  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.
