Poisson kernel: Avoiding self-smoothing in graph convolutional networks

Abstract

Graph convolutional network is now an effective tool to deal with non-Euclidean data, such as social behavior analysis, molecular structure analysis, and skeleton-based action recognition. Graph convolutional kernel is one of the most significant factors in graph convolutional networks to extract nodes’ feature, and some variants of it have achieved highly satisfactory performance theoretically and experimentally. However, there was limited research about how exactly different graph structures influence the performance of these kernels. Some existing methods used an adaptive convolutional kernel to deal with a given graph structure, which still not explore the internal reasons. In this paper, we start from theoretical analysis of the spectral graph and study the properties of existing graph convolutional kernels, revealing the self-smoothing phenomenon and its effect in specific structured graphs. After that, we propose the Poisson kernel that can avoid self-smoothing without training any adaptive kernel. Experimental results demonstrate that our Poisson kernel not only works well on the benchmark datasets where state-of-the-art methods work fine, but also is evidently superior to them in synthetic datasets.