  The information diffusion performance of GCN and its variant models is
limited by the adjacency matrix, which can lower their performance. Therefore,
we introduce a new framework for graph convolutional networks called Hybrid
Diffusion-based Graph Convolutional Network (HD-GCN) to address the limitations
of information diffusion caused by the adjacency matrix. In the HD-GCN
framework, we initially utilize diffusion maps to facilitate the diffusion of
information among nodes that are adjacent to each other in the feature space.
This allows for the diffusion of information between similar points that may
not have an adjacent relationship. Next, we utilize graph convolution to
further propagate information among adjacent nodes after the diffusion maps,
thereby enabling the spread of information among similar nodes that are
adjacent in the graph. Finally, we employ the diffusion distances obtained
through the use of diffusion maps to regularize and constrain the predicted
labels of training nodes. This regularization method is then applied to the
HD-GCN training, resulting in a smoother classification surface. The model
proposed in this paper effectively overcomes the limitations of information
diffusion imposed only by the adjacency matrix. HD-GCN utilizes hybrid
diffusion by combining information diffusion between neighborhood nodes in the
feature space and adjacent nodes in the adjacency matrix. This method allows
for more comprehensive information propagation among nodes, resulting in
improved model performance. We evaluated the performance of DM-GCN on three
well-known citation network datasets and the results showed that the proposed
framework is more effective than several graph-based semi-supervised learning
methods.
