Global InformationMulticover bifiltration information
The multicover bifiltration is a two-parameter sequence of nested topological spaces derived from the covering of a finite set in a metric space by growing metric balls. It is a multidimensional extension of the offset filtration that captures density information about the underlying data set by filtering the points of the offsets at each index according to how many balls cover each point.[1] The multicover bifiltration has been an object of study within multidimensional persistent homology and topological data analysis.[2][3][4][5][6][7]
- ^ Botnan, Magnus Bakke; Lesnick, Michael (2022). "An Introduction to Multiparameter Persistence". p. 26. arXiv:2203.14289 [math.AT].
- ^ Edelsbrunner, Herbert; Osang, Georg (2021). "The Multi-Cover Persistence of Euclidean Balls". Discrete & Computational Geometry. 65 (4): 1296–1313. doi:10.1007/s00454-021-00281-9. ISSN 0179-5376. PMC 8550220. PMID 34720303.
- ^ Corbet, René; Kerber, Michael; Lesnick, Michael; Osang, Georg (2023-02-20). "Computing the Multicover Bifiltration". Discrete & Computational Geometry. arXiv:2103.07823. doi:10.1007/s00454-022-00476-8. ISSN 0179-5376.
- ^ Blumberg, Andrew J.; Lesnick, Michael (2022-10-17). "Stability of 2-Parameter Persistent Homology". Foundations of Computational Mathematics. arXiv:2010.09628. doi:10.1007/s10208-022-09576-6. ISSN 1615-3375. S2CID 224705357.
- ^ Botnan, Magnus B.; Hirsch, Christian (2022-12-22). "On the consistency and asymptotic normality of multiparameter persistent Betti numbers". Journal of Applied and Computational Topology. arXiv:2109.05513. doi:10.1007/s41468-022-00110-9. ISSN 2367-1726. S2CID 237491663.
- ^ Kerber, Michael (2022-07-29). "Multi-Parameter Persistent Homology is Practical (Extended Abstract)".
{{cite journal}}: Cite journal requires|journal=(help) - ^ Corbet, Rene (2020). "Improvements to the Pipeline of Multiparameter Persistence".
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