Zigzag Persistence. Carlsson, G. & family=Silva , g.
Zigzag Persistence [link]Paper  abstract   bibtex   
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.
@article{carlssonZigzagPersistence2008,
  archivePrefix = {arXiv},
  eprinttype = {arxiv},
  eprint = {0812.0197},
  primaryClass = {cs},
  title = {Zigzag {{Persistence}}},
  url = {http://arxiv.org/abs/0812.0197},
  abstract = {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.},
  urldate = {2018-09-08},
  date = {2008-11-30},
  keywords = {Computer Science - Computational Geometry,I.3.5},
  author = {Carlsson, Gunnar and family=Silva, given=Vin, prefix=de, useprefix=true},
  file = {/home/dimitri/Nextcloud/Zotero/storage/PKSM89FF/Carlsson and de Silva - 2008 - Zigzag Persistence.pdf;/home/dimitri/Nextcloud/Zotero/storage/QF37EI5F/0812.html}
}

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