Corpus ID: 195218652

Jaccard Filtration and Stable Paths in the Mapper

@article{Arendt2019JaccardFA,
  title={Jaccard Filtration and Stable Paths in the Mapper},
  author={D. Arendt and M. Broussard and B. Krishnamoorthy and Nathaniel Saul},
  journal={ArXiv},
  year={2019},
  volume={abs/1906.08256}
}
The contributions of this paper are two-fold. We define a new filtration called the cover filtration built from a single cover based on a generalized Jaccard distance. We provide stability results for the cover filtration and show how the construction is equivalent to the Cech filtration under certain settings. We then develop a language and theory for stable paths within this filtration, inspired by ideas of persistent homology. We demonstrate how the filtration and paths can be applied to a… Expand
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