Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 4: Borderline reject: Technically solid paper where reasons to reject, e.g., limited evaluation, outweigh reasons to accept, e.g., good evaluation. Please use sparingly.
review_content: summary: The paper proposes a method called NFGNN which utilizes generalized translation operator to learn local patterns contributing to homophily/heterophily.

strengths_and_weaknesses: Strengths:
1. A new GNN method with ability to capture the local patterns.
2. Well organized and easy to follow (in general).


Weaknesses/Questions:

1. My main concern is the performance of the proposed method as compared to existing baselines. 
Also, FAGCN adresses heterophily by considering low as well as high frequency information. 
The numbers reported in FAGCN are superior to the proposed method. 
Therefore it is difficult to establish the usefulness of the proposed method.

2. The evaluation on only node classification task seems limited to me. 
Additional experiments on graph classification tasks will further strengthen the paper. 

3. Even though Section 6 is well motivated, the content does not justify it to be a separate section.

4. Citation method is not proper. (please use \citep{} or \citet{} accordingly)

5. The purpose of reparameterization with low-rank approximation against first (or higher) order polynomial is not clear to me. 

6. How does generalized translated operator help in adapting to local patterns? It is defined through spectral domain. 
What is the intuition of this translation operator in spatial domain when a filter is translated to a node?


questions: Please see the section above.
limitations: n/a
review_title: null

final_score: rating: 7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
review_content: summary: This work proposes a new graph neural network by designing a node-oriented spectral filtering method. The developed algorithm is motivated by the observation that the subgraphs centered at different nodes have different properties. Experimental results demonstrate superior performance compared to baseline models.
strengths_and_weaknesses: Strength:

1. This paper indicates the fact that real-world graphs are often a mixture of diverse subgraph patterns.
2. This paper shows that the standard near-neighborhood aggregation mechanisms fail to work for the non-homophily graph.
3. This paper proposes a novel node-oriented graph spectral filtering method, which gives rise to a more powerful GNN model.

Weakness:

Overall, I am satisfied with the experimental findings and observations. The proposed model seems to be novel and useful. Some minor issues are as follows:

1. What if using 3 or more hop neighborhood aggregation methods? Standard multi-layer GNN models implicitly perform multi-hop neighbor aggregation. A discussion on this point is needed.

2. Will using learnable node-oriented graph spectral filtering involve more trainable parameters? Will this incur more severe overfitting?

3. It would be better to give a more clear comparison between the proposed filtering method and the prior methods in Section 4.1 (i.e., give more equations) to better highlight the difference and novelty of the proposed method.
questions: See weakness section
limitations: see weakness section
review_title: null

final_score: rating: 7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
review_content: summary: In this work the authors address the problem of local structure variation and non-homophily by introducing a generalized translation operator in order to implement a node centered spectral filter for graph neural networks. They demonstrate the empirical effectiveness of their method by confirming the realization of the filter localization in practice and showing performance gains on datasets with different homophily ratios.
strengths_and_weaknesses: ### Strengths

**Quality/Clarity**: The preliminaries and technical details of their proposed method are sound. The motivations section is particularly in depth as it provides not only theoretical but also empirical analysis of the homophily versus heterophily characteristics of the datasets to be used in the evaluation.

**Significance**: Though the modification is small, it fundamentally increases the adaptiveness of the family of spectral GNN approaches that, while having some nice theoretical properties, in their standard formulation, lack fine grained expressiveness or the ability to scale to large scale graphs where global filters are likely not as meaningful. Figure 3 and Table 2 provide targeted evidence of the effectiveness of the translation operator/NF modification.

### Weaknesses

**Significance**: The margins of improvement in Table 1 are not very significant except in Squirrel and Texas 

**Clarity**: There is not adequate discussion devoted prior to Section 5 in the preliminaries or the other theoretical prose on how exactly the localized filter is expected to better address variations in homophily characteristics. This is somewhat borne out by the results anyway, but it should be motivated earlier on.

**Originality**: Also relating to the significance, the fact that the core modification itself is quite compact, is noted, and thus the likelihood that the approach is completely novel is potentially low. But this isn't a focus of this review.
questions: 1. I'm a little confused by the wording of line 224 - it's stated as if $\Psi$ should be included in Eq. 9 somewhere? 
2. It is somewhat out of scope I'm sure, but as a convincing sanity check, it would be nice to have the _complement_ to the demonstration that the NF method indeed improves node oriented predictions, the complement being how it effects the full graph classification task. Would your hypothesis be that it doesn't improve/alter global representations much in that setting? (this would be a meta ablation of sorts)
limitations: 1. Barely a limitation, more a comment, that Table 1 is not as interesting/relevant to me as Fig 3 and Table 2. The direct analysis on the ability of the NF method to address heterophily should be the focus of the empirical section, even extended if possible.
review_title: null

final_score: rating: 4: Borderline reject: Technically solid paper where reasons to reject, e.g., limited evaluation, outweigh reasons to accept, e.g., good evaluation. Please use sparingly.
review_content: summary: This paper discusses node oriented spectral filtering as an extension to Chebyshev polynomial of normalized adjacency matrix. As motivation the paper argues on the aggregation of neighbors of labeled nodes. The paper argues on superiority on non-homophilic graphs through experiments.   
strengths_and_weaknesses: Strengths:
1.) Experimental results are promising

Weaknesses:
1.) Highly Incremental work. Very closely related to ChebNet and related method.
2.) Homophily definition is not up to date and experiments are not adequate.

questions: The argument of 2-hops and 3-hops aggregation is a bit confusing. It is mainly based on experiments using a few set of datasets. To my knowledge, methods such as the GPRGNN and Mixhop which uses higher-order convolutions (acting as convolution from multiple hops) do not impose such limits. Can authors elaborate on this?  


This paper only contain experiments with graph data by [Pei et al]. Further, the homophily measure described in the paper is a bit dated.
There is a new homophily measure and new non-homophilic benchmark datasets introduced by [Lim et al., 2021a, Lim et al., 2021b].
It would be interesting know how the proposed method perform with some of the new non-homophilic data. Can the authors provide few more experiment with the new dataset?

Two important non-GCN/GNN bechmark method that are important for comparison are the MLP and LINK [Zheleva and Getoor, 2009]. MLP would allow us to know about learning ability of node features itself and LINK tells us about direct learning from graph data only (adjacency matrix). Can the authors add these two benchmark methods in the paper? Another benchmark method that is useful for comparison is LINKX [Lim et al., 2021a].


Reference
   
[Zheleva and Getoor, 2009] Zheleva, E. and Getoor, L. (2009). To join or not to join: The illusion of privacy in  social networks with mixed public and private user profiles. WWW ’09.
 
 [Lim et al., 2021a] Lim, D., Hohne, F. M., Li, X., Huang, S. L., Gupta, V., Bhalerao, O. P., and Lim, S.-N.  (2021a). Large scale learning on non-homophilous graphs: New benchmarks and strong simple methods. In  NeurIPS.
 
 [Lim et al., 2021b] Lim, D., Li, X., Hohne, F., and Lim, S.-N. (2021b). New benchmarks for learning on  non-homophilous graphs. Workshop on Graph Learning Benchmarks, WWW 2021.
limitations: Limitations are not well discussed.
review_title: null

Meta-review: metareview: The paper has mixed reviews. While some reviewers feel that the paper is novel and interesting, other reviewers think that additional experiments are needed to justify the proposed method and that the proposed methods are somewhat incremental.
The paper will benefit from another revision that will address the raised concerns. 
confidence: Less certain
Decision: Reject