The Gromov-Wasserstein distance between networks and stable network invariants
Abstract
We define a metric---the network Gromov-Wasserstein distance---on weighted, directed networks that is sensitive to the presence of outliers. In addition to proving its theoretical properties, we supply network invariants based on optimal transport that approximate this distance by means of lower bounds. We test these methods on a range of simulated network datasets and on a dataset of real-world global bilateral migration. For our simulations, we define a network generative model based on the stochastic block model. This may be of independent interest for benchmarking purposes.
Keywords
Cite
@article{arxiv.1808.04337,
title = {The Gromov-Wasserstein distance between networks and stable network invariants},
author = {Samir Chowdhury and Facundo Mémoli},
journal= {arXiv preprint arXiv:1808.04337},
year = {2019}
}
Comments
To appear in Information and Inference. Current version is a substantial update from the previous version and includes new computational experiments and also new results on the Gromov-Prokhorov distance between spheres