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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.
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.
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.
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.
Inhaltsverzeichnis
Introduction.- Persistence Modules.- Rectangle Measures.- Interleaving.- The Isometry Theorem.- Variations.- References.- Index.
Details
| Erscheinungsjahr: | 2016 |
|---|---|
| Genre: | Mathematik, Medizin, Naturwissenschaften, Technik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Inhalt: |
x
120 S. 2 s/w Illustr. 15 farbige Illustr. 120 p. 17 illus. 15 illus. in color. |
| ISBN-13: | 9783319425436 |
| ISBN-10: | 3319425439 |
| Sprache: | Englisch |
| Herstellernummer: | 978-3-319-42543-6 |
| Einband: | Kartoniert / Broschiert |
| Autor: |
Chazal, Frédéric
de Silva, Vin Glisse, Marc Oudot, Steve |
| Auflage: | 1st ed. 2016 |
| Hersteller: |
Springer
Springer, Berlin |
| Verantwortliche Person für die EU: | Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com |
| Abbildungen: | X, 120 p. 17 illus., 15 illus. in color. |
| Maße: | 237 x 161 x 8 mm |
| Von/Mit: | Frédéric Chazal (u. a.) |
| Erscheinungsdatum: | 17.10.2016 |
| Gewicht: | 0,213 kg |