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Title: Graph Classification with 2D Convolutional Neural Networks

Paper content:
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-of-the-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.
Replacing the raw counts by the empirical joint probability density function, either by normalizing the histograms, or with a Kernel Density Estimate, significantly deteriorated performance.
This suggests that keeping the absolute values of the counts is important, which makes sense, because some categories might be associated with larger or smaller graphs, on average.
Therefore, preventing the model from using size information is likely to decrease accuracy.
We also observed that increasing the number of channels to more than 5 does not yield better results (which makes sense, as channels contain less and less information), but that reducing this number improves performance in some cases, probably because it plays a regularization role.The main contribution of our study is a novel method for representing graphs as multi-channel image-like structures from their node embeddings, that allows them to be processed by 2D CNNs.
How the embeddings are computed, and which 2D CNN architecture is used, does not matter.
We hold this flexibility to be a major strength.
First, the embedding-agnostic nature of our method means that it can be seamlessly extended to directed, weighted, or labeled graphs with continuous or categorical node/edge attributes, simply by using an embedding algorithm that accepts such graphs, e.g., BID21 .
The independence of our approach with respect to the image classification model used is another advantage.
Here, we employed a vanilla 2D CNN architecture as it was offering an excellent trade-off between accuracy and simplicity, but more recent models, such as the one of BID15 , may yield even better results.
Above all, performance should improve as graph node embedding algorithms and CNN architectures for images improve in the future.Even though results are very good out-of-the-box in most cases, finding an embedding algorithm that works well, or the right combination of parameters for a given dataset, can require some efforts.
For instance, on COLLAB, we hypothesize that our results are inferior to that observed on the other datasets because optimizing p and q for COLLAB may require more than a coarse grid search, or because node2vec may not be well-suited to very dense graphs such as the ones found in COLLAB.
The main contribution of this paper is to show that CNN architectures designed for images can be used for graph processing in a completely off-the-shelf manner, simply by representing graphs as stacks of two-dimensional histograms of their node embeddings.
Despite the simplicity of our approach, results indicate that it is very competitive to state-of-the-art graph kernels and graph CNN models, sometimes outperforming them by a wide margin.
Furthermore, these good results were obtained with limited parameter tuning and by using a basic 2D CNN model.
From a time complexity perspective, our approach is preferable to graph kernels too, allowing to process larger datasets featuring bigger graphs.

assistant: text: We introduce a novel way to represent graphs as multi-channel image-like structures that allows them to be handled by vanilla 2D CNNs.