Vines and vineyards by updating persistence in linear time

312 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Wasserstein Stability for Persistence Diagrams (2020, unknown): “As noted in the introduction, this idea was previously used in [18] to show a bottleneck stability result for functions on simplicial complexes.”
The Structure and Stability of Persistence Modules (2012, methodology): “We finish this section by using the ‘vineyard’ technique of [12] to visualise the 1-parameter family of persistence modules produced by each of the three constructions.”
Ripser: efficient computation of Vietoris–Rips persistence barcodes (2019, background): “1 (Cohen-Steiner et al. 2006) Let D be a filtration boundary matrix, and let V be a full rank upper triangular matrix such that R = D ·V is reduced.”
Proximity of persistence modules and their diagrams (2009, background): “Thus, a reduction from the piecewise-constant setting to some continuous setting is made.”
Homological illusions of persistence and stability (2008, methodology): “I would like to thank my advisor Herbert Edelsbrunner.”