Zigzag Persistence
Copyright policy )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 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.
32 pages, 7 figures
- Pomona College United States
- Claremont Colleges United States
- Stanford University United States
Computational Geometry (cs.CG), FOS: Computer and information sciences, Mathematics(all), Computational Mathematics, Computational Theory and Mathematics, I.3.5, Applied Mathematics, Computer Science - Computational Geometry, Theoretical Computer Science
Computational Geometry (cs.CG), FOS: Computer and information sciences, Mathematics(all), Computational Mathematics, Computational Theory and Mathematics, I.3.5, Applied Mathematics, Computer Science - Computational Geometry, Theoretical Computer Science
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