Poisson kernel: Avoiding self-smoothing in graph convolutional networks

Highlights：

• We theoretically study how exactly different graph structures influence the performance of graph convolutional kernels, and several theorems about the properties and effects are given.

• By building an eigenvalue mapping of the symmetrically normalized adjacency matrix, we skillfully propose the Poisson kernel to avoid self-smoothing in graph convolutional networks without being sensitive to the parameter and dataset selections.

• Our results are evidently superior to state-of-the-art kernels on synthetic datasets with specific structures, where they will lead to severe self-smoothing inevitably. And in most situations, such as on three benchmark datasets (Cora, Citeseer and Pubmed), our Poisson kernel still works well and almost better without training any adaptive kernel.

摘要

•To the best of our knowledge, our work is the first to reveal the self-smoothing phenomenon of graph convolutional kernels in graph convolutional networks, which is a major vulnerability to reduce accuracy, robustness, and adaptability of trained models.•We theoretically study how exactly different graph structures influence the performance of graph convolutional kernels, and several theorems about the properties and effects are given.•By building an eigenvalue mapping of the symmetrically normalized adjacency matrix, we skillfully propose the Poisson kernel to avoid self-smoothing in graph convolutional networks without being sensitive to the parameter and dataset selections.•Our results are evidently superior to state-of-the-art kernels on synthetic datasets with specific structures, where they will lead to severe self-smoothing inevitably. And in most situations, such as on three benchmark datasets (Cora, Citeseer and Pubmed), our Poisson kernel still works well and almost better without training any adaptive kernel.