DCA: Graph-Guided Deep Embedding Clustering for Brain Atlases

General response

We thank all reviewers for their time and constructive feedback. We appreciate the recognition of the importance of our problem (Reviewers puq2, uHxM), the flexibility of our framework (Reviewers o9NK, uHxM), and the strengths of our method in both similarity metrics and downstream evaluations (Reviewers puq2, o9NK, zwAk).

We also provide additional experiments to address reviewers' concerns on (1) model effectiveness by comparisons with recent state-of-the-art fMRI foundation model (Reviewer zwAk), (2) inadequate atlas comparison by additional atlas baselines (Reviewers uHxM), (3) downstream performance interpretation by new task evaluations and performance difference explanations (Reviewers puq2, o9NK), and (4) the impact of the number of parcels (Reviewers o9NK, zwAk).

Q1: Choice of Swin-UNETR

We appreciate your insightful comments on the backbone selection. We chose Swin-UNETR as our encoder because it remains a widely adopted backbone for 3D medical image analysis, especially in volumetric neuroimaging tasks. To justify its suitability, we compared Swin-UNETR against two recent state-of-the-art foundation models [1, 2] using the full HCP and CHCP datasets. Possibly due to its ability to preserve dense voxel-level information, Swin-UNETR outperformed both models across two downstream tasks (Rebuttal Table 1).

We agree that alternatives such as Hiera-based models (e.g., Medical-SAM2) represent promising and efficient backbones. Due to time constraints, we were unable to complete a systematic comparison of their training stability, computational cost, and downstream performance. We will include this discussion in the revised version.

Table 1: Backbone comparison: Classification for age and gender

Q2: DCA 7/17/41 performance

In our framework, DCA requires spatially contiguous ROIs, whereas Yeo 7 and 17 are functionally defined and spatially fragmented. Enforcing a very small number of parcels (e.g., 7 or 17) under spatial contiguity may compromise the functional interpretability of the resulting regions, which is why DCA 7/17 were not included in the main paper. To address the reviewer’s concern, we have now added these baselines (Rebuttal Tables 2-3).

DCA still achieves high homogeneity at 7 and 17 parcels, but its silhouette scores are lower, likely because spatially adjacent yet functionally distinct regions are merged, while functionally similar but spatially distant regions (e.g., PCC and ACC in the DMN) are split into separate ROIs, reducing distinctiveness between ROIs. This spatial constraint also impacts downstream performance. For example, DCA 7/17 performs worse than Yeo in task decoding. In contrast, DCA 41 performs much better. In future work, relaxing the contiguity constraint from hard to soft may enable more meaningful network-level parcellation at extremely low resolutions.

Table 2: Evaluation of similarity metrics across atlases

Table 3: Evaluation of downstream task performance across atlases

Q3: Homogeneity and silhouette performance interpretation

We thank the reviewer for raising this point. While the absolute values of homogeneity and silhouette scores may appear low, their overall scale is comparable to those reported in previous work [3]. Minor differences are likely due to variations in preprocessing pipelines, especially ICA-based denoising and spatial smoothing, which can affect the absolute magnitude of these metrics. Moreover, evaluation results can also differ depending on whether the atlas is assessed in the volume space or on the surface representation of the brain. With other conditions controlled, the relative ranking of atlases remains consistent, and DCA consistently outperforms baselines across resolutions (Appendix Tables 3-4).

Q4: Comparison with Schaefer atlases

To assess spatial overlap, we compared DCA and Schaefer atlases at 100, 200, and 500 parcels using Hungarian matching. It obtained mean Dice scores of 0.443, 0.433, and 0.427, and corresponding IoU scores of 0.307, 0.302, and 0.293. Network-specific analysis showed higher overlap in the visual network (Dice = 0.489-0.531; IoU = 0.338-0.380), and lower overlap in the default mode network (Dice = 0.421–0.446; IoU = 0.290–0.304), suggesting that DCA preserves structure in sensory regions and refines higher-order areas.

While reference [4] is highly relevant, its volume-space data is not yet publicly available. We therefore used the Brodmann atlas, one of the most widely adopted manually labeled volumetric references, for anatomical comparison. We computed normalized mutual information (NMI) with the Brodmann atlas, which does not require label matching. DCA consistently achieved slightly higher NMI than Schaefer (e.g., 0.592 vs. 0.580 at 100 parcels), indicating better preservation of macro-anatomical organization.

Q5: Homogeneity metric definition

We apologize for the oversight. The main paper only presented the simplified form of the global homogeneity metric. In practice, we correctly account for parcel size variations following Equation (2) from [5] (see Code lines 84–90 in AtlaScore/similarity/eva.py). We will revise it.

Q6: DCBC metric performance interpretation

While DCBC is a surface-based metric, our DCA atlases are constructed in volumetric space. To compute DCBC, we projected both fMRI data and atlas labels onto the fsLR-32k surface using the neuromaps toolbox [6]. This transformation may introduce coordinate discrepancies, especially in regions with complex cortical folding, and reduce the performance of voxel-based atlases like DCA. This could partly explain the lower DCBC scores. We included this metric to enable comprehensive comparisons with prior surface-based methods.

Q7: Choice of number of neighbors

We apologize for the lack of clarity. We adopt the standard 26-neighborhood in 3D, which includes all voxels in a 3×3×3 cube excluding the center. It captures both adjacent and diagonal interactions. We additionally tested with 6 and 18 neighbors, and observed similar performance ($p>0.05$. See Rebuttal Table 3 in response to Reviewer uHxM).

Q8: Cosine similarity truncation

We appreciate your thoughtful observation. While our earlier implementation required graph positive semi-definiteness, the current version (see line 123 in DCA/utils.py) no longer truncates cosine similarity. We regret the documentation oversight and will ensure all methods are accurately described in the revision.

Weakness 1: Choice of number of parcels $K$

When $K$ is small, heterogeneous functional areas tend to be merged into a single parcel. Increasing $K$ usually improves accuracy (Rebuttal Tables 2-3), but may fragment a single functional region into multiple parcels and substantially raises computational cost.

Varying $K$ provides insights into how different resolutions capture task-relevant structure (Rebuttal Tables 2-3 in response to Reviewer o9NK). While an optimal $K$ is task-dependent and may not exist in a task-agnostic setting, certain resolutions may better suit specific applications. Our framework naturally supports multiresolution parcellations and can be extended with automatic-$K$ clustering and task-supervised objectives to generate individualized, performance-optimized atlases.

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Reference:

[1] Brain-JEPA: Brain Dynamics Foundation Model with Gradient Positioning and Spatiotemporal Masking. NeurIPS 2024.

[2] BrainLM: A foundation model for brain activity recordings. ICLR 2024.

[3] Atlas-guided parcellation: Individualized functionally-homogenous parcellation in cerebral cortex. Computers in Biology and Medicine 2022.

[4] A precision functional atlas of personalized network topography and probabilities. Nature Neuroscience 2024.

[5] Local-global parcellation of the human cerebral cortex from intrinsic functional connectivity MRI. Cerebral Cortex 2018.

[6] Neuromaps: structural and functional interpretation of brain maps. Nature Methods 2022.

We appreciate your insightful question regarding the interpretation and limitations of internal clustering metrics. Indeed, homogeneity and silhouette scores can be affected by the high dimensionality and intrinsic noise of voxel-level fMRI data. Moreover, increasing the number of parcels ($K$) would inevitablely increase homogeneity score, due to the inherently smooth nature of fMRI signals. As a result, comparing homogeneity scores across different parcellation scales can be misleading, and internal metrics alone are insufficient for comprehensive evaluation. In addition, the requirement for spatial contiguity further constrains cluster boundaries, making it more challenging to achieve very high performance on these metrics.

Nonetheless, these measures remain widely used and meaningful for atlas evaluation. Homogeneity directly reflects within-parcel signal similarity, while the silhouette coefficient captures the tradeoff between within- and between-parcel separability—both of which align with the core goal of functionally coherent and spatially distinct brain regions [1, 2]. Importantly, in DCA, we do not optimize these two metrics directly; instead, they emerge from unsupervised clustering in latent space, which underscores the quality of the learned representations.

While task-specific metrics (e.g., decoding accuracy or diagnostic performance) can provide additional insight, they often favor atlases tuned to particular applications or populations. In contrast, homogeneity and silhouette offer task-agnostic, interpretable measures for evaluating general-purpose atlases. Therefore, although the absolute values may appear modest due to the complexity of the problem, the consistent relative improvements across methods and resolutions reflect meaningful progress in this challenging setting.

[1] Atlas-guided parcellation: Individualized functionally-homogenous parcellation in cerebral cortex. Computers in Biology and Medicine 2022

[2] Local-Global Parcellation of the Human Cerebral Cortex from Intrinsic Functional Connectivity MRI. Cerebral Cortex. 2018

We demonstrate that our framework can be readily adapted to task-specific settings, achieving substantial improvements on the corresponding evaluation metrics. Specifically, we replace the reconstruction self-supervised Swin-UNETR with a version fine-tuned for gender classification (Table 1) and use its encoder to derive a task-specific atlas, denoted $\text{DCA}_{100}^{\mathrm{gender}}$. Using this atlas to aggregate fMRI signals into 100 ROIs for $N=200$ subjects drawn from the Swin UNETR fine-tuning test split to avoid data leakage, we train a compact neural network, two 1D convolutional layers followed by two fully connected layers, on the ROI-level time series (identical to the setup in Weakness 1 / Table 3 to Reviewer puq2) and evaluate on 20% held-out. Accuracy increases to 82% (+12% over original method).

These results indicate that targeted encoder fine-tuning yields task-specific atlases that deliver measurable gains on the target task, without compromising the spatial continuity of the atlas.

Table 4: Gender Classification Results

Thank you once again for your valuable feedback—especially your remarks on evaluation metrics inspired us to explore atlas fine-tuning, which has strengthened the paper. We are now in the final stage of the rebuttal process and have addressed each reviewer’s concerns point by point, receiving positive responses.

Could we kindly invite you to take a brief look at the latest discussion thread? If you have any additional comments or questions, please let us know at your earliest convenience so we have sufficient time to incorporate them. We hope the new material will also earn your positive assessment.

General response

We thank all reviewers for their time and constructive feedback. We appreciate the recognition of the importance of our problem (Reviewers puq2, uHxM), the flexibility of our framework (Reviewers o9NK, uHxM), and the strengths of our method in both similarity metrics and downstream evaluations (Reviewers puq2, o9NK, zwAk).

We also provide additional experiments to address reviewers' concerns on (1) model effectiveness by comparisons with recent state-of-the-art fMRI foundation model (Reviewer zwAk), (2) inadequate atlas comparison by additional atlas baselines (Reviewers uHxM), (3) downstream performance interpretation by new task evaluations and performance difference explanations (Reviewers puq2, o9NK), and (4) the impact of the number of parcels (Reviewers o9NK, zwAk).

Weakness 1: Outdated comparative baselines

Thank you for your valuable suggestion. In the main paper, our comparative baselines were selected based on popularity and historical influence, including widely used atlases such as Yeo, Brodmann, Schaefer, and MMP. We acknowledge that this focus on classical atlases may have excluded more recent methodological advances, potentially limiting the completeness of our comparison.

Recent approaches in our Related Work generate probabilistic maps or segment only specific regions, without offering whole-brain or cortex-wide deterministic atlases directly comparable to ours [1, 2]. We recognize the importance of including recent atlases for a fair comparison and will add more up-to-date atlases to Related Work. To address this concern, we added comparisons with GIANT, Watershed , Allen, and MUSE. Specifically, we incorporated three representative recent atlases from [3]. We also added the Allen Human Reference Atlas - 3D, 2020. These additions improve the breadth and contemporaneity of our comparisons (Rebuttal Table 1-2). Our approach still demonstrates overall better performance. While the new atlas shows lower scores on certain evaluation metrics, it should be noted that these atlases are whole-brain rather than cortex-only, which offers clear advantages for tasks that likely involve subcortical features. In the supplementary material, we also provide a non-cortical version of the atlas. We believe that integrating our DCA atlas with subcortical regions could further enhance its utility.

Table 1: Evaluation of similarity metrics across atlases at low (≤ 100 parcels) and medium (> 100 parcels) resolution

Table 2: Evaluation of downstream task performance across atlases at low (≤ 100 parcels) and medium (> 100 parcels) resolution

Weakness 2: Low-resolution figures in main text

Thank you for pointing this out. We will improve the resolution of the figures in the main text to enhance clarity and overall presentation quality.

Weakness 3: Coarse ablation and Loss analysis

Due to space limitations, we provide additional ablations and discussions in the supplementary material, covering multiple aspects of our framework. We will also include a more detailed discussion of the ablation results in the main paper in the revised version.

1. Model architecture – removing key components degrades performance and breaks spatial continuity (Appendix 6.1);

2. Regularization options and SimMIM loss – adding these has a negligible impact on final metrics (Appendix 6.2);

3. Pretraining data preprocessing – different preprocessing strategies do not affect model performance (Appendix 6.3);

4. Data smoothing – all smoothed variants evaluated with DCA outperform baseline atlases (Appendix 5.1);

5. Graph segmentation methods – spectral clustering consistently outperforms alternative approaches (Appendix 6.4);

6. Tissue segmentation templates – results remain superior to baselines regardless of template choice (Appendix 6.5);

7. Hyperparameters for group-level atlas generation – Impact of different hyperparameters on downstream tasks (Appendix 7).

And following the reviewers’ suggestions, we have now included additional ablation studies to further validate our design choices.

(1) Number of Neighbors. We adopt the standard 26-neighborhood in 3D, which includes all voxels in a 3×3×3 cube excluding the center voxel, thereby capturing both adjacent and diagonal spatial interactions. To analyze its effect, we further tested different neighborhood sizes ($K=6,18,26$), corresponding respectively to: (i) only face-connected voxels, (ii) face+edge connections, and (iii) all voxels in the 3×3×3 cube excluding the center.

As shown in Table 3, the results for $K=6$ and $K=26$ are very close ($p>0.05$, t-test/U-test), while using $K=18$ yields a noticeably lower silhouette score ($p<0.05$, U-test). Overall, the choice of $K=26$ provides stable and competitive performance.

Table 3: Ablation study on neighborhood size selection

(2) Distribution-based Loss. We added additional experiments to compare 3 commonly used distribution-based loss functions for atlas generation (Table 4 ). We observe that Wasserstein, JS, and KL divergence losses yield nearly identical performance on both homogeneity and silhouette metrics, with only negligible variations within the standard deviation range ($p>0.05$, t-test/U-test). This suggests that our framework is largely insensitive to the specific choice of distribution-based loss, and all 3 objectives are equally effective in guiding the clustering refinement process.

Table 4: Reliability on distribution-based loss functions

(3) Initialization. We compared three alternative centroid initialization strategies for embedding clustering (random, random+norm, xavier+norm, and orthogonal+norm in Table 5). Using our orthogonal+norm initialization accelerates convergence in the early training stage, while its impact on the final performance metrics is negligible once the model has fully converged ($p>0.05$, t-test/U-test).

Table 5: Comparisons on different initialization methods

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Reference:

[1] A hierarchical Bayesian brain parcellation framework for fusion of functional imaging datasets. Imaging Neuroscience 2025.

[2] A hierarchical atlas of the human cerebellum for functional precision mapping. Nature Communications 2024.

[3] A genetically informed brain atlas for enhancing brain imaging genomics. Nature Communications 2025.

We would like to briefly supplement your Question 1, which referenced “atlas construction” and “brain segmentation.” For (1) new atlas baselines, we have already explained this in our prior response and added four recent, publicly available atlases as baselines. Our method performs better on these comparisons on similarity metrics (Table 1), downstream task performance for group atlas (Table 2) and personalized atlas (Table 3-4 to Reviewer puq2).

Here we clarify why we do not include (2) MRI segmentation baselines. Beyond using fMRI rather than MRI, the key point is that our approach is fully self-supervised, whereas brain segmentation typically requires labels. Training with predefined label templates turns the task into atlas registration rather than atlas generation—for example, DDparcel trains with an atlas template, allowing the atlas to be quickly registered to new subjects [1]. In contrast, our method aims to generate new, personalized atlases. The core innovation is a self-supervised framework that yields spatially continuous atlases without any voxel-level labels.

Moreover, our self-supervised framework can be augmented with fine-tuning to boost task-specific performance. We first fine-tune the encoder on an external dataset with individual labels (e.g., gender) using a supervised classification objective, and then use this encoder to generate atlases in the same unsupervised manner. Without using any additional information from the evaluation subjects, this yields task-specific atlases and substantially improves classification on the corresponding task (+10% with the graph-based method and +12% with the CNN classifier; Tables 6–7 to Reviewer puq2).

[1] DDParcel: Deep Learning Anatomical Brain Parcellation From Diffusion MRI. IEEE Transactions on Medical Imaging 2024.

General response

We thank all reviewers for their time and constructive feedback. We appreciate the recognition of our problem’s importance (Reviewers puq2, uHxM), the framework’s flexibility (Reviewers o9NK, uHxM), and the strength of our method in similarity metrics and downstream evaluations (Reviewers puq2, o9NK, zwAk). We also value the comments on model effectiveness (Reviewer zwAk), downstream performance interpretation (Reviewers puq2, o9NK), and the impact of the number of parcels (Reviewers o9NK, zwAk). We conducted additional experiments to address these concerns. Below we provide point-by-point responses.

Weakness 1: Technical innovation

We thank the reviewer for the thoughtful comments. To our knowledge, this is the first work to construct a spatially continuous voxel-level atlas with large-scale pretraining. This task is considerably more challenging than enforcing continuity on cortical surfaces. Prior voxel-based methods often yield non-contiguous maps [1]. Our main innovations are:

(1) Constructing the atlas in latent space rather than raw signal space, which improves performance (Main Figure 5) and enhances robustness to noise (Appendix 6.3).

(2) A k-nearest neighbor graph is employed as an auxiliary label to guide the encoder, eliminating the need for manually tuned penalty terms and reducing the risk of spatial discontinuity artifacts. The sparse graph reduces complexity to $\mathcal{O}(n)$ and memory usage to ~12 MB (float32, 80k voxels), compared to $\mathcal{O}(n^2)$ and ~20 GB for FC-based methods.

Weakness 2: Functional connectivity method

We apologize for the ambiguity. Functional connectivity is computed using Pearson correlation between averaged time series, which performs well in behavior prediction [2]. We will clarify this in the revision.

Weakness 2: Initialization method

We follow prior work [3] to initialize centroids in orthogonal directions with equal norm, avoiding degenerate clusters and improving optimization stability. Our ablation (Rebuttal Table 5 in response to Reviewer uHxM) shows this choice speeds up early convergence, while its effect on final metrics is negligible after full training ($p>0.05$).

Weakness 2: Number of neighbors

We apologize for the lack of clarity. We adopt the standard 26-neighborhood in 3D, which includes all voxels in a 3×3×3 cube excluding the center. It captures both adjacent and diagonal interactions. We tested with 6 and 18 neighbors, and observed similar performance ($p>0.05$, Rebuttal Table 3 in response to Reviewer uHxM).

Weakness 3: Downstream evaluation

We thank the reviewer for the valuable suggestion. We initially used SVC to reduce overfitting risk but agree that relying on a single model may underestimate some atlases. To broaden evaluation, we additionally trained a compact neural network (two 1D convolutional layers followed by two fully connected layers) on ROI-level fMRI time series for age and gender classification, two widely studied tasks in medical imaging.

We further compared personal DCA atlas against multiple group-level atlases and observed strong and often superior performance across both tasks, suggesting it captures more informative features (Rebuttal Tables 3–5 in response to Reviewer puq2).

Weakness 4: Method stability

We appreciate the reviewer’s concerns about method stability. Below, we clarify how individual-atlas generation ensures stability, why FC stability appears lower, and why performance varies on some tasks.

1. Although our model is randomly initialized, the use of graph-based clustering as soft labels allows the model to converge stably. To evaluate consistency, we generated DCA 100 atlases from 10 non-overlapping fMRI segments per subject across 10 HCP individuals, spanning different runs and phase encoding directions. Similarity was assessed using Dice and intersection over union (IoU). Intra-subject similarity consistently exceeded both inter-subject and null model baselines, supporting the stability of DCA (Rebuttal Table 1). Null model was constructed by randomly partitioning the cortical mask into 100 spatially contiguous and approximately equal-sized parcels, with parcel correspondence across atlases determined using the Hungarian algorithm.

Table 1: Intra- and inter-subject atlas similarity

2. The reported FC stability is based on a fixed group-level DCA atlas. This metric increases with parcel size, so coarse atlases tend to score higher. At matched ROI counts, DCA achieves higher stability than other cortical atlases (Appendix Table 6).

3. For most of 12 downstream tasks, DCA ranks first in at least two of the four resolutions and remains top-two in three. Lower scores on some tasks have reasons: FC stability favors large parcels. Fingerprinting is already near the ceiling at each resolution. Performance on age group [4], crystallized intelligence [5], and general intelligence may be limited by the lack of subcortical coverage. Including subcortical regions in future versions may improve results on these tasks.

Weakness 5: Choice of number of parcels

We thank the reviewer for highlighting this key issue. To examine it, we compiled all downstream results for DCA atlases from 41 to 500 parcels and Schaefer atlases from 100 to 500 (Rebuttal Table 1-2). Three consistent patterns emerge:

1. Peak‑shaped tasks (e.g., cognitive task decoding) improve from low to high resolutions but decline when parcels become excessively small. This behavior holds across both DCA and Schaefer, suggesting robustness and task specificity.

2. Resolution‑insensitive tasks (e.g., AD diagnosis) show no clear trend and differ across atlases. This may reflect their reliance on subcortical regions not covered by cortical atlases.

3. Size‑driven tasks (e.g., FC stability) are largely driven by parcel size. FC stability decreases at higher resolutions, while fingerprinting improves with finer parcellations.

Table 2: Downstream task performance across atlas resolutions for DCA

Table 3: Downstream task performance across atlas resolutions for Schaefer

Taken together, no single parcel count is universally optimal. But certain resolutions may better suit specific applications. Our framework naturally supports multiresolution parcellations and can be extended with adaptive parcel clustering and task-supervised objectives to generate individualized, performance-optimized atlases.

Weakness 6: Computational and storage demands

Our encoder (Swin-UNETR) has 62.6M parameters and requires ~776 GFLOPs per forward pass. During pretraining on 300-length fMRI data, GPU memory usage is ~60 GB (batch size 3) on an A100. One epoch takes ~6 hours, with convergence typically reached in 8 epochs, comparable to other voxel-level models [6]. Shorter sequences reduce time and memory proportionally.

For clustering fine-tuning, generating a 100-parcel atlas for one subject takes ~10 minutes on an AMD R9 7900X CPU and RTX 3080 GPU, scaling roughly linearly with parcel count. The pipeline can also run on CPUs if needed.

Weakness 7: Open access

We acknowledge this oversight. The group-level DCA 100 atlas (HCP-based) is available at AtlaScore/downstream/docs/ as a demo.

Model weights, individual-level atlases and other resolutions (from 100 to 1000) based on different datasets will be released upon acceptance.

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Reference:

[1] A hierarchical atlas of the human cerebellum for functional precision mapping. Nature Communications 2024.

[2] Benchmarking methods for mapping functional connectivity in the brain. Nature Methods 2025.

[3] Provable Benefit of Orthogonal Initialization in Optimizing Deep Linear Networks. ICLR 2020.

[4] Biological brain age prediction using machine learning on structural neuroimaging data: Multi-cohort validation against biomarkers of Alzheimer’s disease and neurodegeneration stratified by sex. eLife 2023.

[5] Predictive models demonstrate age‐dependent association of subcortical volumes and cognitive measures. Human Brain Mapping 2023.

[6] SwiFT: Swin 4D fMRI Transformer. NeurIPS 2023.

Intra-run stability

We appreciate the reviewer’s emphasis that an atlas should be reproducible when re-run on the same fMRI time series. To quantify run-to-run variability, we further repeated the entire pipeline five times on the same fMRI segment and computed Dice, IoU, voxel assignment consistency (VAC; defined as the fraction of voxels that keep the same label after Hungarian alignment of two parcellations), adjusted rand index (ARI), and normalized mutual information (NMI) between runs (Table 4). We find that variability is driven primarily by (i) the initialization of cluster centroids in the spectral graph step and (ii) the initialization of the model’s centroid matrix. With a fixed random seed, the atlas is perfectly deterministic. Because the loss includes a KL term between the model assignments and the graph-clustering assignments, reproducible results require either fixing both the model initialization and the clustering seed, or fixing one and then assigning the other (e.g., initializing the graph-cluster centroids with the model’s centroid matrix). Under realistic stochasticity arising from spectral clustering and model initialization, more than 80% of voxels retain their labels across runs, with disagreements often concentrate in areas where a dominant cluster admits finer sub-parcellations into smaller clusters.

Beyond controlling random seeds, stability can be enhanced by incorporating external priors (e.g., initializing cluster centroids from a population template), after which DCA refines these priors into subject-specific atlases. This strategy preserves the benefits of established atlases, such as structural basis and multimodal information, while capitalizing on DCA’s strengths in fine-tuning and individualized atlas construction.

Table 4: Model reproducibility

Graph-based evaluation

We agree that graph-based evaluation is important. Following the first protocol in the review article [1], we implemented a $k$-GNN classifier with $k=2$ and evaluated gender classification on $N=200$ subjects. For each subject-atlas pair, we construct a base graph with $K=100$ nodes (ROIs), use the functional connectivity (FC) matrix as weighted edges, and sparsify the graph by retaining the top 30% of edges by absolute FC magnitude. We then apply a standard 2-GNN to obtain a subject-level embedding via a readout operation, which is fed to a linear classifier. Training uses a 70/10/20 subject-level split for train/validation/test. The Schaefer-100 baseline reproduces performance that is slightly higher than reported in the review article, and our approach achieves a comparable level of accuracy (Table 5).

Moreover, our framework can also inject task-specific knowledge into the atlas. We fine-tune Swin-UNETR on HCP/CHCP gender labels (ensuring that evaluation subjects never appear in fine-tuning to prevent leakage), and replace the reconstruction-based encoder with the fine-tuned one. Then we use the same self-supervised framework to generate a task-specific atlas $\text{DCA}_{100}^{\text{gender}}$. This task-adapted atlas delivers substantial improvements on the target task: +10% with the graph method and +12% with the CNN classifier (Table 4 to Reviewer zwAk).

Table 5: Classification results for gender by k-GNN

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Reference:

[1] NeuroGraph: Benchmarks for Graph Machine Learning in Brain Connectomics. NeurIPS 2023.

General response

We thank all reviewers for their time and constructive feedback. We appreciate the recognition of the importance of our problem (Reviewers puq2, uHxM), the flexibility of our framework (Reviewers o9NK, uHxM), and the strengths of our method in both similarity metrics and downstream evaluations (Reviewers puq2, o9NK, zwAk).

We also provide additional experiments to address reviewers' concerns on (1) model effectiveness by comparisons with recent state-of-the-art fMRI foundation model (Reviewer zwAk), (2) inadequate atlas comparison by additional atlas baselines (Reviewers uHxM), (3) downstream performance interpretation by new task evaluations and performance difference explanations (Reviewers puq2, o9NK), and (4) the impact of the number of parcels (Reviewers o9NK, zwAk).

DCA 400 performance

We appreciate the reviewer’s concern about DCA’s performance inconsistency across the 12 downstream tasks. The reference to DCA 400 was a misunderstanding, as it was not used in the main results. The mention may stem from a misinterpretation of the Schaefer 400 results. In main paper, we used DCA 360, aligned with the HCP-derived MMP atlas. In Appendix Table 6, DCA 360 achieved the best overall performance among high-resolution atlases.

To address the suggestion, we constructed and evaluated DCA 400 (Rebuttal Table 1-2). In pairwise comparisons, DCA 400 wins 7 vs. 5 against MMP, and 5 vs. 6 with 1 tie against Schaefer 400. These results suggest that DCA offers comparable practical utility to Schaefer, with potentially complementary strengths across specific tasks.

Table 1: Evaluation of similarity metrics across atlases

Table 2: Evaluation of downstream task performance across atlases

Weakness 1: Transferability of similarity metrics

We believe that the observed gains in homogeneity and silhouette scores likely translate into improved downstream performance. Below, we present supporting evidence.

In our evaluation across 12 downstream tasks (Appendix Table 6), DCA achieved the highest number of top rankings across medium, high, and ultra-high resolutions. At lower resolution, DCA 100 obtained five first-place and four second-place results, just one first-place fewer than Schaefer 100. In pairwise comparisons at the same resolution, DCA won at least 6 out of 12 tasks against every competing atlas except one, where DCA 360 recorded 5 wins, 6 losses, and 1 tie against Schaefer 300.

To further support our claim, we extended our evaluation beyond the original SVC classifier. We also added several recently published atlases for comparison [1], to ensure a fair and up-to-date benchmark. Specifically, we trained a compact neural network (two 1D convolutional layers followed by two fully connected layers) on ROI-level fMRI time series for age and gender classification, two widely studied tasks in medical imaging. In addition to accuracy, we reported F1 scores, providing a more comprehensive assessment of atlas capability. As shown in Rebuttal Tables 3–5, our DCA-based individual atlases consistently achieve strong and often superior performance across low, medium, and high resolution settings, particularly on gender classification and at higher resolutions. These findings further support the utility of our atlas framework in diverse downstream tasks.

Table 3: Classification results (low resolution)

Table 4: Classification results (medium resolution)

Table 5: Classification results (high resolution)

Weakness 2: Task selection criteria

We understand the reviewer's concern about potential result selection. As we mentioned, the model is competitive on most downstream tasks, beyond the six benchmarks reported in the main paper. We selected these six benchmarks specifically to cover three key aspects of evaluation: two resting-state tasks, two task-state tasks, and two clinical classification tasks. For resting‑state we selected fluid intelligence and gender classification, as our cortex‑only atlas is most suited to the fronto‑parietal patterns behind these traits [2], while we left out FC stability (affected by parcel-size bias), fingerprinting (ceiling effect per resolution), age (rely on subcortical features) [3], crystallized and general intelligence (rely on subcortical features) [4]. For task decoding, we kept two cognitive tasks since DCA atlas is derived from functional embeddings and should differentiate task states well. For clinical evaluation, we included Autism and AD diagnosis for their clinical relevance and to assess generalization to external datasets, despite not expecting peak performance since the atlas was trained on HCP subjects.

Weakness 2: Task performance inconsistency

DCA excels on cortex‑driven targets (fluid intelligence, task decoding) while providing smaller gains on tasks that depend heavily on subcortical information. This heterogeneity is expected: no atlas can be optimal for every downstream task. AtlaScore therefore supplies a broad task battery so each atlas can reveal its most suitable application areas rather than striving for uniformly superior performance. We will also add a brief paragraph in Section 5 explaining why DCA shows larger gains on certain tasks than on others.

Furthermore, as the number of parcels increases, performance on tasks such as crystallized and general intelligence fluctuates without a consistent trend, unlike task decoding which shows a peak at high resolution (see Rebuttal Tables 2-3 in response to Reviewer o9NK). This observation further supports the notion that these tasks rely on subcortical features not captured by our cortex-only atlas, and may benefit from incorporating subcortical regions in future atlas designs.

Weakness 3: Evaluation metric clarity

We thank the reviewer for pointing this out. We realize that we only stated the use of classification accuracy in Appendix Section 4.2 and omitted it elsewhere. We will revise the main text and figure/table captions to clarify this. Specifically, all downstream tasks report classification accuracy under 10-fold subject-level cross-validation, except for FC stability, which is quantified as the mean Pearson correlation between FC matrices from non-overlapping fMRI segments (Appendix Section 4.7).

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Reference:

[1] A genetically informed brain atlas for enhancing brain imaging genomics. Nature Communications 2025.

[2] The frontoparietal network: function, electrophysiology, and importance of individual precision mapping. Dialogues in Clinical Neuroscience 2018.

[3] Biological brain age prediction using machine learning on structural neuroimaging data: Multi-cohort validation against biomarkers of Alzheimer’s disease and neurodegeneration stratified by sex. eLife 2023.

[4] Predictive models demonstrate age‐dependent association of subcortical volumes and cognitive measures. Human Brain Mapping 2023.

Dear Reviewer,

Thank you again for your thoughtful review and for recognizing the contributions of our work. We wanted to briefly follow up to ensure our rebuttal and additional results addressed your concerns. In our previous reply, we clarified the earlier ambiguity regarding DCA-400, demonstrated that our method performs well relative to other atlases, and explained why some tasks perform less strongly.

Because our method aims to generate personalized atlases, we also report individual-level metrics, including results from both a CNN and a GCN classifier, which perform favorably relative to the baseline. Moreover, our framework readily adapts to task-specific atlases DCA$_{100}^{\text{gender}}$: replacing the reconstruction-only Swin-UNETR with a gender-fine-tuned version yields +12% on the CNN classifier (Table 6) and +10% on the GCN classifier (Table 7), substantially outperforming the baseline atlas. And we confirm that there is no label leakage during fine-tune for the subjects used in evaluation; the individual atlases are still generated entirely via an unsupervised procedure.

During the rebuttal, we added further evaluations covering backbone performance (Table 1 to zwAk), additional baseline atlases (Table 3-4) and the effect of parcel count (Table 2-3 to o9NK). We hope these comprehensive supplementary experiments address most of your concerns regarding performance. Your feedback means a lot to us.

Table 6: Classification results for gender by CNN

Table 7: Classification results for gender by kGNN

Dear Reviewer,

Thank you again for your time and thoughtful feedback. As we have not yet heard back after our initial rebuttal, we would greatly appreciate any additional suggestions you may have.

• On homogeneity & silhouette. Please note that our model does not optimize these metrics explicitly; they emerge naturally after clustering in the learned latent space. We report them because (i) homogeneity measures within-parcel signal similarity and (ii) the silhouette coefficient balances within- vs. between-parcel separability—both of which directly reflect the goal of functionally coherent, spatially distinct regions.

• On downstream performance. As discussed in our response, we evaluated a wide range of tasks to build a comprehensive benchmark. Our atlas consistently ranks first or second across the majority of these downstream tasks. We acknowledge that because our atlas is derived exclusively from cortical fMRI, it's at a natural disadvantage for a few subcortical-heavy tasks. However, it's crucial to note that no single atlas can be truly optimal for every possible task. We've also shown that our newly added task-specific fine-tuning pipeline (e.g., DCA$_\text{gender}$), provides significant performance gains, proving that the DCA method can be readily adapted for specific applications when needed.

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Beyond raw performance, we believe our work makes several broader contributions:

• First atlas to cluster learned voxel-level fMRI embeddings. Clustering directly in a rich spatiotemporal embedding space (rather than FC matrices or surface signals) produces more coherent, high-resolution parcels.

• Task-adaptive and anatomically grounded. Fine-tuning the encoder allows rapid creation of task-specific atlases. At the same time, our voxel-wise parcels align more closely with macro-anatomy (higher NMI with Brodmann areas than Schaefer; see our reply to Reviewer zwAk Q4).

• Open benchmarking platform. We release AtlaScore, a unified toolkit for evaluating group- and subject-level atlases across diverse tasks, providing a robust foundation for future research.

We would be grateful for any further comments that could help us improve the paper. Thank you once more for your constructive review.

I appreciate the very detailed responses from the authors regarding my comments and questions. My concerns on task selection criteria evaluation metric clarity, and why DCA have more advantages on certain tasks than others have been sufficiently addressed. The additional results also show that DCA reaches the best or competitive performance at most resolutions in more downstream benchmarks and datasets.

Given all my concerns have been addressed, I have increased my rating.