Understanding Coarsening for Embedding Large-Scale Graphs

TL;DR

This paper investigates how graph coarsening, a pre-processing step, affects the efficiency and accuracy of large-scale graph embedding, revealing an interplay between coarsening quality and embedding performance.

Contribution

It provides a thorough analysis of the impact of coarsening quality on graph embedding speed and accuracy, highlighting the importance of coarsening decisions.

Findings

Coarsening reduces embedding computational cost.

Quality of coarsening influences embedding accuracy.

Optimal coarsening balances speed and precision.

Abstract

A significant portion of the data today, e.g, social networks, web connections, etc., can be modeled by graphs. A proper analysis of graphs with Machine Learning (ML) algorithms has the potential to yield far-reaching insights into many areas of research and industry. However, the irregular structure of graph data constitutes an obstacle for running ML tasks on graphs such as link prediction, node classification, and anomaly detection. Graph embedding is a compute-intensive process of representing graphs as a set of vectors in a d-dimensional space, which in turn makes it amenable to ML tasks. Many approaches have been proposed in the literature to improve the performance of graph embedding, e.g., using distributed algorithms, accelerators, and pre-processing techniques. Graph coarsening, which can be considered a pre-processing step, is a structural approximation of a given, large graph with a smaller one. As the literature suggests, the cost of embedding significantly decreases when coarsening is employed. In this work, we thoroughly analyze the impact of the coarsening quality on the embedding performance both in terms of speed and accuracy. Our experiments with a state-of-the-art, fast graph embedding tool show that there is an interplay between the coarsening decisions taken and the embedding quality.