Paper:
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 as defined in graph signal processing. Further, as no approximation to the convolution is needed, TAGCN exhibits better performance than existing graph-convolution-approximation methods on a number of data sets. As only the polynomials of degree two of the adjacency matrix are used, TAGCN is also computationally simpler than other recent methods.

Review:
The paper introduces Topology Adaptive GCN (TAGCN) to generalize convolutional
networks to graph-structured data.
I find the paper interesting but not very clearly written in some sections,
for instance I would better explain what is the main contribution and devote
some more text to the motivation. Why is the proposed approach better than the
previously published ones, and when is that there is an advantage in using it?
The main contribution seems to be the use of the "graph shift" operator from
Sandryhaila and Moura (2013), which closely resembles the one from
Shuman et al. (2013). It is actually not very well explained what is the main
difference.
Equation (2) shows that the learnable filters g are operating on the k-th power
of the normalized adjacency matrix A, so when K=1 this equals classical GCN
from T. Kipf et al.
By using K > 1 the method is able to leverage information at a farther distance
from the reference node.
Section 2.2 requires some polishing as I found hard to follow the main story
the authors wanted to tell. The definition of the weight of a path seems
disconnected from the main text, ins't A^k kind of a a diffusion operator or
random walk?
This makes me wonder what would be the performance of GCN when the k-th power
of the adjacency is used.
I liked Section 3, however while it is true that all methods differ in the way they
do the filtering, they also differ in the way the input graph is represented
(use of the adjacency or not).
Experiments are performed on the usual reference benchmarks for the task and show
sensible improvements with respect to the state-of-the-art. TAGCN with K=2 has
twice the number of parameters of GCN, which makes the comparison not entirely
fair. Did the author experiment with a comparable architecture?
Also, how about using A^2 in GCN or making two GCN and concatenate them in
feature space to make the representational power comparable?
It is also known that these benchmarks, while being widely used, are small and
result in high variance results. The authors should report statistics over
multiple runs.
Given the systematic parameter search, with reference to the actual validation
(or test?) set I am afraid there could be some overfitting. It is quite easy
to probe the test set to get best performance on these benchmarks.
As a minor remark, please make figures readable also in BW.
Overall I found the paper interesting but also not very clear at pointing out
the major contribution and the motivation behind it. At risk of being too reductionist:
it looks as learning a set of filters on different coordinate systems given
by the various powers of A. GCN looks at the nearest neighbors and the paper
shows that using also the 2-ring improves performance.