Graph neural networks (GNNs) have demonstrated great success in representation learning for graph-structured data. The layer-wise graph convolution in GNNs is shown to be powerful at capturing graph topology. During this process, GNNs are usually guided by pre-defined kernels such as Laplacian matrix, adjacency matrix, or their variants. However, the adoptions of pre-defined kernels may restrain the generalities to different graphs: mismatch between graph and kernel would entail sub-optimal performance. For example, GNNs that focus on low-frequency information may not achieve satisfactory performance when high-frequency information is significant for the graphs, and vice versa. To solve this problem, in this paper, we propose a novel framework - i.e., namely Adaptive Kernel Graph Neural Network (AKGNN) - which learns to adapt to the optimal graph kernel in a unified manner at the first attempt. In the proposed AKGNN, we first design a data-driven graph kernel learning mechanism, which adaptively modulates the balance between all-pass and low-pass filters by modifying the maximal eigenvalue of the graph Laplacian. Through this process, AKGNN learns the optimal threshold between high and low frequency signals to relieve the generality problem. Later, we further reduce the number of parameters by a parameterization trick and enhance the expressive power by a global readout function. Extensive experiments are conducted on acknowledged benchmark datasets and promising results demonstrate the outstanding performance of our proposed AKGNN by comparison with state-of-the-art GNNs. The source code is publicly available at: https://github.com/jumxglhf/AKGNN.
翻译:图表神经网络(GNNS) 显示在图形结构数据的代表学习中取得了巨大成功。 GNNS 的图层图变图在图示表层图变中表现有力。 在此过程中, GNNS通常由预定义的内核(如 Laplacian 矩阵、 相邻矩阵或变体) 指导。 但是, 采用预定义的内核( 预定义的内核) 可能会限制对不同图表的概略性: 图形和内核之间的不匹配将带来亚最佳的性能表现。 例如, 侧重于低频率信息的GNNNNNP 的图变图变图变显示, 当高频率信息对图形和反向的GNG 高频率信息时, 我们提出一个全新的框架, 即调心电图图图图的精确值和GAKNNNNG 最高值之间, 以统一的方式适应最佳的图变现。 在拟议的AKGGNNNN, 我们首次设计一个数据驱动的图变图变图变码学习机制, 以不断调整的GMNDG 和G 最高级的G 最高级的G 最高级的G 的模型, 通过最高级的GLNDRND 和最高级的G 的调的调的G 和最高级的G 以最高级的G 最高级的G 进行最高级的调的G 最高级的G 的调的G 进程来进行最高级的变压的调的调的G 。