The structure and stability of persistence modules / by Frédéric Chazal, Vin de Silva, Marc Glisse, Steve Oudot.

Format:

Book

Author/Creator:

Chazal, Frédéric., Author.

de Silva, Vin., Author.

Glisse, Marc., Author.

Oudot, Steve., Author.

Series:

SpringerBriefs in Mathematics, 2191-8198

Language:

English

Subjects (All):

Algebraic topology.

Algebra.

Computer science—Mathematics.

Computer science--Mathematics.

Computer science.

Algebraic Topology.

Mathematical Applications in Computer Science.

Local Subjects:

Algebraic Topology.

Algebra.

Mathematical Applications in Computer Science.

Physical Description:

1 online resource (X, 120 p. 17 illus., 15 illus. in color.)

Edition:

1st ed. 2016.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2016.

Summary:

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.

Contents:

Introduction

Persistence Modules

Rectangle Measures

Interleaving

The Isometry Theorem

Variations

References

Index.

Notes:

Includes bibliographical references and index.