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The Structure and Stability of Persistence Modules

  • Frédéric Chazal
  • Vin de Silva
  • Marc Glisse
  • Steve Oudot

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-x
  2. Frédéric Chazal, Vin de Silva, Marc Glisse, Steve Oudot
    Pages 1-13
  3. Frédéric Chazal, Vin de Silva, Marc Glisse, Steve Oudot
    Pages 15-29
  4. Frédéric Chazal, Vin de Silva, Marc Glisse, Steve Oudot
    Pages 31-66
  5. Frédéric Chazal, Vin de Silva, Marc Glisse, Steve Oudot
    Pages 67-80
  6. Frédéric Chazal, Vin de Silva, Marc Glisse, Steve Oudot
    Pages 81-107
  7. Frédéric Chazal, Vin de Silva, Marc Glisse, Steve Oudot
    Pages 109-113
  8. Back Matter
    Pages 115-120

About this book

Introduction

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.

Keywords

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

Authors and affiliations

  • Frédéric Chazal
    • 1
  • Vin de Silva
    • 2
  • Marc Glisse
    • 3
  • Steve Oudot
    • 4
  1. 1.Inria Saclay - Ile-de-FrancePalaiseauFrance
  2. 2.Pomona CollegeClaremontUSA
  3. 3.Inria Saclay - Île de FrancePalaiseauFrance
  4. 4.Inria Saclay - Île de FrancePalaiseauFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-42545-0
  • Copyright Information The Author(s) 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-42543-6
  • Online ISBN 978-3-319-42545-0
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • Buy this book on publisher's site