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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)
DOI: https://doi.org/10.1090/surv/209
MathSciNet review: MR3408277
MSC: Primary 55N35; Secondary 16G20, 55U10, 62-07, 68U05
Table of Contents
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Front/Back Matter
Chapters
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