Dimension-divided feature smoothing for graph neural network

Graph Neural Networks(GNNs) learn the node representation of multi-hops through stacking layers. However, deep GNNs often suffer from over-smoothing, which drives people to the road of model simplification. With the deepening of research, it is found that the representation of nodes is more related to feature smoothing. More and more simplified models show that the nonparametric feature smoothing scheme can not only reduce computational complexity but also improve performance. Because the features of nodes in GNNs propagate along the edges, the denoising of graph data mainly focuses on the modification of graph topology. Based on this, we propose a feature smoothing scheme on the topology modification graph named Topology-modified Feature Smoothing(TMFS). Experiments show that the smoothed features calculated by TMFS can improve the performance of GNNs. Graph data usually have high-dimension features. Some feature dimensions contribute more to node classification, while others may only be the personality features of specific nodes. However, the existing propagation schemes cause all dimensional features to propagate along the edge at the same time. Such schemes as dropedge and addedge cannot change this situation. This feature propagation method is very mechanized. To solve this problem, we divide the dimension of features according to commonality nature, and modify the graph topology respectively, to realize the Dimension-divided Feature Smoothing(DDFS) of personalized propagation. Our experiments show that the deep features obtained by DDFS can not only improve the performance of GNNs but also be more stable. Our feature smoothing scheme can be seen as a plug-and-play module. On the Cora dataset, the smoothed features of our DDFS have improved the accuracy of MLP by 27.88% and other GNNs by 2.29% at most.