Implications of sparsity and high triangle density for graph representation learning
Machine Learning
2023-04-24 v2 Machine Learning
Abstract
Recent work has shown that sparse graphs containing many triangles cannot be reproduced using a finite-dimensional representation of the nodes, in which link probabilities are inner products. Here, we show that such graphs can be reproduced using an infinite-dimensional inner product model, where the node representations lie on a low-dimensional manifold. Recovering a global representation of the manifold is impossible in a sparse regime. However, we can zoom in on local neighbourhoods, where a lower-dimensional representation is possible. As our constructions allow the points to be uniformly distributed on the manifold, we find evidence against the common perception that triangles imply community structure.
Cite
@article{arxiv.2210.15277,
title = {Implications of sparsity and high triangle density for graph representation learning},
author = {Hannah Sansford and Alexander Modell and Nick Whiteley and Patrick Rubin-Delanchy},
journal= {arXiv preprint arXiv:2210.15277},
year = {2023}
}