MILE: A Multi-Level Framework for Scalable Graph Embedding

TL;DR

MILE is a versatile multi-level framework that enables existing graph embedding methods to efficiently scale to large graphs with millions of nodes by coarsening, embedding, and refining the graph.

Contribution

The paper introduces MILE, a generic multi-level framework that significantly improves scalability and embedding quality for large-scale graph embedding tasks.

Findings

MILE achieves an order of magnitude speedup in graph embedding.

MILE scales to graphs with 9 million nodes and 40 million edges.

Embeddings produced by MILE outperform baseline methods in node classification.

Abstract

Recently there has been a surge of interest in designing graph embedding methods. Few, if any, can scale to a large-sized graph with millions of nodes due to both computational complexity and memory requirements. In this paper, we relax this limitation by introducing the MultI-Level Embedding (MILE) framework -- a generic methodology allowing contemporary graph embedding methods to scale to large graphs. MILE repeatedly coarsens the graph into smaller ones using a hybrid matching technique to maintain the backbone structure of the graph. It then applies existing embedding methods on the coarsest graph and refines the embeddings to the original graph through a graph convolution neural network that it learns. The proposed MILE framework is agnostic to the underlying graph embedding techniques and can be applied to many existing graph embedding methods without modifying them. We employ our framework on several popular graph embedding techniques and conduct embedding for real-world graphs. Experimental results on five large-scale datasets demonstrate that MILE significantly boosts the speed (order of magnitude) of graph embedding while generating embeddings of better quality, for the task of node classification. MILE can comfortably scale to a graph with 9 million nodes and 40 million edges, on which existing methods run out of memory or take too long to compute on a modern workstation. Our code and data are publicly available with detailed instructions for adding new base embedding methods: \url{https://github.com/jiongqian/MILE}.