Diffusion Scattering Transforms on Graphs
Stability is a key aspect of data analysis. In many applications, the natural notion of stability is geometric, as illustrated for example in computer vision. Scattering transforms construct deep convolutional representations which are certified stable to input deformations. This stability to deformations can be interpreted as stability with respect to changes in the metric structure of the domain. In this work, we show that scattering transforms can be generalized to non-Euclidean domains using diffusion wavelets, while preserving a notion of stability with respect to metric changes in the domain, measured with diffusion maps. The resulting representation is stable to metric perturbations of the domain while being able to capture **high-frequency** information, akin to the Euclidean Scattering.
 The paper presents in interesting and new analysis of stability of scattering transforms on graphs, when the domain (graph) is perturbed by deformations. It combines key ingredients of scattering transforms (extended here to graphs through graph diffusion wavelets), deformation of graphs (based on graph diffusion distances) and a theoretical stability analysis. Similarly to the Euclidian domain, it is shown that linear filters cannot provide representations that are simultaneously rich and stable. Generally, the paper is pretty complete, interesting and sufficiently well presented. One might wonder if the choice of the diffusion framework for both the representation construction, and the deformation analysis, is a simplistic choice, and how similar ideas could extend to different domain deformation for example. The experiments and comparisons are also very minimal, and hard to interpret. Comparing things only with GFT and SVM is probability a *easy* choice, with the advent of a plethora of new graph convnets architectures (GFT is probably not a *graph baseline*, as mentioned in the conclusion). This is however an interesting work, that will likely generate exciting discussions at ICLR.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Diffusion Scattering Transforms on Graphs
Stability is a key aspect of data analysis. In many applications, the natural notion of stability is geometric, as illustrated for example in computer vision. Scattering transforms construct deep convolutional representations which are certified stable to input deformations. This stability to deformations can be interpreted as stability with respect to changes in the metric structure of the domain. In this work, we show that scattering transforms can be generalized to non-Euclidean domains using diffusion wavelets, while preserving a notion of stability with respect to metric changes in the domain, measured with diffusion maps. The resulting representation is stable to metric perturbations of the domain while being able to capture **high-frequency** information, akin to the Euclidean Scattering.
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>



 The paper presents in interesting and new analysis of stability of scattering transforms on graphs, when the domain (graph) is perturbed by deformations. It combines key ingredients of scattering transforms (extended here to graphs through graph diffusion wavelets), deformation of graphs (based on graph diffusion distances) and a theoretical stability analysis. Similarly to the Euclidian domain, it is shown that linear filters cannot provide representations that are simultaneously rich and stable. Generally, the paper is pretty complete, interesting and sufficiently well presented. One might wonder if the choice of the diffusion framework for both the representation construction, and the deformation analysis, is a simplistic choice, and how similar ideas could extend to different domain deformation for example. The experiments and comparisons are also very minimal, and hard to interpret. Comparing things only with GFT and SVM is probability a *easy* choice, with the advent of a plethora of new graph convnets architectures (GFT is probably not a *graph baseline*, as mentioned in the conclusion). This is however an interesting work, that will likely generate exciting discussions at ICLR.
assistant
 The paper presents in interesting and new analysis of stability of scattering transforms on graphs, when the domain (graph) is perturbed by deformations. It combines key ingredients of scattering transforms (extended here to graphs through graph diffusion wavelets), deformation of graphs (based on graph diffusion distances) and a theoretical stability analysis. Similarly to the Euclidian domain, it is shown that linear filters cannot provide representations that are simultaneously rich and stable. Generally, the paper is pretty complete, interesting and sufficiently well presented. One might wonder if the choice of the diffusion framework for both the representation construction, and the deformation analysis, is a simplistic choice, and how similar ideas could extend to different domain deformation for example. The experiments and comparisons are also very minimal, and hard to interpret. Comparing things only with GFT and SVM is probability a *easy* choice, with the advent of a plethora of new graph convnets architectures (GFT is probably not a *graph baseline*, as mentioned in the conclusion). This is however an interesting work, that will likely generate exciting discussions at ICLR.