# Edit Distance and Persistence Diagrams Over Lattices

arXiv: https://arxiv.org/abs/2010.07337 · HTML: https://mlsanity.com/paper/2010.07337/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Oct 2020.

## Built on by (most cited first, 1 of 1)

- [Kan Extensions in Data Science and Machine Learning](https://mlsanity.com/paper/2203.09018/) (2022)

## Abstract (arXiv)

We build a functorial pipeline for persistent homology. The input to this pipeline is a filtered simplicial complex indexed by any finite metric lattice and the output is a persistence diagram defined as the M"obius inversion of its birth-death function. We adapt the Reeb graph edit distance to each of our categories and prove that both functors in our pipeline are 1-Lipschitz making our pipeline stable. Our constructions generalize the classical persistence diagram and, in this setting, the bottleneck distance is strongly equivalent to the edit distance.