Convolution acts as a local feature extractor in convolutional neural networks (CNNs). However, the convolution operation is not applicable when the input data is supported on an irregular graph such as with social networks, citation networks, or knowledge graphs. This paper proposes the topology adaptive graph convolutional network (TAGCN), a novel graph convolutional network that generalizes CNN architectures to graph-structured data and provides a systematic way to design a set of fixed-size learnable filters to perform convolutions on graphs. The topologies of these filters are adaptive to the topology of the graph when they scan the graph to perform convolution, replacing the square filter for the grid-structured data in traditional CNNs. The outputs are the weighted sum of these filters' outputs, extraction of both vertex features and strength of correlation between vertices. It can be used with both directed and undirected graphs. The proposed TAGCN not only inherits the properties of convolutions in CNN for grid-structured data, but it is also consistent with convolution in traditional signal processing. We apply TAGCN to semi-supervised learning problems for graph vertex classification; experiments on a number of data sets demonstrate that our method outperforms the existing graph convolutional neural networks and achieves state-of-the-art performance for each data set tested.

本篇论文提出了一种基于变量域的新型图卷积网络（TAGCN），通过设计一组可学习的固定大小的滤波器，用于对图执行卷积操作。这些过滤器在扫描图以执行卷积时，可以自适应地适应图的拓扑结构。与现有的谱CNN相比，TAGCN表现更好，并且比近期其他方法计算上更简单。

拓扑自适应图卷积网络