Adaptive Kernel Graph Neural Network
This work addresses a generality problem in graph neural networks for researchers and practitioners in graph representation learning, though it appears incremental as it builds on existing GNN frameworks with a novel kernel adaptation mechanism.
The paper tackles the problem of GNNs being limited by pre-defined graph kernels, which can cause suboptimal performance when there is a mismatch between the graph and kernel, such as in handling high- vs. low-frequency information. It proposes an Adaptive Kernel Graph Neural Network (AKGNN) that learns an optimal graph kernel adaptively, achieving promising results on benchmark datasets compared to state-of-the-art GNNs.
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.