The Structure and Stability of Persistence Modules

1. Auflage 2016
ISBN: 978-3-319-42543-6
Verlag: Springer

Buch, Englisch, 120 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 2117 g

Reihe: SpringerBriefs in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Chazal, Frédéric

de Silva, Vin

Glisse, Marc

Oudot, Steve

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker
• Mathematik | Informatik Mathematik Algebra

Inhaltsverzeichnis

Introduction.- Persistence Modules.- Rectangle Measures.- Interleaving.- The Isometry Theorem.- Variations.- References.- Index.