Academic Journal
Sparse Higher Order Čech Filtrations
| Τίτλος: | Sparse Higher Order Čech Filtrations |
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| Συγγραφείς: | Buchet, Mickaël, B. Dornelas, Bianca, Kerber, Michael |
| Συνεισφορές: | Mickaël Buchet and Bianca B. Dornelas and Michael Kerber |
| Στοιχεία εκδότη: | Schloss Dagstuhl – Leibniz-Zentrum für Informatik |
| Έτος έκδοσης: | 2023 |
| Συλλογή: | DROPS - Dagstuhl Research Online Publication Server (Schloss Dagstuhl - Leibniz Center for Informatics ) |
| Θεματικοί όροι: | Sparsification, k-fold cover, Higher order Čech complexes |
| Περιγραφή: | For a finite set of balls of radius r, the k-fold cover is the space covered by at least k balls. Fixing the ball centers and varying the radius, we obtain a nested sequence of spaces that is called the k-fold filtration of the centers. For k = 1, the construction is the union-of-balls filtration that is popular in topological data analysis. For larger k, it yields a cleaner shape reconstruction in the presence of outliers. We contribute a sparsification algorithm to approximate the topology of the k-fold filtration. Our method is a combination and adaptation of several techniques from the well-studied case k = 1, resulting in a sparsification of linear size that can be computed in expected near-linear time with respect to the number of input points. |
| Τύπος εγγράφου: | article in journal/newspaper conference object |
| Περιγραφή αρχείου: | application/pdf |
| Γλώσσα: | English |
| Relation: | Is Part Of LIPIcs, Volume 258, 39th International Symposium on Computational Geometry (SoCG 2023); https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.20 |
| DOI: | 10.4230/LIPIcs.SoCG.2023.20 |
| Διαθεσιμότητα: | https://doi.org/10.4230/LIPIcs.SoCG.2023.20 https://nbn-resolving.org/urn:nbn:de:0030-drops-178709 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.20 |
| Rights: | https://creativecommons.org/licenses/by/4.0/legalcode |
| Αριθμός Καταχώρησης: | edsbas.8287336A |
| Βάση Δεδομένων: | BASE |
| DOI: | 10.4230/LIPIcs.SoCG.2023.20 |
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