  Graph convolutional networks are becoming indispensable for deep learning
from graph-structured data. Most of the existing graph convolutional networks
share two big shortcomings. First, they are essentially low-pass filters, thus
the potentially useful middle and high frequency band of graph signals are
ignored. Second, the bandwidth of existing graph convolutional filters is
fixed. Parameters of a graph convolutional filter only transform the graph
inputs without changing the curvature of a graph convolutional filter function.
In reality, we are uncertain about whether we should retain or cut off the
frequency at a certain point unless we have expert domain knowledge. In this
paper, we propose Automatic Graph Convolutional Networks (AutoGCN) to capture
the full spectrum of graph signals and automatically update the bandwidth of
graph convolutional filters. While it is based on graph spectral theory, our
AutoGCN is also localized in space and has a spatial form. Experimental results
show that AutoGCN achieves significant improvement over baseline methods which
only work as low-pass filters.
