Learning to Approximate Adaptive Kernel Convolution on Graphs
Jaeyoon Sim Sooyeon Jeon InJun Choi Guorong Wu Won Hwa Kim
Various Graph Neural Networks (GNNs) have been successful in analyzing data
in non-Euclidean spaces, however, they have limitations such as oversmoothing,
i.e., information becomes excessively averaged as the number of hidden layers
increases. The issue stems from the intrinsic formulation of conventional graph
convolution where the nodal features are aggregated from a direct neighborhood
per layer across the entire nodes in the graph. As setting different number of
hidden layers per node is infeasible, recent works leverage a diffusion kernel
to redefine the graph structure and incorporate information from farther nodes.
Unfortunately, such approaches suffer from heavy diagonalization of a graph
Laplacian or learning a large transform matrix. In this regards, we propose a
diffusion learning framework, where the range of feature aggregation is
controlled by the scale of a diffusion kernel. For efficient computation, we
derive closed-form derivatives of approximations of the graph convolution with
respect to the scale, so that node-wise range can be adaptively learned. With a
downstream classifier, the entire framework is made trainable in an end-to-end
manner. Our model is tested on various standard datasets for node-wise
classification for the state-of-the-art performance, and it is also validated
on a real-world brain network data for graph classifications to demonstrate its
practicality for Alzheimer classification.