data analysis
• Chapter 9. Further prospects on the theory
• Appendix A. Introduction to quiver theory with a view toward persistence
Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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