Venue: ICLR 2020 Conference

Reviews:

final_score: rating: 6: Weak Accept
review_content: The paper proposes a new 2-D graph convolution method to aggregate information using both the node relation graph and the attribute graph generated using, e.g., PMI and KNN. The motivation does make sense that using 1-D convolution along the node dimension might not enough for learning representation for those low-degree nodes. Then, the attribute relation might be used to further smooth the node representation. The assumption could be that documents in a class are likely to consist of similar (related) words. To achieve this, the information aggregation along the node and the attribute dimension is implemented via a product of three matrices, the node graph convolutional filter computed from node affinity matrix, the attribute graph convolutional filter computed the attribute affinity matrix given by PMI or KNN, and the node-attribute matrix, which can be one main contribution. 
Besides, the paper also includes a detailed discussion of intra-class variance reduction. They evaluated the proposed method on both the mode classification and the node clustering against several existing methods, demonstrated that the proposed method almost always outperforms those methods on the two datasets. Overall, it is an interesting paper. 

For aggregating the information along the node dimension and the attribute dimension, as mentioned in the paper, is it possible to firstly do the propagation over the attribute graph using a 1-layer GCN, followed by another 1-layer GCN over the node relation graph, similar to dense graph propagation module in “Rethinking knowledge graph propagation for zero-shot learning”?

There are two ways to build an attribute graph. The experiments seem to show that the performance is quite different. It would be good to have some discussion on this. 

One motivation is about the low-degree nodes, where the attribute graph might help. It would be good to have a study on the performance of the methods on those low-degree nodes. 
review_title: Official Blind Review #3

final_score: rating: 6: Weak Accept
review_content: This work proposes a 2D graph convolution to combine the relational information encoded both in the nodes and in the edges.

The basic idea is to reduce the intra-class variance. The authors provide theorems and proofs to support this claim even though it is quite intuitive that smoothing with similar neighbours preserves higher variance with respect to dissimilar neighbours.

It is not straightforward to understand the limitations on the size of graphs.

The experimental analysis provides the empirical evidence of the properties of the proposed method. It is worthwhile to remark that connectivity is not necessarily helpful, like in the wiki dataset where connected nodes are not similar.

review_title: Official Blind Review #3

final_score: rating: 3: Weak Reject
review_content: The authors propose a method that incorporates two types of graphs into a graph convolutional networks:

(1) the given graph, which the authors refer to as node affinity graph, and 
(2) the graph that models an affinity between node attribute values.

The main contribution of their work is a type of graph convolution that combines convolutions operating on these two graphs. 

The paper is densely written and provides several mathematical derivations that are unnecessary to convey the proposed method. Personally, I don't see any benefits in having sections 3.1-3.4 in the main paper. The method actually proposed and evaluated in the paper is described in section 3.5. Sections 3.1-3.4 could be moved to an appendix. They confuse the reader more than they help. (They demonstrate knowledge of graph signal processing on the parts of the authors but little more.)

Trying to provide some theoretical analysis of the proposed method (and standard graph convolutions) by showing that the intra-class variance is reduced is laudable. The theorems, however, only hold under strong assumptions and could, in my opinion, also be moved to an appendix. In the end, they don't have any bearing on the performance of the methods using real-world datasets. Adding some experiments to analyse to what extent the assumptions made by the theorems are met in the given datasets would be an interesting addition to the paper. 

The authors discuss related work sufficiently with one exception: there has been recent work on learning the structure of graph neural networks. See for example [1]. The structure is derived/bootstrapped using node attribute similarities and it is shown that augmenting the graph with these new edges improves accuracy significantly. I would like to point the authors specifically to Figure 2 and Table 1 in said paper, where the authors show that adding edges (e.g., based on some node attribute affinity before or during training) is beneficial and improves accuracy. It would therefore be interesting to see how the authors proposed 2-D convolution would compare to a baseline where the edges based on attribute affinity are added to the original (node affinity) graph. It is a (somewhat simpler) alternative way to combine node affinity and node attribute graphs. 

[1] https://arxiv.org/pdf/1903.11960.pdf

The empirical results are mixed. Due to the numerous different variations of DSGC for which experiments were conducted, the difference between DSGC and existing methods is probably not statistically significant (a bonferroni correction was not performed to counteract the multiple comparisons). 

Overall this an interesting paper that introduces a way to incorporate node attribute affinity graphs. It is too densely written and could benefit from moving the theoretical parts to an appendix. They don't really add much to the core of the paper. Moreover, the authors do not consider approaches that also add edges to the graph (based, e.g., on attribute value similarity or during learning, see e.g. [1]) showing that that improves performance even when using a vanilla GCN. A comparison to a baseline that simply adds edges based on attribute affinity to the graph and applied a vanilla GCN should be part of the evaluation. The empirical results are mixed and don't show a clear advantage of the proposed method. 

review_title: Official Blind Review #1

Meta-review: The paper studies the problem of graph learning with attributes, and propose a 2-D graph convolution that models the node relation graph and the attribute graph jointly. The paper proposes and efficient algorithm and models intra-class variation. Empirical performance on 20-NG, L-Cora, and Wiki show the promise of the approach.

The authors responded to the reviews by updating the paper, but the reviewers unfortunately did not further engage during the discussion period. Therefore it is unclear whether their concerns have been adequately addressed.

Overall, there have been many strong submissions on graph neural networks at ICLR this year, and this submission as is currently stands does not quite make the threshold of acceptance.
Decision: Reject