Node Embedding for Homophilous Graphs with ARGEW: Augmentation of Random walks by Graph Edge Weights

TL;DR

This paper introduces ARGEW, a novel augmentation method for random walk-based node embeddings that enhances the reflection of edge weights in the embeddings, leading to improved performance in weighted homophilous graphs.

Contribution

The paper proposes ARGEW, a new augmentation technique that improves node embeddings by better capturing edge weights, compatible with existing random walk methods.

Findings

ARGEW produces embeddings where nodes with larger edge weights are closer.

Node2vec with ARGEW outperforms standard node2vec in node classification.

ARGEW is robust to hyperparameter changes and achieves results comparable to supervised GCN.

Abstract

Representing nodes in a network as dense vectors node embeddings is important for understanding a given network and solving many downstream tasks. In particular, for weighted homophilous graphs where similar nodes are connected with larger edge weights, we desire node embeddings where node pairs with strong weights have closer embeddings. Although random walk based node embedding methods like node2vec and node2vec+ do work for weighted networks via including edge weights in the walk transition probabilities, our experiments show that the embedding result does not adequately reflect edge weights. In this paper, we propose ARGEW (Augmentation of Random walks by Graph Edge Weights), a novel augmentation method for random walks that expands the corpus in such a way that nodes with larger edge weights end up with closer embeddings. ARGEW can work with any random walk based node embedding method, because it is independent of the random sampling strategy itself and works on top of the already-performed walks. With several real-world networks, we demonstrate that with ARGEW, compared to not using it, the desired pattern that node pairs with larger edge weights have closer embeddings is much clearer. We also examine ARGEW's performance in node classification: node2vec with ARGEW outperforms pure node2vec and is not sensitive to hyperparameters (i.e. consistently good). In fact, it achieves similarly good results as supervised GCN, even without any node feature or label information during training. Finally, we explain why ARGEW works consistently well by exploring the coappearance distributions using a synthetic graph with clear structural roles.