Infinite-Horizon Graph Filters: Leveraging Power Series to Enhance Sparse Information Aggregation
CoRR(2024)
摘要
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.
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