Zigzag Persistence

We describe a new methodology for studying persistence of topological features across a family of spaces or point-cloud data sets, called zigzag persistence. Building on classical results about quiver representations, zigzag persistence generalises the highly successful theory of persistent homology...

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Vydáno v:Foundations of computational mathematics Ročník 10; číslo 4; s. 367 - 405
Hlavní autoři: Carlsson, Gunnar, de Silva, Vin
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer-Verlag 01.08.2010
Springer Nature B.V
Témata:
Algorithms
Applications of Mathematics
Computation
Computer Science
Economics
Foundations
Geometry
Homology
Linear and Multilinear Algebras
Math Applications in Computer Science
Mathematical models
Mathematics
Mathematics and Statistics
Matrix Theory
Numerical Analysis
Representations
Statistics
Theory
68W30
Persistent topology
55N99
Applied topology
Quiver representations
ISSN:1615-3375, 1615-3383
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Shrnutí:We describe a new methodology for studying persistence of topological features across a family of spaces or point-cloud data sets, called zigzag persistence. Building on classical results about quiver representations, zigzag persistence generalises the highly successful theory of persistent homology and addresses several situations which are not covered by that theory. In this paper we develop theoretical and algorithmic foundations with a view towards applications in topological statistics.
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ISSN:1615-3375
1615-3383
DOI:10.1007/s10208-010-9066-0