Hierarchical and Unsupervised Graph Representation Learning with Loukas's Coarsening

TL;DR

This paper introduces an unsupervised, inductive, and end-to-end differentiable graph embedding method that captures multi-scale structures using Loukas's coarsening, achieving competitive results on benchmark classification tasks.

Contribution

It presents a novel combination of Loukas's coarsening with mutual information maximization for high-quality, scalable graph embeddings that are inductive and suitable for deep learning pipelines.

Findings

Achieves state-of-the-art performance among unsupervised methods.

Effectively captures micro- and macro-structures at multiple scales.

Demonstrates strong theoretical guarantees and practical effectiveness.

Abstract

We propose a novel algorithm for unsupervised graph representation learning with attributed graphs. It combines three advantages addressing some current limitations of the literature: i) The model is inductive: it can embed new graphs without re-training in the presence of new data; ii) The method takes into account both micro-structures and macro-structures by looking at the attributed graphs at different scales; iii) The model is end-to-end differentiable: it is a building block that can be plugged into deep learning pipelines and allows for back-propagation. We show that combining a coarsening method having strong theoretical guarantees with mutual information maximization suffices to produce high quality embeddings. We evaluate them on classification tasks with common benchmarks of the literature. We show that our algorithm is competitive with state of the art among unsupervised graph representation learning methods.