AI 中文总结
本文针对有向符号图学习提出NLSD非线性拉普拉斯算子及NLSD-GNN谱图神经网络框架，经节点分类、链接预测实验验证，该框架可有效融合符号与方向数据，性能优于现有方法。
AI 中文摘要
尽管在图神经网络设计中已有研究使用线性拉普拉斯算子处理有向符号图，但针对此类网络的非线性拉普拉斯算子研究相对较少。本文提出一种适用于有向符号网络的非线性拉普拉斯算子（NLSD），该算子扩展了符号图的符号拉普拉斯和有向图的拉普拉斯概念，基于特征计算节点特定势。更准确地说，若势差与边方向不一致，则忽略该势差（反之亦然），仅在势差与边方向一致的边间利用消息传递技术。基于此算子，本文提出一种高效的谱图神经网络框架（NLSD-GNN）。针对节点分类和链接预测任务开展全面评估，考察仅含符号信息、仅含方向信息及两者兼具的场景，结果表明该框架不仅能有效融合符号与方向数据，还在多个数据集上取得优异性能。
英文摘要
While signed-directed graphs have been studied using linear Laplacians in the design of graph neural networks, relatively little research has focused on developing non-linear Laplacian operators for such networks. We introduce a non-linear Laplacian operator specific to signed and directed networks (NLSD). This non-linear operator extends the concepts of the signed Laplacian for signed graphs and the Laplacian for directed graphs. The NLSD calculates node-specific potentials based on features More precisely, if the potential discrepancy is not aligned with the edge direction, we ignore it (and vice versa) leveraging message-passing techniques only across edges where potential discrepancies align with the edge's direction. Utilizing this novel operator, we propose an efficient spectral GNN framework (NLSD-GNN). We conducted comprehensive evaluations focusing on node classification and link prediction, examining scenarios involving signed, directional, or both types of information. Our findings reveal that this spectral GNN framework not only integrates signed and directional data effectively but also achieves superior performance across diverse datasets.
