Graph Neural Networks with Diverse Spectral Filtering

Abstract

Spectral Graph Neural Networks (GNNs) have achieved tremendous success in graph machine learning, with polynomial filters applied for graph convolutions, where all nodes share the identical filter weights to mine their local contexts. Despite the success, existing spectral GNNs usually fail to deal with complex networks (e.g., WWW) due to such homogeneous spectral filtering setting that ignores the regional heterogeneity as typically seen in real-world networks. To tackle this issue, we propose a novel diverse spectral filtering (DSF) framework, which automatically learns node-specific filter weights to exploit the varying local structure properly. Particularly, the diverse filter weights consist of two components -A global one shared among all nodes, and a local one that varies along network edges to reflect node difference arising from distinct graph parts -to balance between local and global information. As such, not only can the global graph characteristics be captured, but also the diverse local patterns can be mined with awareness of different node positions. Interestingly, we formulate a novel optimization problem to assist in learning diverse filters, which also enables us to enhance any spectral GNNs with our DSF framework. We showcase the proposed framework on three state-of-the-arts including GPR-GNN, BernNet, and JacobiConv. Extensive experiments over 10 benchmark datasets demonstrate that our framework can consistently boost model performance by up to 4.92% in node classification tasks, producing diverse filters with enhanced interpretability. Code is available at https://github.com/jingweio/DSF. CCS CONCEPTS• Computing methodologies → Machine learning.

Learning to Approximate Adaptive Kernel Convolution on Graphs

“…For Amazon and Coauthor datasets, seven baselines are used as in Table 3. For the MLP with 3-layers, GCN and 3ference, results are obtained from (Luo et al 2022), and a result for DSF comes from (Guo et al 2023). For others, the experiments were performed by randomly splitting the data as 60%/20%/20% for training/validation/testing datasets as in (Luo et al 2022) and replicating it 10 times to obtain mean and standard deviation of the evaluation metric.…”

“…Several recent works tried to overcome this locality issue. Methods in (Veličković et al 2018;Kim et al 2022) leverage attention to capture long-range relationships among nodes, authors in (Gao et al 2019;Wu et al 2022b) develop pooling scheme to compress graphs, and authors in (Chen et al 2020) improve upon the vanilla GCN with skip connection of residuals as in ResNet (He et al 2016).…”