Zigzag Persistence

By Gunnar E. Carlsson, Vin de Silva. Foundations of Computational Mathematics, 2008

365 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Mathematical Physics, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/a074952c2bd1d2166903373437493a44f1667eb0

How researchers see this paper

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

In Computational Theory and Mathematics

In Mathematical Physics

In Radiology, Nuclear Medicine and Imaging

Citations in the corpus

What are higher-order networks? (2021, background): “a bi-filtration), then zig-zag persistence [54, 55] or multiparameter persistent homology [57,58], respectively, may be more suitable.”
Cliques and cavities in the human connectome (2016, background): “This is the least stringent and is an area of active research [91,92].”
The Gudhi Library: Simplicial Complexes and Persistent Homology (2014, neutral): “From the computational point of view, there are two types of indexing schemes of interest in persistent homology 1 : [16], and [7].”
Wasserstein Stability for Persistence Diagrams (2020, neutral): “On behalf of all authors, the corresponding author states that there is no conflict of interest.”