Edit Distance and Persistence Diagrams Over Lattices

Alexander McCleary; Amit Patel

doi:10.1137/20m1373700

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arXiv · 2010.07337

Edit Distance and Persistence Diagrams Over Lattices

Alexander McCleary·Amit Patel

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Abstract

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.

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BibTeX RIS

Alexander McCleary, Amit Patel. 2020-10-14. Edit Distance and Persistence Diagrams Over Lattices. https://doi.org/10.1137/20m1373700

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