Self-Similar Graph Neural Network for Hierarchical Graph Learning

Abstract

Many real-world networks, such as graph-structured molecules or social networks, exhibit latent hierarchical structures at many different resolutions. Existing hierarchical graph neural networks (GNNs) mainly focus on modifying graph global pooling regions into partitioned clusters, while keeping the convolutional layers unchanged. However, these approaches may suffer from a loss of expressive power in learned representations due to the uncontrolled growth of the neighborhood, leading to a failure in capturing true hierarchies. Furthermore, many real-world hierarchical graphs possess an underlying fractal structure, which is crucial to unraveling the formation mechanism of networks. Unfortunately, existing hierarchical GNNs often overlook this important aspect of graph hierarchy. To tackle these challenges, this paper proposes a generic framework for hierarchical network representation learning. We propose the Self-Similar Graph Neural Network (SS-GNN), which leverages localized representations by excluding redundant nodes and edges. At each resolution of the coarsened map, SS-GNN extracts both intra- and inter-cluster embeddings to preserve the discriminative power of the model with a theoretical guarantee. To exploit the graph fractal structure, we introduce a novel module for measuring self-similarity between resolutions and a characterized objective function for automatic adjustment of model parameters. We demonstrate the strength of our proposed framework through extensive experiments on 13 real-world datasets by outperforming the state-of-the-art GNN models.