DeepAI

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 lattice, and the output is a persistence diagram defined as the Möbius inversion of a certain monotone integral function. We adapt the Reeb graph edit distance of Landi et. al. to each of our categories and prove that both functors in our pipeline are 1-Lipschitz making our pipeline stable.

• 1 publication
• 5 publications
07/03/2020

Universality of the Bottleneck Distance for Extended Persistence Diagrams

The extended persistence diagram is an invariant of piecewise linear fun...
04/15/2021

Approximation algorithms for 1-Wasserstein distance between persistence diagrams

Recent years have witnessed a tremendous growth using topological summar...
06/19/2018

On the Metric Distortion of Embedding Persistence Diagrams into separable Hilbert spaces

Persistence diagrams are important descriptors in Topological Data Analy...
06/19/2018

On the Metric Distortion of Embedding Persistence Diagrams into Reproducing Kernel Hilbert Spaces

Persistence diagrams are important feature descriptors in Topological Da...
02/12/2020

Graph Similarity Using PageRank and Persistent Homology

The PageRank of a graph is a scalar function defined on the node set of ...
03/01/2022

A Lattice-Theoretic Perspective on the Persistence Map

We provide a naturally isomorphic description of the persistence map fro...
12/07/2020

Topological Echoes of Primordial Physics in the Universe at Large Scales

We present a pipeline for characterizing and constraining initial condit...