List of Papers By topics Author List
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Authors
Joonhyuk Park, Yechan Hwang, Minjeong Kim, Moo K. Chung, Guorong Wu, Won Hwa Kim
Abstract
A brain network, viewed as a graph wiring different regions of interest (ROIs) in the brain, has been widely used to investigate brain dysfunction with various graph neural networks (GNNs). However, existing GNNs are built upon graph convolution that transforms measurements on the nodes, where ROI-wise features are not always guaranteed for brain networks. Therefore, the majority of existing graph analysis methods that rely on node features are inapplicable for network analysis unless a proxy such as node degree is provided. Moreover, the complex neurological interactions across different brain regions cannot be directly expressed in a simple node-to-node (i.e., 0-simplex) representation. In this paper, we propose a novel method, Hodge-Graph Neural Network (Hodge-GNN), that allows the GNN to directly derive desirable representations of graph edges and capture complex edge-wise topological features spatially via the Hodge Laplacian. Specifically, representing a graph as a simplicial complex holds a significant advantage over conventional methods that extract higher-order connectivity of a graph through hierarchical convolution in the spatial domain or graph transformation. The superiority of our method is validated in the Alzheimer’s Disease Neuroimaging Initiative (ADNI) study, in comparison to benchmarking GNNs as well as state-of-the-art graph classification models.
Link to paper
DOI: https://doi.org/10.1007/978-3-031-43904-9_76
SharedIt: https://rdcu.be/dnwIp
Link to the code repository
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Link to the dataset(s)
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Reviews
Review #1
- Please describe the contribution of the paper
The paper describes a new graph neural network (GNN) model where the edge-to-edge relations are exploited hence allowing the apply GCN approach to graphs where no natural nodal features exist but rather the information is embedded in the the topology and the edge weights. An application to Alzheimer’s Disease demonstrates an improvement over mainstream approaches.
- Please list the main strengths of the paper; you should write about a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.
The paper has a theoretically sound approach to defining a graph convolution over the edge-to-edge relations where the edge weights form the graph signal. This is not a totally novel viewpoint as researchers have been aware of the need to apply ML/DL approaches on the graph topology and the associated edge weights in brain connectome research. Nevertheless, the paper proposes a theoretically sound approach to this problem, demonstrating an improvement in the domain of AD over a sufficiently large dataset.
- Please list the main weaknesses of the paper. Please provide details, for instance, if you think a method is not novel, explain why and provide a reference to prior work.
- Current GNN methods have been applied to study the topology of binary/weighted brain connectomes by using nodal embeddings as graph signals. This line of approach is ignored.
- Section 3 provides a theoretical background yet it is not clearly connected to Section 4. Hence the contribution of Section 3 to the manuscript is very limited, if not none.
- Brain connectomes are typically undirected graphs. The authors explain that their use of some probabilistic tractography provides them with directed graphs, which is not explained. I strongly suspect that the referred directionality has a neurological basis. Hence, the approach should better be applied to undirected weighted graphs if the target is brain connectome analysis.
- Using a subset of all possible edges to circumvent the problem of huge graph laplacians is questionable because the authors have used the set of edges (node pairs) that do exist (non-zero weight) in ALL subjects. This means that if there is an edge whose existence is a strong discriminating factor among groups, it is ignored. They used 530 edges (node pairs) among C(148,2) potential node pairs. I believe a union of all non-zero edges (node pairs) should have been considered. Section 5.3 refers to a “reduction of connectomes” in diseased subjects. The method of edge (node pair) selection adopted cannot see such a reduction but at best can see a “weakening of connectivity”.
- An analysis on the dependence on edge weight definition (fiber count, etc.) is due for this specific application.
- Line graphs are criticised for not being injective, yet they do perform pretty well and the new method’s injectivity is not discussed.
- Please rate the clarity and organization of this paper
Very Good
- Please comment on the reproducibility of the paper. Note, that authors have filled out a reproducibility checklist upon submission. Please be aware that authors are not required to meet all criteria on the checklist - for instance, providing code and data is a plus, but not a requirement for acceptance
The information and level detail provided is sufficient to reproduce the results.
- Please provide detailed and constructive comments for the authors. Please also refer to our Reviewer’s guide on what makes a good review: https://conferences.miccai.org/2023/en/REVIEWER-GUIDELINES.html
I would refer the authors to my comments in question 6 where I commented on the weak points of the manuscript and made suggestions.
- Rate the paper on a scale of 1-8, 8 being the strongest (8-5: accept; 4-1: reject). Spreading the score helps create a distribution for decision-making
6
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
Theoretically sound paper with a clear description of the method and sufficient experimental assessment. It potentially has applications in other graph analysis problems as well. The problem addressed is relevant to MICCAI community.
- Reviewer confidence
Very confident
- [Post rebuttal] After reading the author’s rebuttal, state your overall opinion of the paper if it has been changed
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- [Post rebuttal] Please justify your decision
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Review #2
- Please describe the contribution of the paper
The authors present a novel approach for brain graph classification via graph convolutional networks using the Hodge Laplacian convolutional operator on the ADNI dataset. This method incorporates brain structure directly into the final prediction via the Hodge Laplacian and outperformed other methods for graph classification. The study also identified important brain regions for Alzheimer’s disease classification, demonstrating the potential of this approach for improving understanding of brain connectivity in the disease.
- Please list the main strengths of the paper; you should write about a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.
The use of the Hodge Laplacian was well motivated and described, this is a very good step forward for edge convolutions which are applicable in situations where the edges of a graph are more important than the nodes. Advancements in this part of graph convolutional methods tends to be sparse as most methods focus on the nodes. The formulation of the operator was clear and easy to understand. The identification of connections between regions of the brain that were critical for the models diagnosis of Alzheimer’s disease was a great showcase of uses for the model.
- Please list the main weaknesses of the paper. Please provide details, for instance, if you think a method is not novel, explain why and provide a reference to prior work.
The architecture of the network should have been better described as it would be needed if someone wanted to reproduce results.
- Please rate the clarity and organization of this paper
Very Good
- Please comment on the reproducibility of the paper. Note, that authors have filled out a reproducibility checklist upon submission. Please be aware that authors are not required to meet all criteria on the checklist - for instance, providing code and data is a plus, but not a requirement for acceptance
The paper is not easily reproducible right now. The proposed convolutional operator should be integrated into torch_geometric, and the architecture needs to be described. A clear description of the model training would also be needed for reproducibility.
- Please provide detailed and constructive comments for the authors. Please also refer to our Reviewer’s guide on what makes a good review: https://conferences.miccai.org/2023/en/REVIEWER-GUIDELINES.html
The authors should comment on the numerical stability of the Hodge Laplacian extendibility to edge spectral convolutions.
If possible make your code available.
- Rate the paper on a scale of 1-8, 8 being the strongest (8-5: accept; 4-1: reject). Spreading the score helps create a distribution for decision-making
6
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
I would recommended accepting this paper based on the novelty alone, however the application of the model to identifying important region connection in Alzheimer’s was great at demonstrating the use of these methods and classification to gain insight into disease processes.
- Reviewer confidence
Very confident
- [Post rebuttal] After reading the author’s rebuttal, state your overall opinion of the paper if it has been changed
N/A
- [Post rebuttal] Please justify your decision
N/A
Review #3
- Please describe the contribution of the paper
The paper proposes the Hodge-GNN framework that extracts edge-to-edge relations in the grapho-spatial domain, which may provide new insights into the underlying biology of AD.
- Please list the main strengths of the paper; you should write about a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.
- Accurate classification of AD stages is an important clinical endpoint.
- The approach was able to extract ‘significant edges’ which seemingly correlate with literature on regions that are related to AD
- Please list the main weaknesses of the paper. Please provide details, for instance, if you think a method is not novel, explain why and provide a reference to prior work.
- Single validation dataset may not be sufficient to make definitive conclusions about the performance of the method.
- Scope of application (AD classification) may be too narrow for the amount of effort required to implement this framework, thus questioning its overall utility. However, the authors do not mention any other applications of their work.
- Please rate the clarity and organization of this paper
Good
- Please comment on the reproducibility of the paper. Note, that authors have filled out a reproducibility checklist upon submission. Please be aware that authors are not required to meet all criteria on the checklist - for instance, providing code and data is a plus, but not a requirement for acceptance
The paper provides formalism to derive their framework, but no source code. Substantial expertise in GNN concepts and implementation may be required to reproduce it.
- Please provide detailed and constructive comments for the authors. Please also refer to our Reviewer’s guide on what makes a good review: https://conferences.miccai.org/2023/en/REVIEWER-GUIDELINES.html
Please consider increasing the scope of application of your framework, as your method seems general enough to limit it by AD classification. It would be interesting to see other applications that might further elucidate the effectiveness of your approach.
- Rate the paper on a scale of 1-8, 8 being the strongest (8-5: accept; 4-1: reject). Spreading the score helps create a distribution for decision-making
5
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
This is an interesting paper with potential impact. The scope of implementation is, on one hand, rather broad. However, evaluation is limited to a single dataset and a single probelm (AD classification task) which may be insufficient to judge on the efficiency of the proposed approach.
- Reviewer confidence
Somewhat confident
- [Post rebuttal] After reading the author’s rebuttal, state your overall opinion of the paper if it has been changed
N/A
- [Post rebuttal] Please justify your decision
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Primary Meta-Review
- Please provide your assessment of this work, taking into account all reviews. Summarize the key strengths and weaknesses of the paper and justify your recommendation. In case you deviate from the reviewers’ recommendations, explain in detail the reasons why. In case of an invitation for rebuttal, clarify which points are important to address in the rebuttal.
The paper describes a new graph neural network (GNN) model where the edge-to-edge relations are exploited hence allowing the apply GCN approach to graphs. An application to Alzheimer’s Disease demonstrates an improvement over mainstream approaches. The work has a theoretically sound approach to defining graph convolution over the edge-to-edge relations, providing a novel approach. The reviewers also identified a few weakness, such as some missing aspects of brain network analysis, etc. The meirts outperformed the weakness. The authors may address some of the concerns in their camera ready version.
Author Feedback
We appreciate the reviewers for sincere and constructive feedback. We hope our additional explanations resolved all concerns raised in the reviews, and comments that require further extension will be addressed in future journal extensions.
R1) Comparison of GNN methods using nodal embeddings: Current GNN methods that use auxiliary node-wise measures or nodal embeddings barely consider the contribution of the neurological connectomic features of brain regions, while our method performs convolution directly on edges to effectively capture such topological features.
R1) Unclear contribution of Section 3: We suggest viewing brain network graph as a simplicial complex, which gave us the idea of expanding 0-simplex to 1-simplex graph representation. Section 3 explains how graphs can be viewed as a 1-skeleton and defines the matrix form of the boundary operator on p-simplex, which is used for defining the Hodge Laplacian matrix in Section 4.1.
R1) Brain connectomes as directed graph?: The direction in a connectivity matrix from tractography stems from probabilistic computation involving uncertainty. Convention is to symmetrize them by averaging, but our method can be applied directly on the asymmetric connectivity matrix. Although not demonstrated in current work, as the reviewer pointed, we expect that specific asymmetry in the adjacency matrix induced by neurological bias can be captured via our framework.
R1) Edge preprocessing: Using union of all non-zero edges, as suggested, was intractable due to the excessive number of remaining edges. To handle such an issue, we took the intersection of non-zero edges of CN subjects which may strengthen the explanation of “reduction of connectomes”. We have tried including additional edges over the limited intersection and observed improvement in the result, but we did not include it in the paper for a clear explanation of the experiment.
R1) Analysis on specific application: While the experiments in the paper primarily focus on Alzheimer’s Disease classification, the definition of edge weight and the analysis of the Hodge-GNN can be adopted for analysis of other diseases or any class of graphs that come without node signals.
R2) Reproducibility: We will share our code soon to address the reproducibility concerns.
R3) Extension on other applications: The transformation to a higher-simplical representation was a key point in capturing complex edge-wise interaction of the brain network. Hence, we expect the edge-wise convolution using Hodge Laplacian can be applied to other graph datasets with limited node features or complex topological features. We anticipate that results for such applications will be explored in future works.