The Structure and Stability of Persistence Modules (eBook)

Frédéric Chazal, Vin de Silva, Marc Glisse, Steve Oudot (Autoren)

eBook Download: PDF

2016 | 1st ed. 2016
X, 120 Seiten
Springer International Publishing (Verlag)
978-3-319-42545-0 (ISBN)

Infos

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.

Inhalt

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

Produkt-Details

• Erscheint lt. Verlag: 8.10.2016
• Reihe/Serie: SpringerBriefs in Mathematics
• Reihe/Serie: SpringerBriefs in Mathematics
• Zusatzinfo: X, 120 p. 17 illus., 15 illus. in color.
• Verlagsort: Cham
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Technik
• Schlagworte: applied algebraic topology • persistence diagrams • persistence modules • persistence stability theorem • quiver representations • topological data analysis • topological persistence
• ISBN-10: 3-319-42545-5 / 3319425455
• ISBN-13: 978-3-319-42545-0 / 9783319425450