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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

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Table of Contents

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Front/Back Matter

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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