Persistence Theory: From Quiver Representations to Data Analysis
About this Title
Steve Y. Oudot, Inria Saclay, Palaiseau, France
Publication: Mathematical Surveys and Monographs
Publication Year: 2015; Volume 209
ISBNs: 978-1-4704-2545-6 (print); 978-1-4704-2795-5 (online)
MathSciNet review: MR3408277
MSC: Primary 55N35; Secondary 16G20, 55U10, 62-07, 68U05
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.
Table of Contents
Part 1. Theoretical foundations
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