A Hierarchical Block Distance Model for Ultra Low-Dimensional Graph Representations

TL;DR

This paper introduces HBDM, a scalable hierarchical graph embedding method that captures multi-scale structures and network properties efficiently, enabling analysis of massive networks with improved accuracy and interpretability.

Contribution

The paper presents a novel hierarchical block distance model that explicitly models multi-scale network structures and properties, with linearithmic complexity suitable for large-scale graphs.

Findings

HBDM outperforms recent scalable methods on large networks.

HBDM achieves accurate low-dimensional embeddings for visualization.

HBDM effectively captures homophily and transitivity in networks.

Abstract

Graph Representation Learning (GRL) has become central for characterizing structures of complex networks and performing tasks such as link prediction, node classification, network reconstruction, and community detection. Whereas numerous generative GRL models have been proposed, many approaches have prohibitive computational requirements hampering large-scale network analysis, fewer are able to explicitly account for structure emerging at multiple scales, and only a few explicitly respect important network properties such as homophily and transitivity. This paper proposes a novel scalable graph representation learning method named the Hierarchical Block Distance Model (HBDM). The HBDM imposes a multiscale block structure akin to stochastic block modeling (SBM) and accounts for homophily and transitivity by accurately approximating the latent distance model (LDM) throughout the inferred hierarchy. The HBDM naturally accommodates unipartite, directed, and bipartite networks whereas the hierarchy is designed to ensure linearithmic time and space complexity enabling the analysis of very large-scale networks. We evaluate the performance of the HBDM on massive networks consisting of millions of nodes. Importantly, we find that the proposed HBDM framework significantly outperforms recent scalable approaches in all considered downstream tasks. Surprisingly, we observe superior performance even imposing ultra-low two-dimensional embeddings facilitating accurate direct and hierarchical-aware network visualization and interpretation.