DEEP GEOMETRICAL GRAPH CLASSIFICATION
Most of the existing Graph Neural Networks (GNNs) are the mere extension of the Convolutional Neural Networks (CNNs) to graphs. Generally, they consist of several steps of message passing between the nodes followed by a global indiscriminate feature pooling function. In many data-sets, however, the nodes are unlabeled or their labels provide no information about the similarity between the nodes and the locations of the nodes in the graph. Accordingly, message passing may not propagate helpful information throughout the graph. We show that this conventional approach can fail to learn to perform even simple graph classification tasks. We alleviate this serious shortcoming of the GNNs by making them a two step method. In the first of the proposed approach, a graph embedding algorithm is utilized to obtain a continuous feature vector for each node of the graph. The embedding algorithm represents the graph as a point-cloud in the embedding space. In the second step, the GNN is applied to the point-cloud representation of the graph provided by the embedding method. The GNN learns to perform the given task by inferring the topological structure of the graph encoded in the spatial distribution of the embedded vectors. In addition, we extend the proposed approach to the graph clustering problem and a new architecture for graph clustering is proposed. Moreover, the spatial representation of the graph is utilized to design a graph pooling algorithm. We turn the problem of graph down-sampling into a column sampling problem, i.e., the sampling algorithm selects a subset of the nodes whose feature vectors preserve the spatial distribution of all the feature vectors. We apply the proposed approach to several popular benchmark data-sets and it is shown that the proposed geometrical approach strongly improves the state-of-the-art result for several data-sets. For instance, for the PTC data-set, we improve the state-of-the-art result for more than 22 %.
 The authors propose a method for learning representations for graphs. The main purpose is the classification of graphs. The topic is timely and should be of interest to the ICLR community. The proposed approach consists of four parts: Initial feature transformation Local features aggregation Graph pooling Final aggregator Unfortunately, each of the part is poorly explained and/or a method that has already been used before. For instance, the local feature aggregation is more or less identical to a GCN as introduced by Kipf and Welling. There are now numerous flavors of GCNs and the proposed aggregation function in (2) is not novel. Graph pooling is also a relatively well-established idea and has been investigated in several papers before. The authors should provide more details on their approach and compare it to existing graph pooling approaches. Neither (1) nor (4) are novel contributions. The experiments look OK but are not ground-breaking and are not enough to make this paper more than a mere combination of existing methods. The experiments do not provide standard deviation. Graph classification problems usually exhibit a large variance of the means. Hence, it is well possible that the difference in mean is not statistically significant. The paper could also benefit from a clearer explanation of the method. The explanation of the core parts (e.g., the graph pooling) are difficult to understand and could be made much clearer.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
DEEP GEOMETRICAL GRAPH CLASSIFICATION
Most of the existing Graph Neural Networks (GNNs) are the mere extension of the Convolutional Neural Networks (CNNs) to graphs. Generally, they consist of several steps of message passing between the nodes followed by a global indiscriminate feature pooling function. In many data-sets, however, the nodes are unlabeled or their labels provide no information about the similarity between the nodes and the locations of the nodes in the graph. Accordingly, message passing may not propagate helpful information throughout the graph. We show that this conventional approach can fail to learn to perform even simple graph classification tasks. We alleviate this serious shortcoming of the GNNs by making them a two step method. In the first of the proposed approach, a graph embedding algorithm is utilized to obtain a continuous feature vector for each node of the graph. The embedding algorithm represents the graph as a point-cloud in the embedding space. In the second step, the GNN is applied to the point-cloud representation of the graph provided by the embedding method. The GNN learns to perform the given task by inferring the topological structure of the graph encoded in the spatial distribution of the embedded vectors. In addition, we extend the proposed approach to the graph clustering problem and a new architecture for graph clustering is proposed. Moreover, the spatial representation of the graph is utilized to design a graph pooling algorithm. We turn the problem of graph down-sampling into a column sampling problem, i.e., the sampling algorithm selects a subset of the nodes whose feature vectors preserve the spatial distribution of all the feature vectors. We apply the proposed approach to several popular benchmark data-sets and it is shown that the proposed geometrical approach strongly improves the state-of-the-art result for several data-sets. For instance, for the PTC data-set, we improve the state-of-the-art result for more than 22 %.
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 authors propose a method for learning representations for graphs. The main purpose is the classification of graphs. The topic is timely and should be of interest to the ICLR community. The proposed approach consists of four parts: Initial feature transformation Local features aggregation Graph pooling Final aggregator Unfortunately, each of the part is poorly explained and/or a method that has already been used before. For instance, the local feature aggregation is more or less identical to a GCN as introduced by Kipf and Welling. There are now numerous flavors of GCNs and the proposed aggregation function in (2) is not novel. Graph pooling is also a relatively well-established idea and has been investigated in several papers before. The authors should provide more details on their approach and compare it to existing graph pooling approaches. Neither (1) nor (4) are novel contributions. The experiments look OK but are not ground-breaking and are not enough to make this paper more than a mere combination of existing methods. The experiments do not provide standard deviation. Graph classification problems usually exhibit a large variance of the means. Hence, it is well possible that the difference in mean is not statistically significant. The paper could also benefit from a clearer explanation of the method. The explanation of the core parts (e.g., the graph pooling) are difficult to understand and could be made much clearer.
assistant
 The authors propose a method for learning representations for graphs. The main purpose is the classification of graphs. The topic is timely and should be of interest to the ICLR community. The proposed approach consists of four parts: Initial feature transformation Local features aggregation Graph pooling Final aggregator Unfortunately, each of the part is poorly explained and/or a method that has already been used before. For instance, the local feature aggregation is more or less identical to a GCN as introduced by Kipf and Welling. There are now numerous flavors of GCNs and the proposed aggregation function in (2) is not novel. Graph pooling is also a relatively well-established idea and has been investigated in several papers before. The authors should provide more details on their approach and compare it to existing graph pooling approaches. Neither (1) nor (4) are novel contributions. The experiments look OK but are not ground-breaking and are not enough to make this paper more than a mere combination of existing methods. The experiments do not provide standard deviation. Graph classification problems usually exhibit a large variance of the means. Hence, it is well possible that the difference in mean is not statistically significant. The paper could also benefit from a clearer explanation of the method. The explanation of the core parts (e.g., the graph pooling) are difficult to understand and could be made much clearer.