# Jaccard Filtration and Stable Paths in the Mapper

@article{Arendt2019JaccardFA, title={Jaccard Filtration and Stable Paths in the Mapper}, author={Dustin L. Arendt and Matthew Broussard and Bala 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…

## One Citation

### Interesting paths in the mapper complex

- Computer Science, MathematicsJ. Comput. Geom.
- 2019

Interesting paths identified on several mapper graphs are used to explain how the genotype and environmental factors influence the growth rate, both in isolation as well as in combinations.

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