The Structure and Stability of Persistence Modules

Frédéric Chazal 1 Steve Y. Oudot 2, 1 Marc Glisse 1 Vin de Silva 3
1 DATASHAPE - Understanding the Shape of Data
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
2 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : 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.
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https://hal.inria.fr/hal-01330678
Contributor : Frédéric Chazal <>
Submitted on : Sunday, June 12, 2016 - 2:31:52 PM
Last modification on : Wednesday, October 10, 2018 - 10:08:57 AM

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  • HAL Id : hal-01330678, version 1

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Frédéric Chazal, Steve Y. Oudot, Marc Glisse, Vin de Silva. The Structure and Stability of Persistence Modules. Springer Verlag, pp.VII, 116, 2016, SpringerBriefs in Mathematics, 978-3-319-42543-6. ⟨http://www.springer.com/us/book/9783319425436⟩. ⟨hal-01330678⟩

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