Persistent Homology based Wasserstein distance for graph networks

Year 2024, Early Access, 1 - 25

Archana Babu Sunil Jacob John

https://doi.org/10.15672/hujms.1317203

Abstract

The technique of measuring similarity between topological spaces using Wasserstein distance
between persistence diagrams is extended to graph networks in this paper. A relationship
between the Wasserstein distance of the Cartesian product of topological spaces and the
Wasserstein distance of individual spaces is found to ease the comparative study of the
Cartesian product of topological spaces. The Cartesian product and the strong product of
weighted graphs are defined, and the relationship between the Wasserstein distance between
graph products and the Wasserstein distance between individual graphs is determined. For
this, clique complex filtration and the Vietoris- Rips filtration are used.

Keywords

Persistent homology, Wasserstein distance, Cartesian product of graphs, Strong product of graphs

References

• [1] A. Adcock, E. Carlsson, and G. Carlsson, The ring of algebraic functions on persistence bar codes, arXiv preprint arXiv:1304.0530, 2013