Graph kernels have been successfully applied to many graph classification problems. Typically, a kernel is first designed, and then an SVM classifier is trained based on the features defined implicitly by this kernel. This two-stage approach decouples data representation from learning, which is suboptimal. On the other hand, Convolutional Neural Networks (CNNs) have the capability to learn their own features directly from the raw data during training. Unfortunately, they cannot handle irregular data such as graphs. We address this challenge by using graph kernels to embed meaningful local neighborhoods of the graphs in a continuous vector space. A set of filters is then convolved with these patches, pooled, and the output is then passed to a feedforward network. With limited parameter tuning, our approach outperforms strong baselines on 7 out of 10 benchmark datasets, and reaches comparable performance elsewhere. Code and data are publicly available 1 .
This paper proposes a graph classification method by integrating three techniques, community detection, graph kernels, and CNNs.
* This paper is clearly written and easy to follow. Thus the clarity is high.
* The originality is not high as the application of neural networks for graph classification has already been studied elsewhere and the proposed method is a direct combination of three existing methods, community detection, graph kernels, and CNNs.
* The quality and the significance of this paper it not high due to the following reasons:
- The motivation is misleading in two folds.
  First, the authors say that the graph kernel + SVM approach has a drawback due to two independent processes of graph representation and learning.
  However, the parameters included in respective graph kernel is usually optimized via the SVM classification, hence they are not independent with each other.
  Second, the authors say that the proposed method addresses the above issue of independence between graph representation and learning.
  However, it also uses the two-step procedure as it first obtain the kernel matrix K via graph kernels and then apply CNN for classification, which is fundamentally the same as the existing approach.
  Although community detection is used before graph kernels, such subgraph extraction process is already implicitly employed in various graph kernels.
  I recommend to revise and clarify this point.
- In experimental evaluation, why several kernels including SP, RW, and WL are not used in the latter five datasets?
  This missing experiment significantly deteriorate the quality of empirical evaluation and I strongly recommend to add results for such kernels.
- It is mentioned that the parameter h is fixed to 5 in the WL kernel. However, it is known that the performance of the WL kernel depends on the parameter and it should be tuned by cross-validation.
  In contrast, parameters (number of epochs and the learning rate) are tuned in the proposed method. Thus the current comparison is not fair.
- In addition to the above point, how are parameters for GR and RW?
- Runtime is shown in Table 4 but there is no comparison with other methods. Although it is mentioned in the main text that the proposed method is faster than Graph CNN and Depp Graph Kernels, there is no concrete values and this statement is questionable (Runtime will easily vary due to the hardware configuration).
* Additional comment:
- Why is the community detection step needed? What will happen if K is directly constructed from given N graphs and what is the advantage of using not the original graphs but extracted subgraphs?
- In the first step of finding characteristic subgraphs, frequent subgraph mining can be used instead community detection.
  Frequent subgraph mining is extensively used in various methods for classification of graph-structured data, for example:
  * Tsuda, K., Entire regularization paths for graph data, ICML 2007.
  * Thoma, M. et al., Discriminative frequent subgraph mining with optimality guarantees, Statistical Analysis and Data Mining, 2010
  * Takigawa, I., Mamitsuka, H., Generalized Sparse Learning of Linear Models Over the Complete Subgraph Feature Set, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2017
  What is the advantage of using the community detection compared to frequent subgraph mining or other subgraph enumeration methods?