Graph classification is currently dominated by graph kernels, which, while powerful, suffer some significant limitations. Convolutional Neural Networks (CNNs) offer a very appealing alternative. However, processing graphs with CNNs is not trivial. To address this challenge, many sophisticated extensions of CNNs have recently been proposed. In this paper, we reverse the problem: rather than proposing yet another graph CNN model, we introduce a novel way to represent graphs as multi-channel image-like structures that allows them to be handled by vanilla 2D CNNs. Despite its simplicity, our method proves very competitive to state-ofthe-art graph kernels and graph CNNs, and outperforms them by a wide margin on some datasets. It is also preferable to graph kernels in terms of time complexity. Code and data are publicly available 1 .
The authors propose to use 2D CNNs for graph classification by transforming graphs to an image-like representation from its node embedding. The approach uses node2vec to obtain a node embedding, which is then compacted using PCA and turned into a stack of discretized histograms. Essentially the authors propose an approach to use a node embedding to achieve graph classification.
In my opinion there are several weak points:
1) The approach to obtain the image-like representation is not well motivated. Other approaches how to  aggregate the set of node embeddings for graph classification are known, see, e.g., "Representation Learning on Graphs: Methods and Applications", William L. Hamilton, Rex Ying, Jure Leskovec, 2017. The authors should compare to such methods as a baseline.
2) The experimental evaluation is not convincing:
- the selection of competing methods is not sufficient. I would like to suggest to add an approach similar to Duvenaud et al., "Convolutional networks on graphs for learning molecular fingerprints", NIPS 2015.
- the accuracy results are taken from other publications and it is not clear that this is an authoritative comparison; the accuracy results published for state-of-the-art graph kernels are superior to those obtained by the proposed method, cf., e.g., Kriege et al., "On Valid Optimal Assignment Kernels and Applications to Graph Classification", NIPS 2016.
- it would be interesting to apply the approach to graphs with discrete and continuous labels.
3) The authors argue that their method is preferable to graph kernels in terms of time complexity. This argument is questionable. Most graph kernels compute explicit feature maps and can therefore be used with efficient linear SVMs (unfortunately most publications use a kernelized SVM). Moreover, the running of computing the node embedding must be emphasized: On page 2 the authors claim a "constant time complexity at the instance level", which is not true when also considering the running time of node2vec. Moreover, I do not think that node2vec is more efficient than, e.g., Weisfeiler-Lehman refinement used by graph kernels.
In summary: Since the technical contribution is limited, the approach needs to be justified by an authoritative experimental comparison. This is not yet achieved with the results presented in the submitted paper. Therefore, it should not be accepted in its current form.