This book provides a broad and modern view of persistence theory, 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 can be used as a text for a course on applied topology or data analysis.
Theoretical foundations: Algebraic persistence
Topological persistence
Stability
Applications: Topological inference
Topological inference 2.0
Clustering
Signatures for metric spaces
Perspectives: New trends in topological data analysis
Further prospects on the theory
Introduction to quiver theory with a view toward persistence
Bibliography
List of figures
Index.
Steve Y. Oudot, Inria Saclay, Palaiseau, France.
