Document Zbl 1204.68242 - zbMATH Open
Zigzag persistence. (English) Zbl 1204.68242
Summary: 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.
MSC:
| 68U05 | Computer graphics; computational geometry (digital and algorithmic aspects) |
| 55N99 | Homology and cohomology theories in algebraic topology |
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