Persistent homology under non-uniform error
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Zigzag persistent homology in matrix multiplication time
Proceedings of the twenty-seventh annual symposium on Computational geometry
Linear-size approximations to the vietoris-rips filtration
Proceedings of the twenty-eighth annual symposium on Computational geometry
A point calculus for interlevel set homology
Pattern Recognition Letters
Zigzag zoology: rips zigzags for homology inference
Proceedings of the twenty-ninth annual symposium on Computational geometry
Computing persistent homology within Coq/SSReflect
ACM Transactions on Computational Logic (TOCL)
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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.