The tremendous success of deep generative models on generating continuous data like image and audio has been achieved; however, few deep graph generative models have been proposed to generate discrete data such as graphs. The recently proposed approaches are typically unconditioned generative models which have no control over modes of the graphs being generated. Differently, in this paper, we are interested in a new problem named Deep Graph Translation: given an input graph, the goal is to infer a target graph by learning their underlying translation mapping. Graph translation could be highly desirable in many applications such as disaster management and rare event forecasting, where the rare and abnormal graph patterns (e.g., traffic congestions and terrorism events) will be inferred prior to their occurrence even without historical data on the abnormal patterns for this specific graph (e.g., a road network or human contact network). To this end, we propose a novel Graph-Translation-Generative Adversarial Networks (GT-GAN) which translates one mode of the input graphs to its target mode. GT-GAN consists of a graph translator where we propose new graph convolution and deconvolution layers to learn the global and local translation mapping. A new conditional graph discriminator has also been proposed to classify target graphs by conditioning on input graphs. Extensive experiments on multiple synthetic and real-world datasets demonstrate the effectiveness and scalability of the proposed GT-GAN.
The paper presents an approach for translating graphs in one domain to graphs in the same domain using a GAN approach. A graph Translator approach is defined and a number of synthetic data sets and one real-world data set are used to evaluate the approach. Most of the paper is written well, though there are some odd sentence structure issues in places. The paper could do with a thorough check for grammatical and spelling mistakes. For example you miss-spell NVIDIA.
The main concerns with the work:
1) Equation 2 is used to minimise the distance between graphs from X and graphs in Y. Yet, the main metric which is used to evaluate the paper is this distance. This would seem to give an unfair advantage to your approach. I would also be concerned about the fact that later you use this for stating if a graph represents good or hacker activity. If you have drawn translated graphs towards real graphs, how do you know that you haven’t pulled a good graph closer to a hacker graph? This is more concerning considering work which came out of NIPS which suggested that GAN’s tend to favour producing similar output rather than spreading it evenly over the domain.
2) It isn’t entirely clear what your results are trying to show. Presumably P, R, AUC and F1 are generated from the results produced from your Discriminator? Were each of the other approaches optimised against your discriminator or not? Also, it is unclear as to what the Gold Standard method is - we’re only told that its a classifier, but what type and how constructed?
3) Your approach seems to be ‘fixed’ in the set of nodes which are in both in the input and output graphs - needing to be the same. This would seem significantly limiting as graphs are rarely of the same node set.
4) Although you comment on other graphs approaches being limited to very small graphs, you do not test your approach on graphs with over 150 nodes. These would also seem to be very small graphs in comparison to real-world graphs. Further evaluation on larger graphs would seem to be essential - how long would it take on graphs with 10^6 nodes?
5) The real-world dataset seems rather odd and not fully explored. Given that you have this data it is surprising that you didn’t complete the loop by showing that you could take data from before a hack attempt and show that you could predict that in the future you had a hack attempt. Perhaps this is due to the fact that you didn’t have the ground-truth data in here to show a graph going from good to bad? But if not it would have been good to have shown, either through this data or some other, how your approach does match in with real-world results.
Given the points above, I would be very concerned on an approach which used the above to identify a future hacking attempt.
Some more specific comments on the paper:
- "The tremendous success of deep generative models on generating continuous data like image and audio” - it is not clear what this continuous data is.
- Hard to parse : “which barely can be available for the accounts worth being monitored.”
- “This requires us to learn the generic distribution of theft behaviors from historical attacks and synthesize the possible malicious authentication graphs for the other accounts conditioning on their current computer networks” - given that these historical attacks are (hopefully) rare, is there enough data here to construct a model?
- Please define GCNN
- “Our GT-GAN is highly extensible where underlying building blocks, GCNN and distance measure in discriminator, can be replaced by other techniques such as (Kipf & Welling, 2017; Arjovsky et al., 2017) or their extensions.” - this sounds more like a feature of what you have contributed rather than a contribution in its own right.
- In the context of synthetic data, what is ground-truth?
- Hard to parse “Modern deep learning techniques operating on graphs is a new trending topic in recent years.”
- Hard to parse “However, these methods are highly tailored to only address the graph generation in a specific type of applications such as molecules generation” 
- Hard to parse “Existing works are basically all proposed in the most recent year,”
- “Typically we focus on learning the translation from one topological patterns to the other one” -> “Typically we focus on learning the translation from one topological pattern to the other”
- It’s not clear in equation 1 how you represent G_X. Only much later is it mentioned about adjacency matrix.
- Hard to parse “Different and more difficult than graph generation designed only for learning the distribution of graph representations, for graph translation one needs to learn not only the latent graph presentation but also the generic translation mapping from input graph to the target graph simultaneously.“
- Hard to parse “graph translation requires to learn”
- Hard to parse “in most of them the input signal is given over node with a static set of edge and their weights fixed for all samples”
- “we propose an graph” -> “we propose a graph”
- Hard to parse “The two components of the formula refers to direction filters as talked above”
- Hard to parse “Next, graph translator requires to”
- “as shown in Equations equation 7 and Equations equation 6,” -> “as shown in Equation 6 and Equation 7”
- Hard to parse “The challenge is that we need not only to learn the”
- Figure 2 would seem to need more explanation. 
- The end of section 3.3 is a bit vague and lacks enough detail to reproduce.
- “our GT-GAN is able to provide a scalable (i.e., O(N2)) algorithm that can generate general graphs.” - what sizes have you tested this up to?
- Hard to parse “we randomly add another kjEj edges on it to form the target graph”
- “The goal is to forecast and synthesize the future potential malicious authentication graphs of the users without any historical malicious behaviors, by the graph translator from normal to malicious graph trained based on the users with historical malicious-behavior records.” - This isn’t entirely clear. Are you trying to create new malicious graphs or show that a current graph will eventually go malicious?
- “All the comparison methods are directly trained by the malicious graphs without the conditions of input graphs as they can only do graph generation instead of translation.” - not clear. For the synthetic data sets how did you choose which ones were malicious?
- “GraphRNN is tested with graph size within 150. GraphGMG, GraphVAE is tested within size 10 and RandomVAE is tested on graphs within size 150.” -> “GraphRNN and RandomVAE are tested with graph up to size 150. GraphGMG, GraphVAE is tested with graphs up to  size 10.”
- “Here, beyond label imbalance, we are interested in “label missing” which is more challenging.” - “missing labels”?
- “In addition, we have also trained a “gold standard” classifier based on input graphs and real target
graphs.” - need to say more about this.