Spectral Graph Neural Network Based on Adaptive Combination Filters
LI Weinuo1, HUANG Meixiang1, LU Fuliang1, TU Liangping1,2
1. School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000 2. School of Science, University of Science and Technology Liao-ning, Anshan 114051
Abstract：Spectral graph neural networks(SGNNs) exhibit strong performance in processing homophilic graph data. However, most existing SGNNs design filters based on polynomial approximations of Laplacian matrix, which struggle to effectively capture high-frequency components of graph signals. Consequently, their performance on heterophilic graphs is limited. Additionally, filters based on Laplacian matrix can only capture global structural features of graph topology, limiting their adaptability to complex local patterns in graph data. To overcome these limitations, a spectral graph neural network based on adaptive combination filters(ACGNN) is proposed. Instead of using polynomial bases, eigenvectors and eigenvalues of Laplacian matrix are combined to design a filter by partitioning node neighborhood patterns, and the filter can effectively capture and learn diverse node neighborhood structural patterns. Moreover, the filter can adaptively adjust weights based on node characteristics by integrating a parameter matrix associated with node features into the filter function. Experimental results on both homophilic and heterophilic graph datasets validate the effectiveness and superior performance of ACGNN.
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