Spectral Convolutional Networks on Hierarchical Multigraphs
Spectral Graph Convolutional Networks (GCNs) are a generalization of convolutional networks to learning on graph-structured data. Applications of spectral GCNs have been successful, but limited to a few problems where the graph is fixed, such as shape correspondence and node classification. In this work, we address this limitation by revisiting a particular family of spectral graph networks, Chebyshev GCNs, showing its efficacy in solving graph classification tasks with a variable graph structure and size. Current GCNs also restrict graphs to have at most one edge between any pair of nodes. To this end, we propose a novel multigraph network that learns from multi-relational graphs. We explicitly model different types of edges: annotated edges, learned edges with abstract meaning, and hierarchical edges. We also experiment with different ways to fuse the representations extracted from different edge types. This restriction is sometimes implied from a dataset, however, we relax this restriction for all kinds of datasets. We achieve state-of-the-art results on a variety of chemical, social, and vision graph classification benchmarks.
 This paper extends spectral GCN to multigraphs, in which graph size and structure may vary. It builds on Chebnets and extends it to graphs with several relations (more than one edge by pair of nodes). While the paper is clearly written and is interesting, the contributions are rather incremental and the experimental section does not show a clear improvement wrt the state-of-the-art, neither a clear conclusion on the impact of learning the edges. Minor comments regarding the experiments: The experimental section may be improved in order to better demonstrate the value of the proposed method. Authors use a standard setting for the experiments: 10 reps. of 10 nested CV on several benchmarked datasets. As pointed out by the authors, some of them contain few samples (mutag). Mean accuracies are reported, but standard deviations are also of interested (difficult to see if a method is better than an other one by comparing avg only). In addition, in table 1, some figures are missing (I believe this is because the methods have not been implemented by the authors). Regarding social graphs datasets, this is an issue as the results do not build on the same datasets (for multigraph chebnet, some features are added -- this is not the case for some competitors). Some experiments on a image classification context are also provided, but some competitive methods are not evaluated (e.g. PSCN). The bold/underlined+bold should be carefully checked as some wrong figures are highlighted.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Spectral Convolutional Networks on Hierarchical Multigraphs
Spectral Graph Convolutional Networks (GCNs) are a generalization of convolutional networks to learning on graph-structured data. Applications of spectral GCNs have been successful, but limited to a few problems where the graph is fixed, such as shape correspondence and node classification. In this work, we address this limitation by revisiting a particular family of spectral graph networks, Chebyshev GCNs, showing its efficacy in solving graph classification tasks with a variable graph structure and size. Current GCNs also restrict graphs to have at most one edge between any pair of nodes. To this end, we propose a novel multigraph network that learns from multi-relational graphs. We explicitly model different types of edges: annotated edges, learned edges with abstract meaning, and hierarchical edges. We also experiment with different ways to fuse the representations extracted from different edge types. This restriction is sometimes implied from a dataset, however, we relax this restriction for all kinds of datasets. We achieve state-of-the-art results on a variety of chemical, social, and vision graph classification benchmarks.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



 This paper extends spectral GCN to multigraphs, in which graph size and structure may vary. It builds on Chebnets and extends it to graphs with several relations (more than one edge by pair of nodes). While the paper is clearly written and is interesting, the contributions are rather incremental and the experimental section does not show a clear improvement wrt the state-of-the-art, neither a clear conclusion on the impact of learning the edges. Minor comments regarding the experiments: The experimental section may be improved in order to better demonstrate the value of the proposed method. Authors use a standard setting for the experiments: 10 reps. of 10 nested CV on several benchmarked datasets. As pointed out by the authors, some of them contain few samples (mutag). Mean accuracies are reported, but standard deviations are also of interested (difficult to see if a method is better than an other one by comparing avg only). In addition, in table 1, some figures are missing (I believe this is because the methods have not been implemented by the authors). Regarding social graphs datasets, this is an issue as the results do not build on the same datasets (for multigraph chebnet, some features are added -- this is not the case for some competitors). Some experiments on a image classification context are also provided, but some competitive methods are not evaluated (e.g. PSCN). The bold/underlined+bold should be carefully checked as some wrong figures are highlighted.
assistant
 This paper extends spectral GCN to multigraphs, in which graph size and structure may vary. It builds on Chebnets and extends it to graphs with several relations (more than one edge by pair of nodes). While the paper is clearly written and is interesting, the contributions are rather incremental and the experimental section does not show a clear improvement wrt the state-of-the-art, neither a clear conclusion on the impact of learning the edges. Minor comments regarding the experiments: The experimental section may be improved in order to better demonstrate the value of the proposed method. Authors use a standard setting for the experiments: 10 reps. of 10 nested CV on several benchmarked datasets. As pointed out by the authors, some of them contain few samples (mutag). Mean accuracies are reported, but standard deviations are also of interested (difficult to see if a method is better than an other one by comparing avg only). In addition, in table 1, some figures are missing (I believe this is because the methods have not been implemented by the authors). Regarding social graphs datasets, this is an issue as the results do not build on the same datasets (for multigraph chebnet, some features are added -- this is not the case for some competitors). Some experiments on a image classification context are also provided, but some competitive methods are not evaluated (e.g. PSCN). The bold/underlined+bold should be carefully checked as some wrong figures are highlighted.