Paper:
Convolution Neural Network (CNN) has gained tremendous success in computer vision tasks with its outstanding ability to capture the local latent features. Recently, there has been an increasing interest in extending CNNs to the general spatial domain. Although various types of graph convolution and geometric convolution methods have been proposed, their connections to traditional 2D-convolution are not well-understood. In this paper, we show that depthwise separable convolution is a path to unify the two kinds of convolution methods in one mathematical view, based on which we derive a novel Depthwise Separable Graph Convolution that subsumes existing graph convolution methods as special cases of our formulation. Experiments show that the proposed approach consistently outperforms other graph convolution and geometric convolution baselines on benchmark datasets in multiple domains.

Review:
The paper presents a Depthwise Separable Graph Convolution network that aims
at generalizing Depthwise convolutions, that exhibit a nice performance in image
related tasks, to the graph domain. In particular it targets
Graph Convolutional Networks.
In the abstract the authors mention that the Depthwise Separable Graph Convolution
that they propose is the key to understand the connections between geometric
convolution methods and traditional 2D ones. I am afraid I have to disagree as
the proposed approach is not giving any better understanding of what needs to be
done and why. It is an efficient way to mimic what has worked so far for the planar
domain but I would not consider it as fundamental in "closing the gap".
I feel that the text is often redundant and that it could be simplified a lot.
For example the authors state in various parts that DSC does not work on
non-Euclidean data. Section 2 should be clearer and used to better explain
related approaches to motivate the proposed one.
In fact, the entire motivation, at least for me, never went beyond the simple fact
that this happens to be a good way to improve performance. The intuition given
is not sufficient to substantiate some of the claims on generality and understanding
of graph based DL.
In 3.1, at point (2), the authors mention that DSC filters are learned from the
data whereas GC uses a constant matrix. This is not correct, as also reported in
equation 2. The matrix U is learned from the data as well.
Equation (4) shows that the proposed approach would weight Q different GC
layers. In practical terms this is a linear combination of these graph
convolutional layers.
What is not clear is the \Delta_{ij} definition. It is first introduced in 2.3
and described as the relative position of pixel i and pixel j on the image, but
then used in the context of a graph in (4). What is the coordinate system used
by the authors in this case? This is a very important point that should be made
clearer.
Why is the Related Work section at the end? I would put it at the front.
The experiments compare with the recent relevant literature. I think that having
less number of parameters is a good thing in this setting as the data is scarce,
however I would like to see a more in-depth comparison with respect to the number
of features produced by the model itself. For example GCN has a representation
space (latent) much smaller than DSCG.
No statistics over multiple runs are reported, and given the high variance of
results on these datasets I would like them to be reported.
I think the separability of the filters in this case brings the right level of
simplification to the learning task, however as it also holds for the planar case
it is not clear whether this is necessarily the best way forward.
What are the underlying mathematical insights that lead towards selecting
separable convolutions?
Overall I found the paper interesting but not ground-breaking. A nice application
of the separable principle to GCN. Results are also interesting but should be
further verified by multiple runs.