| Softcover ISBN: | 978-1-4704-3443-4 |
| Product Code: | SURV/209.S |
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| eBook ISBN: | 978-1-4704-2795-5 |
| Product Code: | SURV/209.E |
| List Price: | $125.00 |
| MAA Member Price: | $112.50 |
| AMS Member Price: | $100.00 |
| Softcover ISBN: | 978-1-4704-3443-4 |
| eBook: ISBN: | 978-1-4704-2795-5 |
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| List Price: | $254.00 $191.50 |
| MAA Member Price: | $228.60 $172.35 |
| AMS Member Price: | $203.20 $153.20 |
| Softcover ISBN: | 978-1-4704-3443-4 |
| Product Code: | SURV/209.S |
| List Price: | $129.00 |
| MAA Member Price: | $116.10 |
| AMS Member Price: | $103.20 |
| eBook ISBN: | 978-1-4704-2795-5 |
| Product Code: | SURV/209.E |
| List Price: | $125.00 |
| MAA Member Price: | $112.50 |
| AMS Member Price: | $100.00 |
| Softcover ISBN: | 978-1-4704-3443-4 |
| eBook ISBN: | 978-1-4704-2795-5 |
| Product Code: | SURV/209.S.B |
| List Price: | $254.00 $191.50 |
| MAA Member Price: | $228.60 $172.35 |
| AMS Member Price: | $203.20 $153.20 |
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Book DetailsMathematical Surveys and MonographsVolume: 209; 2015; 218 ppMSC: 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.
ReadershipGraduate students and researchers interested in algebraic topology and applications to data analysis.
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Table of Contents
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Chapters
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Introduction
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Part 1. Theoretical foundations
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Chapter 1. Algebraic persistence
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Chapter 2. Topological persistence
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Chapter 3. Stability
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Part 2. Applications
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Chapter 4. Topological inference
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Chapter 5. Topological inference 2.0
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Chapter 6. Clustering
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Chapter 7. Signatures for metric spaces
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Part 3. Perspectives
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Chapter 8. New trends in topological data analysis
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Chapter 9. Further prospects on the theory
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Appendix A. Introduction to quiver theory with a view toward persistence
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Additional Material
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RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
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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
