  Spectral graph convolutional neural networks (CNNs) require approximation to
the convolution to alleviate the computational complexity, resulting in
performance loss. This paper proposes the topology adaptive graph convolutional
network (TAGCN), a novel graph convolutional network defined in the vertex
domain. We provide 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. The TAGCN not only inherits the properties of convolutions in CNN
for grid-structured data, but it is also consistent with convolution as defined
in graph signal processing. Since no approximation to the convolution is
needed, TAGCN exhibits better performance than existing spectral CNNs on a
number of data sets and is also computationally simpler than other recent
methods.
