The Structure and Stability of Persistence Modules

Beschreibung

This book is a comprehensive treatment of the theory of persistence modules over the real line. It presents a set of mathematical tools to analyse the structure and to establish the stability of such modules, providing a sound mathematical framework for the study of persistence diagrams. Completely self-contained, this brief introduces the notion of persistence measure and makes extensive use of a new calculus of quiver representations to facilitate explicit computations.
Appealing to both beginners and experts in the subject, The Structure and Stability of Persistence Modules provides a purely algebraic presentation of persistence, and thus complements the existing literature, which focuses mainly on topological and algorithmic aspects.
Provides a comprehensive treatment of 1-parameter persistence modules Presents new tools for studying persistence modules in wide generality Introduces the measure-theory approach to persistence diagrams Offers a definitive treatment of the stability theorem

Autor*in

Frédéric Chazal

Themen in »The Structure and Stability of Persistence Modules«

topological persistence persistence modules persistence diagrams persistence stability theorem topological data analysis applied algebraic topology quiver representations

Stimmen zu »The Structure and Stability of Persistence Modules«

“This book is a very nice contribution to the subject of Topological Data Analysis. In this slim volume, the novice will find a collection of main results with their proofs and many references; additionally, experts will see persistence developed more generally than usual using measure theory. … There are many synthesizing comments throughout the text to help the reader put the material in context, and the writing itself is lucid.” (Michele Intermont, MAA Reviews, October, 2017)

“This monograph develops the theory of persistence modules over the real line in a manner that is well-motivated, accessible, thorough, and self-contained.” (Henry Hugh Adams, Mathematical Reviews, October, 2017)

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