  Graph convolutional networks gain remarkable success in semi-supervised
learning on graph structured data. The key to graph-based semisupervised
learning is capturing the smoothness of labels or features over nodes exerted
by graph structure. Previous methods, spectral methods and spatial methods,
devote to defining graph convolution as a weighted average over neighboring
nodes, and then learn graph convolution kernels to leverage the smoothness to
improve the performance of graph-based semi-supervised learning. One open
challenge is how to determine appropriate neighborhood that reflects relevant
information of smoothness manifested in graph structure. In this paper, we
propose GraphHeat, leveraging heat kernel to enhance low-frequency filters and
enforce smoothness in the signal variation on the graph. GraphHeat leverages
the local structure of target node under heat diffusion to determine its
neighboring nodes flexibly, without the constraint of order suffered by
previous methods. GraphHeat achieves state-of-the-art results in the task of
graph-based semi-supervised classification across three benchmark datasets:
Cora, Citeseer and Pubmed.
