Edit Distance and Persistence Diagrams Over Lattices
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 Möbius 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.
- Pub Date:
- October 2020
- Mathematics - Algebraic Topology;
- Computer Science - Computational Geometry
- Accepted to SIAM Journal on Applied Geometry and Algebra. This is the final accepted version of the paper