Persistent homology lower bounds on network distances
Weiyu Huang, Alejandro Ribeiro
Abstract
High order networks are weighted complete hypergraphs collecting relationships between elements of tuples. Valid metric distances between high order networks have been defined but they are difficult to compute when the number of nodes is large. We relate high order networks to the filtrations of simplicial complexes and show that the distance between networks can be lower bounded by the difference between the homological features of their respective filtrations. Practical implications are explored by comparing the coauthorship networks of engineering and mathematics academic journals. The lower bounds succeed in discriminating engineering communities from mathematics and in differentiating engineering communities with different research interests.
BibTeX
@inproceedings{icassp2016_persistenthomolo,
title = {Persistent homology lower bounds on network distances},
author = {Weiyu Huang and Alejandro Ribeiro},
booktitle = {ICASSP 2016},
year = {2016}
}