Infinite-Horizon Graph Filters: Leveraging Power Series to Enhance Sparse Information Aggregation
This addresses a key bottleneck in graph learning for tasks like node classification, though it appears incremental as it builds on existing message-passing approaches.
The paper tackles the limited receptive field problem in Graph Neural Networks (GNNs) on sparse graphs by proposing a Graph Power Filter Neural Network (GPFN) that uses a power series graph filter to enhance node classification, achieving superior performance over state-of-the-art baselines on three datasets.
Graph Neural Networks (GNNs) have shown considerable effectiveness in a variety of graph learning tasks, particularly those based on the message-passing approach in recent years. However, their performance is often constrained by a limited receptive field, a challenge that becomes more acute in the presence of sparse graphs. In light of the power series, which possesses infinite expansion capabilities, we propose a novel Graph Power Filter Neural Network (GPFN) that enhances node classification by employing a power series graph filter to augment the receptive field. Concretely, our GPFN designs a new way to build a graph filter with an infinite receptive field based on the convergence power series, which can be analyzed in the spectral and spatial domains. Besides, we theoretically prove that our GPFN is a general framework that can integrate any power series and capture long-range dependencies. Finally, experimental results on three datasets demonstrate the superiority of our GPFN over state-of-the-art baselines.