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Abstract

Diffusion tensor imaging (DTI) and functional MRI (fMRI) provide complementary views of the brain by revealing the physical structure connectivity (SC) between brain regions and function connectivity (FC) between those regions during neural processing. Previous evidence has shown that fusing the two modalities facilitates the identification of abnormal connectivity associated with neurocognitive disorders. However, existing fusion approaches are generally performed in Euclidean space and thus cannot effectively capture the intrinsic hierarchical organization of structural/functional brain networks. To this end, we propose a novel hyperbolic kernel graph convolutional network with SC-FC Coupling (HKC) for neurocognitive impairment analysis. The HKC consists of a hyperbolic kernel graph convolutional network for extracting local-to-global features from DTI and fMRI, an SC-FC coupling module that models global SC-FC interactions based on encoded DTI and fMRI features, and a hyperbolic neural network predictor for classification. Our HKC captures both local and global dependencies among structurally and functionally connected brain regions while preserving the hierarchical organization of brain networks. We evaluate HKC on paired DTI and fMRI data from 68 individuals with HIV-associated asymptomatic neurocognitive impairment and 69 healthy controls, with experimental results suggesting its superiority over state-of-the-art methods. Additionally, HKC identifies key SC-FC patterns in ANI, highlighting the visual network and fronto-cerebellar connections as critical biomarkers.

Links to Paper and Supplementary Materials

Main Paper (Open Access Version): https://papers.miccai.org/miccai-2025/paper/3127_paper.pdf

SharedIt Link: Not yet available

SpringerLink (DOI): Not yet available

Supplementary Material: Not Submitted

Link to the Code Repository

N/A

Link to the Dataset(s)

N/A

BibTex

@InProceedings{YanMei_Hyperbolic_MICCAI2025,
        author = { Yang, Meimei AND Sun, Yongheng AND Wang, Qianqian AND Wang, Wei AND Li, Hong-Jun AND Liu, Mingxia},
        title = { { Hyperbolic Kernel GCN with Structure-Function Connectivity Coupling for Neurocognitive Impairment Analysis } },
        booktitle = {proceedings of Medical Image Computing and Computer Assisted Intervention -- MICCAI 2025},
        year = {2025},
        publisher = {Springer Nature Switzerland},
        volume = {LNCS 15971},
        month = {September},
        page = {405 -- 415}
}

Reviews

Review #1

  • Please describe the contribution of the paper

    The authors propose a method to perform disease classification using a modified GCN framework using fMRI (functional connectivity [FC]) and DTI (structural connectivity [SC]) inputs. They modified GCN to a hyperbolic kernel GCN (HKGCN). They also employed an FC-SC coupling module to leverage the enhanced interaction between the two modalities. It was tested on classifying normal controls from HIV-associated asymptomatic neurocognitive impairment. The method performed better than other methods.

  • Please list the major strengths of the paper: you should highlight 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.

    Existing hyperbolic GCN suffered from complexity issues, which was improved with their hyperbolic kernel GCN.

  • Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.
    1. Method: The adopted atlas is suboptimal. AAL atlas is mainly derived from structural properties. There are better alternatives such as Brainnetome, Glasser, and Schafer atlases for studying FC of SC.
    2. Methods: The fMRI data were preprocessed a non-standard method. fMRIprep or HCP pipeline are the well-established methods.
    3. Methods: The authors stated <Here, ReLU(·) approximates the HAC kernel to capture global nonlinear relationships and cos(·) approximates the HRBF kernel to retain local information of SC or FC graphs by aggregating neighborhood features of the graph.> This is unclear. Why the former is suited for global relationships and the latter is suited for local interactions is not explained.
    4. Experiments: There are insufficient comparisons. The SOTA methods they mention are BrainNetCNN (2017) and BrainGNN (2021). As you can see from the recent review paper on brain GNN (ref#1), there are many recent methods. To name a few, BRAINNETTF (NIPS 22), Com-BrainTF (MICCAI 23), and Cross-GNN (TMI 23) were found in the survey. Please see the reference for a complete list. REF#1: Graph Neural Networks for Brain Graph Learning: A Survey. IJCAI 2024.
    5. Results: Table 2 is the ablation results. The first method (HKC-G, replacing their HKGCN with vanilla GCN) had 0.68 AUC and it performed better than the second method (HKC-K, replacing HKGCN with HGCN, AUC 0.64). This is weird because you expect to see performance gain as you apply a hierarchical method compared to a non-hierarchical method. In addition, their method HKGCN had AUC 0.70, a modest improvement from HKC-G casting doubts about why we need complex modules for a marginal increase in performance over simple GCN.
    6. Results: Authors claim their method is computationally more efficient than existing methods. I would like to see FLOPs compared among different methods.
  • Please rate the clarity and organization of this paper

    Satisfactory

  • Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.

    The submission does not provide sufficient information for reproducibility.

  • Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2025/en/REVIEWER-GUIDELINES.html

    N/A

  • Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.

    (3) Weak Reject — could be rejected, dependent on rebuttal

  • Please justify your recommendation. What were the major factors that led you to your overall score for this paper?

    Please see the weakness section.

  • Reviewer confidence

    Confident but not absolutely certain (3)

  • [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.

    Reject

  • [Post rebuttal] Please justify your final decision from above.

    Some issues have been clarified but some remain unsolved. Overall, the study did not show significant improvements over existing methods.



Review #2

  • Please describe the contribution of the paper

    This paper introduces a novel framework for the analysis of neurocognitive impairment using paired DTI and fMRI data. The authors motivate their work by noting that conventional Euclidean-space fusion methods may not adequately capture the inherently hierarchical and non-Euclidean structure of brain networks. To address this, the proposed method leverages hyperbolic geometry for both feature extraction and network modeling. The HKC framework integrates a hyperbolic kernel GCN, a structural-functional coupling module, and a hyperbolic classifier to jointly model local-to-global dependencies and cross-modality interactions. Empirical results on a moderate-sized dataset suggest that the method performs favorably compared to several established baselines. Moreover, the model appears to provide interpretable biomarkers, although further validation in broader clinical settings may be warranted.

  • Please list the major strengths of the paper: you should highlight 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 structure of the paper is very clear, and the novel approach makes it interesting to read. The paper designs a new structure to address these issues. Although the paper is limited in length, the experimental design effectively demonstrates the overall methodology and design approach.

  • Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.

    1. The paper uses hyperbolic graph neural networks, and a few sentences discussing why this scenario is suitable for hyperbolic space would be helpful. The methodology includes a large number of formulas, but the underlying concepts are not fully explained and should be clarified.

    2. Should “Data and Image Preprocessing” be included in the experimental section?

    3. The size of the experimental data used is a bit small, so the variance in the results is somewhat large.

    4. Many subplots in Fig. 2 look strange. Could you explain why there are so many rings?

  • Please rate the clarity and organization of this paper

    Good

  • Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.

    The submission does not mention open access to source code or data but provides a clear and detailed description of the algorithm to ensure reproducibility.

  • Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2025/en/REVIEWER-GUIDELINES.html

    N/A

  • Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.

    (4) Weak Accept — could be accepted, dependent on rebuttal

  • Please justify your recommendation. What were the major factors that led you to your overall score for this paper?

    The approach is novel and worth encouraging, but more rigorous justification is needed.

  • Reviewer confidence

    Confident but not absolutely certain (3)

  • [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.

    N/A

  • [Post rebuttal] Please justify your final decision from above.

    N/A



Review #3

  • Please describe the contribution of the paper

    This paper introduces HKC, a novel framework combining a Hyperbolic Kernel GCN (HKGCN) with structure-function (SC-FC) connectivity coupling for neurocognitive impairment analysis. HKGCN uses hyperbolic kernels in the tangent space to capture hierarchical brain network features efficiently, avoiding the computational burden of Möbius operations. The SC-FC coupling module models global interactions between structural and functional graphs, enhancing multimodal fusion. After this, a Hyperbolic Neural Network (HNN) is used for classification. Applied to HIV-associated asymptomatic neurocognitive impairment data, HKC outperforms several baselines and identifies discriminative SC, FC, and SC-FC connections, offering both improved accuracy and potential biomarkers.

  • Please list the major strengths of the paper: you should highlight 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 HKC framework is overall solid with clear design motivations, including GCN with hyperbolic kernels to handle hierarchical data and the SC-FC coupling to integrate multimodal information.
    • The authors conducted comprehensive benchmarking against baseline methods, along with ablation studies. The proposed approach demonstrates strong performance, and the ablation results support the effectiveness of its key design components.
    • The authors identified discriminative connectivity patterns that may serve as potential biomarkers.
  • Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.
    • While I largely agree with the statement that “this is among the first attempts to design and integrate hyperbolic kernels with GCNs for neurocognitive impairment analysis”, note that similar approaches have been explored in prior work (e.g., [1]). The authors may want to clarify how their method differs from existing studies to better highlight its novelty.
    • The authors identified the top 10 discriminative connectivities using features extracted by the HKGCN. However, the robustness of these findings remains unclear. Specifically, it is not evident whether similar connectivity patterns would emerge under different HKGCN initializations or with different subject groupings.

    Ref: [1] Xie, Chengyao, et al. “Multimodal Hyperbolic Graph Learning for Alzheimer’s Disease Detection.” Australasian Joint Conference on Artificial Intelligence. Singapore: Springer Nature Singapore, 2024.

  • Please rate the clarity and organization of this paper

    Good

  • Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.

    The submission does not mention open access to source code or data but provides a clear and detailed description of the algorithm to ensure reproducibility.

  • Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2025/en/REVIEWER-GUIDELINES.html

    N/A

  • Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.

    (4) Weak Accept — could be accepted, dependent on rebuttal

  • Please justify your recommendation. What were the major factors that led you to your overall score for this paper?

    The proposed method is overall effective and meaningful, though certain aspects of its novelty would benefit from further clarification. The experiments and result analysis are thorough and insightful.

  • Reviewer confidence

    Somewhat confident (2)

  • [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.

    Accept

  • [Post rebuttal] Please justify your final decision from above.

    The authors addressed all my concerns.



Author Feedback

We appreciate AC and Reviewers for constructive feedback and positive remarks on our novel approach (R1&R3), interpretable biomarkers (R1), solid framework (R3), comprehensive benchmarking with strong performance (R3) and superior performance (R4). We address main concerns below.

R1: More on Why Hyperbolic Space

  • As noted in Introduction, prior studies show that the brain is hierarchically organized in structure and function [1]. Most methods are designed in Euclidean space, causing distortion when embedding hierarchical data [2]. Hyperbolic space encodes hierarchies with minimal distortion [3], making it a sound choice for modeling brain networks.
  • We’ll clarify this in the final version.
    [1] DOI: 10.1152/jn.00338.2011 [2] DOI: 10.1007/BF01200757 [3] Hyperbolic neural networks. NeurIPS2018

R1: Small Data and Somewhat Large Variance

  • We agree the variance stems from limited paired fMRI and DTI data, a key challenge in ANI analysis. We are working to use large-scale auxiliary data for model pretraining to improve generalizability.
  • We’ll include this in future work.

R1: Many Rings in Fig.2

  • Following [4], we apply t-SNE to each model’s final low-dimensional features to visualize decision-level information. The combination of low-dimensional input and complex decision boundaries often projects into rings. Our HKC produces the tightest, most separable clusters, highlighting its strong discriminative ability.
  • We’ll clarify this in the final version.
    [4] A simple framework for contrastive learning of visual representations. ICML2020

R3: Difference from [5]

  • Our work differs from [5] in 3 keyways: 1) We design novel hyperbolic kernels and incorporate them into a new HKGCN, while [5] uses existing hyperbolic graph convolution. 2) We create SC-FC coupling, while [5] uses contrastive learning for multimodal fusion. 3) We design HNN to adapt hyperbolic features of HKGCN for prediction, while [5] uses hyperbolic distance to make decisions. [5] DOI: 10.1007/978-981-96-0351-0_29

R3: Robustness of Discriminative Connection

  • To assess robustness to data partition, we compare discriminative connections identified with different random splits for 5-fold cross-validation. Despite some variation, key connections (ACG.R-THA.R and INS.L-DCG.R) and involved brain regions (ACG, CRBL6, and PCUN) are consistently identified.
  • To assess robustness to initialization, we vary weight initialization with the data split fixed, and find discriminative connections (INS.L-STG.L and INS.L-DCG.R) and involved ROIs (ACG, CRBL6, and PCUN) remain stable.
  • We will discuss this in the final version.

R4: Why Use ReLU for Global and Cosine for Local Interactions

  • ReLU is a degree-1 HAC kernel that encodes global angular similarity between embeddings, enabling long-range dependency modeling. Cosine approximates an HRBF kernel and decays rapidly with geodesic distance, effectively capturing local interactions.
  • We’ll include this in the final version.

R4: Ablation Results

  • HKC-K vs. HKC-G: HGCN used in HKC-K relies on log_0^c and exp_0^c mappings with a fixed base point at the origin, which can introduce geometric distortion. And its inherent Möbius operations may lead to numerical instability [6]. This could explain why HGCN backbone (in HKC-K) is inferior to vanilla GCN (in HKC-G).
  • HKC-G vs. HKC: We achieve a p-value of 0.0094 in AUC between HKC-G and HKC, indicating that HKC’s improvement is statistically significant. [6] The Numerical Stability of Hyperbolic Representation Learning. ICML2023

R4: Computation Complexity

  • With an NVIDIA RTX 4090 GPU, the inference time per sample of our HKC is 0.0154s, faster than HGCN (0.0225s).
  • HGCN requires 31.69M and 17.82M FLOPs to encode DTI and fMRI features, respectively. Our HKC reduces them to 19.27M and 12.38M FLOPs, suggesting less computational complexity.

R4: Atlas and Processing

  • Great suggestion! We’ll use other atlases and processing pipelines in future work.



Meta-Review

Meta-review #1

  • Your recommendation

    Invite for Rebuttal

  • If your recommendation is “Provisional Reject”, then summarize the factors that went into this decision. In case you deviate from the reviewers’ recommendations, explain in detail the reasons why. You do not need to provide a justification for a recommendation of “Provisional Accept” or “Invite for Rebuttal”.

    N/A

  • After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.

    Accept

  • Please justify your recommendation. You may optionally write justifications for ‘accepts’, but are expected to write a justification for ‘rejects’

    N/A



Meta-review #2

  • After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.

    Accept

  • Please justify your recommendation. You may optionally write justifications for ‘accepts’, but are expected to write a justification for ‘rejects’

    This paper proposes a novel HKC framework combining hyperbolic kernel graph convolutional networks (HKGCN) and structure-function connectivity (SC-FC) coupling for neurocognitive impairment analysis. By leveraging hyperbolic space to model the hierarchical structure of brain networks, HKGCN extracts local-to-global features from DTI and fMRI, while the SC-FC coupling module captures global interactions between modalities. Experiments on HIV-associated asymptomatic neurocognitive impairment data show HKC outperforms state-of-the-art methods in classification metrics and identifies key SC-FC biomarkers like visual network and fronto-cerebellar connections, demonstrating its effectiveness and clinical interpretability.The author also provides good responses to the comments raised.



Meta-review #3

  • After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.

    Reject

  • Please justify your recommendation. You may optionally write justifications for ‘accepts’, but are expected to write a justification for ‘rejects’

    Although the authors have addressed several reviewer question, particularly regarding their choice of hyperbolic space, visualization clarifications, and ablation studies, the key concern raised about the convincingness of results remains insufficiently resolved.. Lacking convincing results to demonstrate significant improvement is the inherent limitations identified by reviewers.



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