DCA: Graph-Guided Deep Embedding Clustering for Brain Atlases
Authors: Mo Wang
Kaining Peng
Jingsheng Tang
Hongkai Wen
Quanying Liu
Venue: NeurIPS 2025 poster ()
Keywords: Neuroscience
Brain atlas
Parcellation
Pretraining
Graph
Deep embedding clustering
voxel-level
Primary area: neuroscience_and_cognitive_science
TL;DR: Personalized functional brain atlas via deep embedding clustering and graph constraints achieves new state-of-the-art performance on atlas metrics and downstream tasks.

Abstract: Brain atlases are essential for reducing the dimensionality of neuroimaging data and enabling interpretable analysis. However, most existing atlases are predefined, group-level templates with limited flexibility and resolution. We present Deep Cluster Atlas (DCA), a graph-guided deep embedding clustering framework for generating individualized, voxel-wise brain parcellations. DCA combines a pretrained voxel-level fMRI autoencoder with spatially regularized deep clustering to produce functionally coherent and spatially contiguous regions. Our method supports flexible control over resolution and anatomical scope, and generalizes to arbitrary brain structures. We further introduce a standardized benchmarking platform for atlas evaluation, using multiple large-scale fMRI datasets. Across multiple datasets and scales, DCA outperforms state-of-the-art atlases, improving functional homogeneity by 98.8% and silhouette coefficient by 29%, and achieves superior performance in downstream tasks. Furthermore, atlases demonstrate heterogeneous performance across various tasks and an atlas derived from a fine-tuned model yields superior results for its specific application. Codes are available at https://github.com/ncclab-sustech/DCA.

DCA: Graph-Guided Deep Embedding Clustering for Brain Atlases
Mo Wang
Kaining Peng SUSTech
Jingsheng Tang SUSTech
SUSTech & University of Warwick
Hongkai Wen
Quanying Liu
University of Warwick hongkai wendwarwick.ac..u
SUSTech Lingy@sustech.edu.
Abstract
Brain atlases are essential for reducing the dimensionality of neuroimaging data and enabling interpretable analysis. However, most existing atlases predefined, group-level templates with limited flexibility and resolution. We present Deep Cluster Atlas (DCA), graph-guidee deep embedding clustering framework for generating individualized, voxel-wise brain parcellations. DCA combines pre- trained voxel-level IMRI autoencoder with spatially regularized deep clustering to produce functionally coherent and spatially contiguous regions. Our method supports flexible control over resolution and anatomical scope, and generalizes to arbitrary brain structures. We further introduce a standardized benchmarking platform for atlas evaluation, using multiple large-scale fMRI datasets. Across multiple datasets and scales, DCA outperforms state-of-the-arr atlases, improving functional homogeneity by 98.5 98.8% and silhouette coefficient by 29%, and achieves superior performance in downstream tasks. Furthermore, atlases demonstrate het- erogeneous performance across various tasks and an atlas derived from fine-tume fine-tuned model yields superior results for its specific application. Codes are available at https::/gitte hwwpn/clllbssssssshhaaaooaaa
Introduction
Traditional method
IMRI
Brain atlases, as predefined parcellations that group voxel-wise fMRI signals into gions, are essential tools for reducing data dimensionality and improving interpretabil- ity in neuroimaging studies. Over the decades. hundreds of atlases have been pro- posed, based on anatomical [22 3), func- tional [)] and cytoarchitectonic [7] criteria. These atlases vary widely in spa- tial resolution (from fewer than to over 1000 regions) and anatomical coverage (e.g., cortical vs. subcortical), and have become foundational resources in neuro- science.
Surface origin signals
surface-level group
Average
dewae
rofer
Ours
Avbool
Sub
Sub da
FC
&
Untrie
Sub
styne
Voxei-level embeddings
personalized atlases
Voxel-level group atlas
Figure 1: Motivation. (top) Traditional atlases cluster coarse, group-averaged functional connectivity (FC), limiting resolution and individual specificity. (bottom) DCA learns voxel-wise embeddings for personalized parcellations, enabling flexible, high-resolution group atlases.
Equal contribution: M. J. Corresponding author: H. W., Q. L.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Despite their ubiquity, existing brain atlases suffer from several key limitations that hinder their adaptability and performance data-driven analysis pipelines. Most atlases are built on cortical surfaces, neglecting subcortical and white-matter structures. However, growing evidence suggests that large-scale brain function emerges from interactions across the whole brain, motivating the need for voxel-based, full-brain parcellations (Fig TT. Atlas granularity is often fixed and predefined, forcing users to compromise between anatomical coverage and resolution. For example, the cortical mask in Yco[[] spans 33k voxels per hemisphere, whereas MMP covers 58k-dessp nominally referring to similar regions, A more flexible framework should support arbitrary region-of-interes (ROI) selection and user-specified parcel counts. In addition, most atlases constructed as group- level templates derived from averaged data or majority vote, which, while generalizable, overlook substantial indiviindiv variability in brain function and structure. Recent studies have emphasized the value of subject-specific models in enhancing reproducibility and precision [
Clustering is cornerstone of brain atlas construction, but off-the-shelf algorithms as K- Means 10), hierarchical clustering [[]], and vanilla spectral methods 12 are ill-suited to the characteristics of fMRI data. First, the inherently low signal-to-noise ratio of fMRI hampers these methods ability to recover clear boundaries as the number of parcels grows. Second, even gray- matter mask may contain tens of thousands of voxels, making the computation and storage of full matrix prohibitive. Finally, standard clustering optimizes only functional similarity and lacks any notion of spatial continuity, yielding fragmented anatomically implausible parcels. Although one can incorporate bissance-based penalties to encourage spatial contiguity, such strategies demand careful tuning lest they compromise the atlas's functional coherence.
cunntionallconnectiin
To overcome these limitations, we introduce Deep Cluster Atlas (DCA), a graahhguuddd deep em- bedding clustering framework for constructing both individualized and group-level voxel-wise brain parcellations (Fig. Dp. DCA leverages a pretrained Swin-UNETR encoder to extract spatiotemporal embeddings from IMRI data and employs a ppatiallyrregularizze deep clustering module guided by a voxel-wise n-nearest-neighhor (KNN) graph. This design ensures that resulting parcels are not only functionally coherent in embedding space but also anatomically contiguous in voxel space. To systematically assess performance, we introduce a benchmarking platform (Table [) that evaluates any input atlas using standardized internal metrics (c.g., homogeneity, silhouette coefficient) and external metrics from downstream tasks (c.g., autism diagnosis, cognitive state decoding). Across datasets and resolutions, DCA achieves 98.8% improvement in homogeneity and 29% in silhouette coefficient over existing atlases, while outperforming them in multiple classification tasks.
Our key contributions are:
We propose scalable deep clustering framework that integrates Swin-UNETR embeddings and spatial graph regularization to generate voxel-wise brain atlases.
DCA enables flexible control over parcellation granularity and anatomical scope, supporting both personalized and group-level atlas construction.
We release standardized benchmarking platform evaluate atlas quality via internal metrics and downstream tasks such as cognitive task decoding and disease diagnosis.
2
Related work
MRI based brain atlas Atlas generation based on magnetic resonance imaging (MRI) is the pre-
dominant approach for constructing parcellations. Widely adopted algorithms include k-means [10
hierarchical clustering [1I] spectral clustering [12), community detection [13], normalized cuts [4]
and statistical learning methods[15]. These techniques aim to maximize within-parde homogeneity and minimize between- similarity. However, functionally similar voxels are not always spatially contiguous, so enforcing spatial coherence remains challenging. To address this, spatial regularization strategies-such Markov random field priors (2), spatially weighted clustering [14], and deep
Boltzmann machine frameworks [15] hhave been introduced to ensure that resulting parcels are both functionally coherent and anatomically contiguous.
Deep clustering Traditional clustering methods measure similarity directly in the original data space, and even when manifold-based techniques are employed, feature extraction and clustering remain two disjointed stages 16. 17 18 19]. Deep clustering, by contrast, integrates these steps. It

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A. Group Pretraining on Voxel-Ievel fMRI
Swin encoder
Unetr decoder
fMRI dataset
masked fMRI
autoencoder
reconstructed
B. Personalized Clustering with Spatial Constraints
embedded point
soft assignment
g
g
Swin encoder
Kkt
(2)
(k)
(
p
individual fMRI
embeddings
learnable centroids
auxiliary target
vertex of graph guide
update edge weights
graph cut
k-parcel atlas result
Figure 2: (A) Self-supervised pretraining of Swin-UNETR group fMRI data: 80% of each volume Random continuous masked in space and time and reconstructed across 1, 1,000 resting-state trials. Fire icon denotes trainable encoder-decoder weights. (B) Personalized atlas generation at voxel resolution. Individual IMRI volumes are passed through pretrained encoder to extract both local and global embeddings. Each voxel (red cube) is softly assigned to one of K learnable centroids by measuring its distance to every centroid (top row). Simultaneously, a given ROI mask defines the nodes of 26-neighborhood graph, whose edge weights are set the cosine similarity between adjacent embeddings. Sparse spectral clustering on this graph produces hard auxiliary labels (bottom row). A KL-divergence loss then aligns the soft assignments with these auxiliary targets, updating both the centroids and the encoder's final projection layer. By iterating between refining embeddings, re- weighting graph edges, and updating cluster centers, the method converges spatially contiguous, functionally coherent parcellations.
jointly refines encoder parameters and cluster centers through an auxiliary target distribution derived from the current soft assignments (20 21.. Beyond its success in image clustering, deep clustering has proven effective for time-series segmentation [22). cell detection [23). and disease discovery (4)
When constructing brain atlas, both functional similarity and spatial continuity must be preserved. In our framework, each voxel of single subject serves as an individual sample for deep clustering, and we incorporate graph-guide spatial prior ensure contiguous parcels. To our knowledge, this is the first use of deep clustering for generating fully continuous, voxel-level brain atlas.
Brain segmentation To extent, brain atlas construction shares conceptual similarities with semantic segmentation of brain [25] 26 27]. as both aim to partition the brain into meaningful regions. However, key differences distinguish the two tasks. First, they differ in granularity and objective: brain segmentation typically categorizes voxels based on tissue types-such as whole tumor, tumor core, and enhancing tuereawhereas brain atlases delineate functionally relevant areas, such as precentral gyrus, thalamus, hippocampus. Second, semantic segmentation is generally supervised learning task with well-defined ground truth labels, while atlas construction inherently unsupervised and must be evaluated using more complex criteria, such as functional or structural homogeneity, Although segmentation techniques have been employed to map existing atlases, they rely heavily on predefined templates and primarily serve to replicate rather than discover novel parcellations. For example, DDparcel assigns voxel-wise labels for 101 anatomical regions based on Killiany atlas, effectively reconstructing rather than redefining atlas (28).
the Desikan- Desikan-Killiany

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3 Methods
3.1 Data and preprocessing
Atlas construction data We use resting-state fMRI data from 1000 subjects in the Human Con- nectome Project (HCP) [29] for atlas construction. All data were processed using the HCP minimal preprocessing pipeline 330 which includes gradient distortion correction, motion correction, EPI distortion correction, registration to Tw-weighted images, and spatial normalization to MNI152 space, The preprocessed volumetric images resampled to 2 mm isotropic resolution. To improve signal quality and spatial coherence, we applied spatial smoothing using AFNI's 3dBlurToFWHN [II, targeting 3 mm FWHM. The ablation study on smoothing levels is provided in Appendix.
Downstream task data For downstream evaluation, we use three public datasets: HCP, ABIDE [2], and ADNI [33] HCP provides both resting-state and task-based IMRI data, preprocessed using the minimal preprocessing pipeline. ABIDE data come from the AB I dataset, using the version preprocessed by the Preprocessed Connectomes Project (PCP) [34]. ADNI resting-state fMRI is processed using the DPABI toolbox [35], including removal of the first 10 volumes, slice timing
correction, spatial normalization to the MNI152 space, smoothing with mm FWHM Gaussian kernel, linear detrending, and nuisance signal regression.
3.2 Personalized atlas generation
We introduce DCA (Deep Clustering Arlas), a self-supervised framework that turns a pretrained 4D encoder into spatially consistent whole-brain fMRI parcellator (Fig. 2 Firstly, we pretrain Swin- UNETR autoencoder on masked 4D iMRI blocks (80% spatiotemporal masking), reconstructing the missing voxels. The encoder preserves the full spatial dimensions (H x W x D), producing voxel-level embeddings that capture both local and global context (Fig. 2A). The region of interest is defined by any ROI mask. From these embeddings belong to the mask, maintain K cluster centroids. Each voxel's embedding is converted into a soft assignment by measuring its distance to every centroid (top row, Fig. 2 In parallel, we build 26-nearest-neighhourr graph over the ROI masked voxels, weighting edges by pairwise embedding correlations. A graph-cut then yields hard auxiliary targets that enforce spatial contiguity (bottom row, Fig. BB.. Finally, we minimize the KL divergence between the soft assignments and these hard targets. backpropagating through both the encoder's final layers and the centroids. By alternating between updating embeddings and regenerating auxiliary targets, DCA converges to a voxel-level atlas that is both functionally meaningful and spatially contiguous.
Voxel-level 4D IMRI pre-train To extract meaningful features from high-dimensional fMRI data, we adopt Swin-UNETR as the backbone for 26 2 Swin- UNETR built upon the Swin Transformer architecture, which introduces a hicrarchical structure with shifted windows to compute self-attention in a local and spatially-aware manner Unlike standard Vision Transformers (ViT) that operate on flattened global patches and often ignore local continuity (77), Swin Transformers preserve spatial hierarchies and are thus better suited for voxel-level modeling in neuroimaging. This property is particularly advantageous for fMRI, where fine-graines spatial relationships between voxels are critical.
We perform self-supervised pretraining using masked reconstruction objective. During pretraining, we randomly mask out contiguous blocks in both space and time. Specifically, we divide the fMRI volume into non-overlapping spatiotemporal patches and then zero out 80% of those patches along the chosen spatial or temporal axis (more details in Appendix). By forcing the encoder to reconstruct missing segments using information from the surrounding unmasked regions, the model Iearns representations that capture both local detail and long-range dependencies across space and time. Using Swin-UNETR's 's encoder-decoder structure in this masked auto-encoding framework, we obtain strong voxel-wise embeddings that serve as the foundation for subsequent clustering and parcellation.
Learnable cluster centres. Let M E {0, 1) HXWxD be a binary mask defining the region of interest, and let V = {i) M; = 1} index the N = |V] non-background voxels. We parameterize K cluster centroids as a trainable matrix 1 C Rd, initialized with orthogonal rows and noroomaalizdd so that μ 4² I. During each forward pass, extract the non backbaoggddnd voxel

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embeddings hev from the Swin-UNETR encoder, compute their Euclidean distances to all centroids, and convert these distances into soft assignments:
A = Z M3 la,
Wij = exp(-Ax))
W
(I)
Σ, Wij
where Å denotes min-may max normalization and q, E AK11
Voxel graph construction. The vertex V is defined by the binary mask M. We extract embeddings {z. Rd hev from the pretrained. tine-tunable Swin-UNETR encoder. A 26-neighbourhood graph G= (V, B), which includes all voxels 3x3x3 cube excluding the center, then constructed by linking each E V to its up to 26 spatial neighbours j E V, yielding an edge-index array E E N2x Edge weights given by the cosine similarity of demeaned embeddings:
aij
cos z; 2, 2j 2z);
where 2, the mean of 2,. This produces a sparse adjacency W with |E] R 26N nonzero entries.
Graph spectral clustering. On the weighted graph G, we compute hard auxiliary labels p E {I...., K] VI via sparse spectral clustering. We form the unnormalized Laplacian L = D W. extract the K eigenvectors corresponding the smallest eigenvalues of L, and finally apply K-Means on the resulting N x K embedding to assign each voxel its auxiliary label p;- To preserve cluster identity across iterations, realign each new p; to the previous labels via the Hungarian algorithm, yielding an optimal one-to-one mapping. For each iteration, given the previous labels Pprev and the newly obtained labels Pnew: we first build a cost matrix C E Z x where
Ct.
(Ppiov,n A Pnew,n =),
ie. the number of voxels assigned to cluster é previously and cluster j now. We then solve the linear assignment problem
K
max Σ Ci,(())
(4)
388 on CC, which yields an optimal one-to-one mapping и {I...., K} + (I,...,K) KJ. Finally, we relabel the new clusters P. according to by P; (p.). thereby preserving label correspondence with earlier iterations.
via the Hungarian algorithm
Objective. Let Q (0,1) be the soft-assignment matrix whose ith row is qu and let P E {0, 1 be the one-hot encoding of the aligned auxiliary labels p. We optimize the Kulbback-Leibler divergence
L= KL
Σ
Pij log
Psi Çi
(5)
Gradients are back-propagated only to the centroids {1y) and the final projection block of Swin- UNETR; all other encoder weights remain fixed. This procedure jointly refines both the encoder's output and the cluster centroids to produce functionally coherent, voxel-level parcellations.
Group atlas generation. To facilitate downstream use and fair comparison, we also developed streamlined procedure for deriving group-level atlas from individual parcellations. We construct the group-level atlas in three steps detailed in Appendix. First, we pick template label vectors, each capturing the voxel assignments of one parcel in subjects. Next, we assign every gray-matter voxel to the template vector with which it has the highest label similarity. Finally, to guarantee spatial contiguity, we keep only each parcel's largest connected component and reassign any smaller, isolated regions adjacent parcels based on local similarity. This yields K contiguous, functionally coherent parcels.
5

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3.3 Atlas evaluation
To comprehensively assess the quality of any candidate atlas, we provide an interactive evaluation playground. Each input atlas is first spatially normalized to a common template space and resampled to match the reference resolution. We then perform suite of quantitative tests, including intra-cluster similarity metrics and performance on downstream tasks. This framework enables researchers to compare and validate parcellations across multiple criteria in standardized environment.
Similarity metrics To assess the quality of brain parcellations. we adopt two evaluation metrics:
global homogeneity 339 40 and the silhouette coefficient 41] Global homogeneity quantifies the functional coherence within each brain parcel. In our implementation, we use Pearson's 's correlation coefficient A(v;, v;) between the functional time series of two voxels v; and V/ as the similarity metric. The global homogeneity score W Weighted_ ee is computed as the weighted mean within-paree correlation across all K parcels, with higher values indicating more functionally homogeneous and coherent parcellations, my denotes the number of voxels in corresponding parcel Ps-
Σ (m²H)
H mh
R(u,, Uz), Weighted H JEE 491
Σ
(6)
Σ
k= mk
The silhouette coefficient measures the spatial separability and internal coherence of brain parcels. For each voxel, we compute the average dissimilarity to all other voxels within the same parcel w/ and the average dissimilarity to voxels in adjacent parcels b,. The dissimilarity between two voxels is defined as 1 R. The silhouette coefficient then obtained by weighted averaging across all parcels, which ranges from -1 (poor separation) to +1 (excellent separation and cohesion).
Wi
1
R(v, U)),
b
Σ jEnb Pc)
[ R(Vi, my)], S max (W), b:)
b, Wi:
(7)
N
jEP
373
Downstream tasks To assess the utility of brain atlases in functional modeling, we evaluate six representative downstream classification tasks spanning trait prediction, cognitive decoding, and clinical diagnosis. We use a linear support vector classifier (SVC) based on region-level functional connectivity features. Among the 12 AtlaScore benchmarks (Table T2 we selected two resting- -tate traits (gender 44), fluid intelligence (l), two task- based decoding tasks [44, and two clinical diagnoses (ASD from ABIDE, AD/MCI from ADNI), while excluding tasks heavily driven by subcortical features (c.g., crystallized/generaal intelligence, age). This choice ensures a fair evaluation of cortex-only atlases. DCA tends to yield stronger improvements cortex-driven tasks such as cognitive decoding, while gains on benchmarks relying more on subcortical features are less pronounced, consistent with its cortical specialization.
Implementation details
We pretrain our model using masked reconstruction objective on fMRI data blocks of size 96 x 96 x 96 x 300, representing 3D spatial volumes with 300 temporal frames. The model trained for 8 epochs on 2 NVIDIA A 100 GPUs using a batch size of 4. The optimizer and learning rate are Adam and 0.01 respectively for both pretraining and fine-tuning. During pretraining, we adopt a masking ratio of 0.8, randomly masking 80% of the input in both spatial and temporal dimensions. downsampled to = 48, and the encoder produces feature map of shape 96 x 96 x 96 x 256 for clustering, d is 256.
The temporal length the internal representation of UNin-UNETR
For all downstream evaluations, we use data from three public datasets: HCP, ABIDE, and ADNI. All fMRI time series are masked to brain regions, detrended, and z-scored. FC matrices are computed using Pearson correlation between voxel-wise time series, and the upper triangular entries are vectorized to form feature vectors. When the feature dimension exceeds 100, we apply PCA to reduce to 100 dimensions, balaneing model complexity and sample size to ensure fair comparison. test the efficacy of the atlas,
simple linear SVC for the downstream classification task.

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Experimental results
To rigorously benchmark our method, we developed comprehensive evaluation framework that assesses parcellation quality via intra- and inter-region fMRI signal correlations. Next, we apply each group atlas to a suite of real-world downstream tasks, such as cognitive task decoding to evaluate prac- tical utility. We compare DCA against several widely used atlases: Yeo et al. [ parcellates cortex into seven large-scale functional networks derived from resting-state connectivity. Brodmann 7 defined cortical areas based on cytoarchitectonic boundaries. Schaefer et al. [2] published multi-resolution functional atlas (100-1000 parcels) using gradient-informed clustering of functional connectivity.
AAL (Automated Anatomical Labeling) [5) and MUSE (MUlti-atlas region Segmentation utiliz- ing Ensembles) [46] divide the brain into hundreds of anatomy- based regions. MMP (Multi-Modal Parcellation) 8 integrates structural, functional, and connectivity data to define 360 cortical areas.
GIANT (Genetically Informed brAiN aTlas) 47 achieves brain parcellation by genetically-drive integration of voxel-wiss wise heritability and spatial proximity. Additionally, the Watershed Atlas and the Allen Human Reference Atlas-3D, 3D, 2020, were incorporated. To study the effect of granularity, further generate DCA group atlases with K {41, 100, 200, 360, 400, 500, 800) parcels constrained the FreeSurfer gray-matter mask. The mask is derived from the cortical gray matter regions in FreeSurfer's aparc+aseg.ngg (48) and transformed into MNI152 space. In the following sections, we report correlation metrics and downstream task accuracies for each atlas configuration.
5.1 Main results
Fig. summarizes clustering performance for several existing atlases alongside DCA method, evaluated by Homogeneity (Fig. 3B) and Silhouette Coefficient (Fig. BC). We sample 100 subjects from HCP randomly. Full quantitative results are given Table As the number of parcels increases from 7 to 1000, both metrics rise for all methods. To ensure a fair comparison, we match each atlas to DCA at the similar ROI numbers. Across every evaluated resolution, DCA consistently outperforms the best- pest-performing baseline atlas, yielding higher homogeneity and silhouette scores at each scale. For example, at 200 parcels, DCA improves Homogeneity by 77.7% and Silhouette by 19.5% over the Schaefer baseline. On average, across 41 to 800 parcels, DCA improves Homogeneity by 98.88 98.8% and Silhouette by 29%, demonstrating consistent gains in functional homogeneity and spatial separation. This highlights that DCA provides more refined and effective parcellation solution across various atlas configurations, regardless of the cluster count.
A. Visualization of atlases
B. Homogeneity
0.20
DCA 100
DCA 200
DCA 360
DCA 500
0.16
0.12
0.08
AAL1
AAL
AAL
DCA 800
0.04
0.00
C. Silhouette coefficient
0.10
Brodmann
0.08
0.06
0.04
Schaefer 100
Schaefer 500
Schaefer 1000
0.02
MANI
DWA
Watniies
Alker 38 MU52 A Schecfer DCA
0.00
100
200
300
400
600
600
1000
Number Parcels
Figure 3: (A) Surface renderings of our DCA group parcellations alongside 12 mainstream atlases. (B) Homogeneity measured over 100 HCP subjects at varying numbers parcels. (C) Silhouette coefficients for the same 100 HCP subjects and resolutions.

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5.2 Downstream tasks
We evaluate the utility of DCA atlases on six downstream classification tasks covering behavioral prediction, cognitive decoding. and clinical diagnosis on the same 100 subjects as in the previous section (Fig. Across resolutions, DCA consistently matches or outperforms the strongest baseline within each group. Full results, including extended benchmarks on additional tasks, are reported in the Appendix (Table
At low resolution, DCA100 outperforms widely used atlases such Yeo and Brodmann, which exhibit lower homogeneity and reduced classification accuracy across tasks. In medium and high resolutions, DCA200 and DCA360 achieve top performance on cognitive decoding and autism diagnosis tasks, suggesting that fine-grained voxel embeddings and spatial continuity contribute to better functional alignment than anatomically or connectivity-derived alternatives such as AAL or MMP. At ultra-high resolution (500 parcels), DCA maintains strong and stable performance across behavioral and clinical tasks. While some atlases (e.g.. Schaefer500) marginally outperform DCA on individual tasks, DCA exhibits more consistent generalization across domains.
Low resolutiin
Medium resolution
High resclution
Ultra-high resolution
(3)
(2)
(3)
(3)
(2)
(3)
(2)
69
266
0.3
0.2
(1)
(9)
100
(9)
18]
(5)
(8)
(9)
(8)
Yeo
Yio 17
AAL1
AAL2
Schwwler 300
Schowlerr 400
Schwwlfer 500
DCA 520
Brodmwnn 41
Schswder 100
AALSS
Schowler 200
MMP 360
DCA 960
DCA 100
DCA 200
Figure 4: Performance of DCA and baseline atlases across different spatial resolutions on six downstream tasks: (1) gender prediction from resting-state FC (HCP), (2) fluid intelligence prediction from resting-state FC (HCP), (3) classification of 7 cognitive tasks from task-based FC (HCP), (4) classification of 24 cognitive tasks from task- FC (HCP). (5) ASD vs. control classification from resting-statt FC (ABIDE), (6) AD/MCI/CN classification from resting-state FC (ADNI). DCA achieves competitive or superior performance at each resolution level. Values are linearly scaled per task with 0 and corresponding to the lowest and highest performing atlases, respectively.
5.3 Task-specific atlas
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 version fine-tuned for gender classification and use its encoder to derive task-specific atlas, denoted DCA gender
100 We then aggregate fMRI signals into K 100 ROIs for N 200 subjects drawn from the Swin-UNETR fine-tuning test split to avoid data leakage and evaluated using two downstream classifiers:
compact 1-D CNN (two convolutional layers followed by two fully mully-connected layers), graph-based k-GNN (k: = 2), built from functional graphs sparsified to the top 30 % of edges.
Both evaluations used a 70 / 10 20 subject split for train/validationntess.. fully disjoint from fine- tuning subjects to avoid leakage. Tables S1 and S2 summarise the results. The task-adapted atlas preserving
yields consistent gains-as up to +12 % with the CNN and +10 % with the spatial continuity (Table and
5.4 Ablation study
To quantify the contribution of each component, we conducted two ablation studies on 100 random subjects from HCP. First, we applied (1) K-Means clustering and (2) the same graph construction and

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Table I: CNN-based gender classification (higher is better).
Atlas
Accuracy
F1 (Macro)
Fl (Weighted) 1
Watershed (100)
0.73
0.73
0.73
Schaefer100
0.65
0.65
0.65
DCA 100 (group)
0.70
0.70
0.70
DCA100 (individual)
0.70
0.69
0.70
DCA109
gender
(group)
0.70
0,67
0,67
DCA
gender
(individual)
0.82
0.82
0.82
Table k-GNN-based gender classification (higher is better).
Atlas
Accuracy
F1 (Macro)
Fl (Weighted)
Watershed (100)
0.600
0.596
0.596
Schaefer100
0.725
0.723
0.723
DCA100 (group)
0.650
0.650
0.650
DCA100 (individual)
0.725
0.716
0,716
DCA gender
(group)
0.675
0.670
0.670
DC A.CAgema (individual)
gender
0.825
0.825
0.825
graph-cut pipeline from our method directly to the raw fMRI time series. This baseline highlights the necessity of our pretrained encoder for extracting informative features. Second, K-Means and (4) the same graph cut pipeline on the encoded embeddings without the KL.-guided joint optimization of encoder parameters and centroids, isolating the impact of our graph-guided deep clustering mechanism. In both ablations, all similarity metrics (homogeneity and silhouette) drop noticeably below those of (5) the full DCA model (Fig. Jadd Table Moreover, K-Means fails to produce spatially contiguous parcels. And graph-cut improves continuity, but it still yields isolated regions. In contrast, DCA's iterative KL-driven refinement which alternates updating graph weights, encoder parameters, and cluster centers produces brain atlases that are highly homogeneous. We also tested the model reproducibility (Table [n) the effects of the loss (Table 15 and 20 Fig. T2)
both (3)
and normalization (Table 15). the smoothing (Table graph cut method (Fig. 10 and Table 17]
gray matter region (Table 18. number of neighbors (Table and centroid initialization (Table 21 as detailed in Appendix.
Homogeneity
Silhouette coefficient
0.12
0.035
Figure 5: Directly applying K- means or graph-cut method to raw fMRI time-series or embed- dings produces parcellations with substantially lower homogeneity and silhouette scores than our itera- tively optimized method. Moreover, K-means on the unprocessed sig- nals cannot guarantee spatially con- tiguous regions, and while graph- cut method partially enforce contiguity, still fails to produce fully continuous parcels. Our method yields brain atlases that are both highly homogeneous and spa- tially contiguous.
0.11
0.030
0.10
0.025
0.09
0.08
0.015
0.010
0.005
KMeans on IMRI
Graph cut on 1MRI
KMeans
Graph cut on embeddings
Ours
embeddings

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Table 3: Evaluation for fMRI and embedding-basee clustering with K-Means, Graph Cut, and DCA.
Homogeneity?
Silhoucttet
Connected components per parcel.
K-Means
0.0740:10.0186 0.0061=0.0045
447.90
[MRT
Graph Cut
0.0860++000001
0.0179=000053
8.92
K-Means
0.0790++0.000 0.0154=0.0073
322.32
Embedding
Graph Cut
0.08971000210
0.0208=0.0001
4.94
DCA
0.1004++0.021
0.0304=0.0068
1.0052
Discussion & Conclusion
In this study, we presented DCA, a unified framework for generating personalized and group-level voxel-wise brain parcellations. By combining a pretrained fMRI encoder with spatially regularized deep clustering voxel embeddings, DCA produces anatomically contiguous and functionally meaningful atlases that capture local and global brain dynamics.
Resolution Dependence of Downstream Tasks We further examined how downstream task perfor- mance varies with the number of parcels. Based on these trends, tasks can be broadly grouped into three categories: (i) resolution-optimal tasks, which peak at intermediate resolutions, (ii) resolution- insensitive tasks, which remain largely stable across scales, and (iii) size-driven tasks, which mono- tonically track parcel granularity (Table 13). Importantly, this pattern is consistently observed for both DCA and Schaefer atlases (Table 14), indicating that there is no universally optimal resolution. Instead, the choice of parcel count should be guided by the target application. In addition, DCA offers the flexibility to further optimize atlases for specific tasks at a given resolution, as demonstrated in our task-adapted atlas experiments (Table [ and
and 2). What's more, single atlas generalizes optimally across tasks different tasks favor different parcellations [49 so developing task-specific atlases is warranted.
Technical Impact Clustering core operation in brain atlas construction, transforming high- dimensional neural data into interpretable regional structures. However, conventional clustering algorithms are ill-suited for the spatial and functional constraints of brain organization- they often ignore anatomical continuity, rely on coarse- grained features, and lack individual specificity. DCA addresses these challenges with deep clustering pipeline built on a Swin-UNETR encoder pretrained for spatiotemporal representation learning. The toxel-wise embeddings are clustered using a KNN graph prior that enforces spatial smoothness, enabling anatomically contiguous regions that better reflect functional topology. A KL-divergence loss between learnable centroids and graph-induced pseudo-label allows joint refinement of both the embedding space and clustering assignments. This design ensures that the resulting parcels are not only functionally coherent but also spatially contiguous- critical requirement for valid brain parcellation. Our evaluation platform confirms that DCA yields superior internal consistency and downstream utility, outperforming existing atlases on homogeneity, silhouette coefficient, and classification tasks such as autism diagnosis and task decoding.
Limitations and future directions Despite its strengths, DCA has several limitations. First, voxel-wise representation learning and clustering incur substantial memory and computational costs, especially at whole-brain scales. Future work may explore region-specific parcellation or sparse embedding schemes to reduce overhead. Second, our reliance on fixed KNN graphs to enforce spatial continuity may inadvertently attenuate long-range functional relationships, which may suppress long-range functional relationships. Integrating adaptive or learned graphs could help balance spatial continuity with network-level functional coherence. Lastly, the current pipeline uses only single- modality fMRI data. Incorporating structural and diffusion imaging, or even electrophysiologica data ge.g. sEEG), could further enhance the biological fidelity of parcellations
(50 Meanwhile, traditional atlas construction methods struggle to reconcile conflicting signals across modalities [5]] motivating the development of a multimodal deep-clustering framework as a promising avenue for building richer, functionally and structurally grounded brain atlases.
10

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Acknowledgements
We thank Wenhao YE for his assistance during the rebuttal. This work was supported by the National Natural Science Foundation of China (62472206), Shenzhen Science and Technology Innovation Committee (RCYX2023121 101000000000000000,, 11Z2 Laboratory of Advanced Biomaterials (2022B 211220000003 and the open research fund of the Guangdong Provincial Key Laboratory of Mathematical and Neural Dynamical Systems, the Center for Computational Science and Engineering at Southern University of Science and Technology.
Guangdong Provincial Key
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A Appendix
A.1 Evaluation of similarity metries
We evaluated several atlases-including Yeo, Brodmann, GIANT, Watershed, Schaefer, AAL, Allen, MUSE, and MMP- wiith parcel counts ranging from 7 1000, using both homogeneity and the silhouette coefficient as evaluation metrics (Table 4
Table 4: Evaluation of similarity metrics against DCA and other atlases. Values are shown as mean + standard deviation.
100
116
149
Houmgancity
0.012
019922
s00is
0.251
0J1892
0.0148
488873
BARZH
0,0141
88.000
0,1084
018244
E40144
0.9566
0,0210
0,0718
OLOYSS
Sibooeete
201060
200885
20000
100854
201005
28 0030
200005
201001
28 909
20100
200007
DCAouus)
Schaefer
DCMour))
DCM/urs)
Schueder
DCAlours)
2-9.222
20109
10238
88830
2- 8-40
B3325
2: 3-4
0.0389
0.4177
0,048
0,0416
0.0565
0.0572
0.4S4
0.0000
0U8644
0M537
0.0615
0.0865
01853
0,883
A.2 Cross-dataset generalization on CHCP
We further assess model's cross-dataset generalization by applying the Swin-UNETR coder--rettraieed on the HCP dataset-to individual atlas generation on the other independent dataset (Fig. 6 and Table 5). The Chinese Human Connectome Project (CHCP) dataset comprises high-resolution multimodal MRI-including structural, diffusion, and resting-state fMRI-from healthy Chinese adults, and uses the same acquisition parameters and HCP preprocessing pipeline (52). Our results demonstrate that, without any additional fine-tuning, DCA produces coherent, spatially contiguous parcellations CHCP dataset that surpass other atlases in both metries, underscoring the robustness of the learned voxel embeddings.
DCA 100
Homogeneity
Silhouette coefficient
0.15
0.075
DCA 200
0.10
0.050
0.05
0.033
DCA 360
0.000
100
200
400
YesT Yes17
36 Brofmon AML: MAA22
AA13 A Scheefer MNP
DCA
Figure 6: Homogeneity and Silhouette coefficients measured over 100 CHCP subjects varying numbers of parcels.
A.3 Atlas of the subcortex and white matter
Because our method learns voxel-level embeddings across the entire brain, it is applicable any arbitrary brain structure. Given region-of-interes (ROI) mask, our framework can generate par- cellations at specified resolution. Here, we demonstrate two applications: atlas construction for the subcortex and white matter (Fig- 7 The corresponding ROI masks are extracted from FreeSurfer's s aparc+aseg.mg. [48] and transformed into MNI152 space. We evaluate parcellations with (10, 20, 40, 50} clusters for the subcortex and (50, 100, 200, 400) clusters for the white matter.
22

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Table 5: Evaluation of similarity metrics against DCA and other atlases on the CHCP dataset
Atlas
Yco
Brodmann
Schaefer
DCA
AAL
Metries
7
17
41
100
100
116
120
0.0413
0.0500
0.0324
0.6560
0.1162
0.0407
0.0409
Homogeneity
::0.0171
+0.0179
+0.0127
+0.0188
0.0205
20.0136
=0.0136
Silhouctte
0,0255
0,0303
0,0169
0,0371
0.0382
0.0213
0,0215
1000069
10.0072
1:00008
1:00071
2000038
Atlas
AAL
Schaefer
DCA
Schaefer
MMP
DCA
Schaefer
Metrics
166
200
200
300
360
360
400
0.0418
0.0784
0.1300
0.0873
0.0848
0.1451
0.0948
Homogeneity 1
1:000.36
1:001155
0.0211
1:0.1199
10.0187
1:0.0114
+:00200
Silhouette
0.0224
0.0435
0.0506
0,0492
0,0501
0.0643
0.0542
+:0.0037
1:00006
0.0082
1:0.007
1:0.0064
::0.099
#0.0072
In future work, incorporating additional structural information, such as white matter fiber orientations, could further improve the quality of the parcellations.
Subcortex
10
20
40
50
White Matter
50
100
200
400
Figure 7: Voxel-wise parcellations of subcortical and white matter regions under varying granularity levels.
A.4 Model reproducibility
To quantify variability across repeated executions, ran the complete pipeline five times on the same fMRI segment and compared the resulting parcellations using Dice, intersection-over: (IoU), voxel assignment consistency (VAC: the fraction of voxels that keep the same label after Hungarian alignment), adjusted Rand index (ARI), and normalized mutual information (NMI) (Table (6). Variability stems chiefly from (i) the random initialization of cluster centroids in spectral-graph step and (ii) the initialization of the model's ''s centroid matrix. With fixed random seed, the atlas is perfectly deterministic. Because the loss contains Kullback-Leibh (KI.) term that aligns model assignments to graph graph-clustering assignments, reproducible results require fixing
23

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both seeds or fixing one seed and deriving the other from it (e.g., initializing the graph centroids with the model's centroid matrix). Under realistic stochasticity from spectral clustering and model initialization, more than 80% of voxels retain their labels across runs; disagreements are typically confined to regions where dominant parcel can be subdivided into finer clusters.
Beyond seed control, stability can be boosted by seeding cluster centroids with an external prior-such as population template- allowing DCA to refine these priors into subject-specific atlases. This strategy preserves the anatomical grounding of established atlases while exploiting DCA's capacity for individualized refinement.
Table 6: Model reproducibility across five runs.
Dice t
IoU
VAC
ARI 1
NMI
Both-Fixed
1.000 = 0.000
1.000 = 0.000
1.000 + 0.000
1.000 = 0.000
1.000 = 0.000
Model sced-Fixed
0.809 0.025
0.737 + 0.031
0.809 0.025
0.748 + 0.030
0.904 + 0.009
Graph seed-Fixed
0.832
0.020
0.769 + 0.027
0.845
0.022
0.808 + 0.027
0.921 + 0.009
Roth-Random
0.822 + 0.023
0.753 + 0.030
0.823
0.021
0.768 = 0.025
0.911 + 0.009
Null
0.500 + 0.017
0.352 + 0.016
0.500 + 0.017
0.386 + 0.011
0.747 + 0.005
While the method produces consistent atlases when run multiple times on the same fMRI segment with identical settings, we then evaluated cross-segment stability. To quantify consistency, we produced DCA 100 atlases from ten non-overlapping fMRI segments for each of ten HCP participants, spanning multiple runs and both phase-encoding directions. Atlas similarity was measured with Dice and intersection-over over-union (IoU). As summarised in Table [7] intra-subject similarity is markedly higher than both inter-subject similarity and null baseline obtained by randomly partitioning the cortical mask into 100 spatially contiguous, equal-sized parcels (with parcel correspondence solved via the Hungarian algorithm). These results confirm that DCA yields reproducible atlases despite stochastic initialisation.
Table 7: Intra- and inter-subject atlas similarity.
Dice t
IoU f
Inter-subjer (null)
0.497
0.349
Inter-subject
0.614
0.481
Intra-subject (null)
0.506
0.358
Intra-subject
0.789
0.707
A.5 Group atlas generation
To facilitate downstream use and fair comparison, we developed a streamlined procedure to construct group-level atlas from individual parcellations (Algorithm I]. Given N subject-specific atlases with a common label system of K parcels, we generate a spatially contiguous group-level atlas through three steps:
Step 1: Template label selection. We first identify a set of reliable voxels Veore that are absent in at most a N subjects (we use a = 0.2). For each voxel u E Veore. we form a label vector Z, = [A()))) (v), A(N) (v)), where (t) denotes the label assigned to voxel in subject i. We sort all such vectors by frequency of occurrence, and select the top K vectors that have pairwise Hamming distance less than N (we use 3 0.2) as the template label vectors (tk.
Step 2: Voxel-to-template assignment. We then identify Vassigns the of voxels absent in at most 7 N subjects (with = 0.8), and assign each v E Vassign to the template & that maximizes the agreement:
N
L(v) = arg max D (OA
This results in a K -lael volumetric map L that is not necessarily spatially contiguous.
24

---

Step 3: Spatial contiguity enforcement. For each parcel k. we retain only its largest 6-connected component, and mark all other voxels in k as unlabeled. We then iteratively reassign these dropped voxels as follows: for each unlabeled voxel with at least one labeled 6-connected neighbor, we compute the Hamming distance between 2p and the label vectors {z.) of its labeled neighbors E (v)... The voxel is then assigned the same label as the neighbor u" with the smallest distance, ie., L(v) = L(u"). ). This process repeats until all voxels are labeled, resulting a group-level atlas with K spatially contiguous and functionally consistent regions.
Algorithm 1 Group-level atlas generation from individual parcellations
Require: Subject-wise atlases (A A ( ( A (
number of parcels K, thresholds o. 3
Ensure: Group-level atlas L
1: Identify Veore f- {v voxel absent in I aNV subjects) }
2: For each Voore. construct label vector 2, [A (v). (c)]
3: Count frequency each Ze; sort descending
4: Select top K vectors fti..... tx with pairwise Hamming distance & BN
5: Identify V. Vassign + {or voxel absent in I yN subjects)
6: for all Vassign do
7: Assign L(v) + arg max Ex (v) (
8: end for
9: for all label == 1 to K do
Keep the largest 6-connected component of label
11: Mark all other voxels in k as unlabeled
end for
13: while any voxel is unlabeled do for all unlabeled voxel do if v has at least one labeled 6-neighbor then Find
15:
16:
arg miteeeNote), labeled Hamming(zy, (Z., Z.)
Assign L(v) < L(u*)
18: end if
end for end while
20:
A.6 AtlaScore: atlas evaluation platform
Due to space constraints, we have omitted the full set of results from the main text. In the Supple- mentary Material, we present detailed experimental designs and complete outcomes for similarity evaluations and 12 downstream tasks (Table (2).
In addition to the 12 downstream tasks provided by AtlaScore, we further evaluated atlas utility using modern neural classifiers. Specifically, we trained compact 1-D CNN on ROI-level time series (Table and grsph k-GNNN on FC graphs (Table These models provide complementary perspective by directly testing whether atlas parcellations facilitate feature extraction for nonlinear learning. These findings reinforce that DCA not only benefits classical SVC pipelines but also enhances performance in deep learning-based settings.
A.6.1 Distance-controlled boundary coefficient (DCBC)
In the main text, we have introduced Homogeneity and Silhouette in Section 3. Such conventional metries overlook the intrinsic spatial smoothness of brain signals, often overestimating parcellation quality by conflating spatial proximity with functional similarity, especially in high-resolution cortical data, where false boundaries may emerge due to smoothness rather than genuine functional distinctions [50). To mitigate this bias, DCBC groups vertex pairs based on their spatial separation and evaluates functional similarity differences between within- and between-parcel pairs at each distance level. The DCBC metric is formally defined follows:
25

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Table 8: Experiment index, name, and description.
#
Name
Description
1
Similarity Simoleeiyy
Measure mean intra-cluster correlation
2 Similarity-Sllhouette
Compute silhouette coefficient over voxels
3
Similarit-DCBB A.6.1
Evaluating brain parcellations using the distance-controolled boundary coeffi- cient [50]
4
Downstream- classification A.662
Predict biological sex using FC Predict fluid intelligence level using FC Classify cognitive tasks using FC Classify 24 cognitive tasks using FC Classify autism vs. healthy controls us- ing FC
5 Downstream- Intelligence A.6.3
6
Downstream- Downstream-Cognitive task (7-way (7-way)A.6..
A.6.4
7
Downstream- Cognnitive task way
A.6.4
8
Downstream-Autiin diagmosis A.6.5
9 Downstream-AD diagnosis A.6.6
Classify AD / MCI / CN using FC Within-subject FC similarity
10
Downstream-FCC stabiill A.6.7
11
Downsteamm-Fingerprinnngg A.6.8 A.6.8
Subject identification via FC matching Predict age group labels
12
Downstream-Age group classification A.6.9
13
Downstream- CaaaarecammCyttallizzeedd intelligence A.6.3
Predict crystallized intelligence level us- ing FC
14
Downstream-Gent intelligence A.6.3
Predict overall cognitive ability level using FC
15
Downstream-Autish cross-site A.6.5
Cross-site classification of autism vs. healthy controls using FC Predict biological sex using time series Predict biological sex using FC
16 Downstream- classification (CNN) A.6.10
17
Downstream- classification (k-GNN) A.6.1]
DCBC Σ widi,
where per-bin correlation difference d; corTwithin (i) and corTbetween (i) are the mean functional correlations of within-pant parcel and between-pane parcel vertex pairs in the i-th spatial distance bin, respec- tively; The variance var(d,) reflects how vertex pair counts (Nw.is n4,5)) affect the reliability of d, in each spatial bin, while the precision weights subsequently compensate for this uncertainty by assigning higher influence bins with lower variance during DCBC computation. var(d,) and w; take the following forms:
Rew 7ob,5
car(d:) = Twosk + Tbb
Tounk & + 7b.s
(9)
The
Do 1bb.j
Doo.j + Th.
By controlling for spatial distance in this way, DCBC disentangles true functional boundaries from artifacts of spatial smoothness, providing a more reliable parcellation assessment. In our evaluation process, all parameters followed the settings specified [50]. However, we note that DCBC was mainly developed for serface-based parcellations and becomes computationally prohibitive at the fine voxel resolution employed by DCA. Therefore, we computed DCBC scores by projecting volumetric atlases onto the cortical surface (fsLR 32k template) (53), analyzing only data from the left hemisphere. This surface-based approach exceeds the scope of our native volumetric framework.
A.6.2 Gender classification
We evaluated the ability of each atlas to support gender classification based on resting-state functional connectivity (FC). We used data from 100 unrelated subjects the Human Connectome Project (HCP) 29 each contributing multiple FC samples constructed from 300 consecutive TRs of resting-state
26

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fMRI. For each atlas, FC matrices were computed and their apper-triangule entries were used as features.
To ensure subject-level generalization, we performed 10-fold cross-validation across subjects: in each fold, 90 subjects were used for training and 10 for testing. A linear support vector classifier (SVC) was trained on the training set. If the FC dimensionality exceeded 100, we applied principal component analysis (PCA) to reduce dimensionality: features were projected onto the top 100 principal components computed from the training data, and test samples were projected into the same subspace. Classification accuracy on the test subjects was recorded for each fold and averaged to obtain the final performance.
A.6.3 Fluid, crystallized, and general intelligence level prediction
We evaluated whether atlas-based FC features can predict individual differences in fluid, crystallized, and general intelligence. We used the corresponding HCP behavioral score (CogFluidComp AgepAAgeAjj CogCrystalComp_Ageee
and CogTotalComp AAgAdd) to define three classes: low (<85), medium (85-115), and high (>1 (>115) intelligence. Each subject contributed multiple FC samples from resting- state fMRI (300 TRs per sample). 10-fold cross-validation was performed across subjects, using a linear SVC. When the number of FC features exceeded 100, PCA was applied to project the data onto the top 100 principal components computed from the training set.
A.6.4 Cognitive task classification
We assessed whether atlas-based FC can distinguish different cognitive states using task-fMRI data from 100 HCP subjects. For the 7-class classification, each subject completed seven tasks-working memory, gambling, motor, language, social, relational, and emotional each contributing one FC matrix. For the 24-class classification, we further segmented each task into its constituent conditions (c.g., O-back faces, math, fear), resulting in 24 fine- ine-grained task labels. Each subject contributed one FC matrix per task condition.
We trained a linear SVC to predict the task label from FC features using 10-fold cross- cross-validation across subjects. When the number of FC features exceeded 100, PCA was applied to project the data onto the top 100 principal components computed from the training set.
A.6.5 Autism diagnosis and cross-site generalization
We evaluated whether FC features can distinguish individuals with autism spectrum disorder (ASD) from healthy controls using resting-state fMRI data from the ABIDE dataset (n = 871) (2). For each subject, an FC matrix was computed and used to train linear SVC for binary classification. We considered two evaluation settings. In the first, we performed 10-fold cross-vas validaaiit at the subject level assess within-dataset classification performance. In the second, we tested cross-site generalization by holding out one acquisition site for testing while training on subjects from all other sites, repeating this procedure across all sites. When the number of FC features exceeded 100, PCA was applied to project the data onto the top 100 principal components computed from the training set.
A.6.6 AD diagnosis
We evaluated the ability of FC features to classify individuals into Alzheimer's 's disease (AD), mild cognitive impairment (MCI), cognitively normal (CN) groups We used resting-state fMRI data from 267 subjects in the ADNI dataset B3), each labeled as AD. MCI, or CN. FC matrices were computed for each subject and used to train linear SVC for 3-class classification. 10-fold cross- validation was performed across subjects. When the number of FC features exceeded 100, PCA was applied to project the data onto the top 100 principal components computed from the training set.
A.6.7 FC stability
We evaluated the within-subject stability of FC to assess how consistently an atlas captures individual functional architecture (54). We used resting-state fMRI data from 100 HCP subjects. Each fMRI scan was segmented into multiple non-overlapping windows of 300 TRs, and an FC matrix was computed per window. For each subject, we calculated the Pearson correlation between the vectorized upper triangles of all FC matrix pairs and averaged the resulting values to obtain single stability
27

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score. These scores were then aggregated across all subjects to evaluate the group-level FC stability supported by each atlas.
A.6.8 Fingerprinting
To evaluate how well an atlas captures individual-speciff features in FC, we conducted subject identification (fingerprinting) task [55]. We used resting-state fMRT data from 100 subjects, each providing multiple FC matrices. For each subject, one FC was randomly selected as the reference. The remaining FCs were matched all reference FCs by computing the Pearson correlation between the vectorized upper triangle of each pair. A prediction was considered correct if the most highly correlated reference FC belonged to the same subject as the query FC. Each subject's identification accuracy was computed, and group-level performance was obtained by averaging across subjects.
A.6.9 Age group classification
We evaluated whether atlas-based FC features can predict individual differences in age group. We used the HCP- -rovviddd Age variable to assign subjects into three age groups: 21-25, 26-30, and 31 years or older. Each subject contributed multiple FC samples from resting-state fMRI (300 TRs per sample). 10-fold cross-validation number of FC features exceeded 100, PCA was applied to project the data onto the top 100 principal components computed from the training set.
performed across subjects, using linear SVC. When the
A.6.10 Gender classification (CNN)
We further evaluated atlas performance on a CNN- gender classification task. We used ROI-level resting-state fMRI time series from the HCP dataset. The classifier neural network, consisting of two convolutional layers followed by two fully connected layers, trained end-to-end predict gender from the input time series. To avoid subject leakage, data were split the subject level into separate train, validation, and test sets, and all atlases were evaluated under the same protocol.
compact 1-D convolutional
A.6.11 Gender classification (k-GNN)
We also evaluated atlas performance on a graph-based gender classification task using a k-GNN classifier with i: 2. Following the protocol in [56]. constructed base graph where each node corresponds to an ROI, and weighted edges were defined by functional connectivity (FC). The graph was sparsified by retaining the top 30% of edges by magnitude, and the resulting graph was fed to standard 2-GNN with a readout operation to obtain subject-level embeddings, which were then passed linear classifier. Training used a 70/10/20 subject-level split for train/validation/ess.. ensuring no subject leakage. All atlases were evaluated under the same protocol.
A.7 Complete DCA performance on AtlaScore
A.7.1 Evaluation on different smoothing levels
In the main text, evaluated similarity-relater metrics using data smoothed with 3mm FWHM kernel. Here, we additionally report the results obtained with unsmoothed data and data smoothed with 6mm FWHM kernel. The overall conclusions remain consistent across different smoothing levels (Fig. 8 Table 9 and Table I0).
28

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No smoothing
FWHM 6mm
Honkggrncct
3.75
100
10
66
6000
Figure 8: Homogeneity and silhouette were measured over 100 HCP subjects on different smoothing levels.
Table 9: Evaluation on no smoothing data.
Metrics
Atlas
Yen
Hrodmann
Schaefer
DCA
AAI
Schaefer
DCA
Schaefer
Homogeneity
0.01 10
20,058
D.0133
200033
20,068
0.0122
0.0669
-0099
0.0100
300043
200043
0.0101
20.043
0.0103
0.0300
200073
0.0717
-00055
0.0251
20.076
Silhowstte
0.0067
0.0080
0.0099
0.0105
0.0057
0.0058
0,0062
0.0122
0.0148
0.0143
00023
200025
20.025
0.0026
100004
200014
20004
200005
-U032
20,009
Atlas
Metrics
Schuefer
360
360
500
500
700
800
900
1000
Homogeneity
0.0231
-0,0074
0.0774
24000099
1000079
0.0253
20.0081
0.0270
0,0815
:4000099
10.0033
0.0285
0.0301
2400085
0.0314
=0.0066
0.0890
:000003
0.0327
2400085
0.0340
=0,0059
Silhouette
0.0235
0.0268
-0,0028
Table 10: Evaluation 6mm FWHM smoothed data.
Metrics
Atlas
Yeo
Brodmann
Schaefer
DCA
AAL
Schaefer
DCA
Schaefer
Homogencity
0.1239
200300
0.1472
200512
0,1102
200160
20.557
0,2102
0.2475
200604
0.1434
300413
230813
0.144]
0.1476
20.411
0.2502
2000225
0.2909
0.2784
20.015
Silhowste
0.0722
D.0700
0.0560
0.1204
0.12013
0.0766
0.0773
0.0803
0.1439
0.1615
0.1699
200171
20010
100000
2000
240019
10000
10.000
200008
2.00059
200155
Atlas
Schuefer
Metrics
360
360
500
500
700
800
1000
Homogeneity
0.2682
=0,0991
0.3368
:8.0499)
0.3016
#00504
0.3198
#0.0494
0.3671
=98.472
0.3332
#0.064
0,3473
#000476
#0.0667
0.3587
0.4159
#40441
0,3705
#0.0460
0.3809
=0.3451
Silhouette
A.7.2 DCBC performance across Atlases
DCBC was mainly developed for surface-basse parcellations and becomes computationally pro- hibitive at fine voxel resolution employed by DCA. Therefore, we computed DCBC scores by projecting volumetric atlases onto the cortical surface (fsLR 32k template (53) ) analyzing only data from the left hemisphere. This surface-based approach exceeds the scope our native volumetric
framework (Fig. and Table II]
29

---

Yeo17
36 AALZ
0.02
0.00
100
200
300
400
800
1000
Figure DCBC measured over 100 HCP subjects at varying numbers of parcels.
Table 11: DCBC values and standard deviations for various atlases.
Atlas
#Parcels
mean
std.
Yeo7
0.0234
0.0127
Yeo17
17
0.0172
0.0116
Brodmann
41
-0.0019
0.0050
Schaefer
100
0.0073
0.0051
DCA
100
0.0030
0.0055
AAL
116
0.0051
0.0043
AAL 2
120
0.0054
0.0043
A
166
0.0057
0.0045
Schaefer
200
0.0045
0.0050
DCA
200
0.0023
0.0042
Schaefer
300
-0,0000
0.0049
MMP
360
0.0127
0.0095
DCA
360
0.0039
0.0049
Schaefer
400
-0.0021
0.0042
Schaefer
500
-0.0024
0.0051
DCA
500
0.0052
0.0046
Schaefer
600
-0.0018
0.0044
Schaefer
700
-0.0038
0.0057
Schaefer
800
-0,0046
0.0073
DCA
800
0.0075
0.0041
Schaefer
900
-0,0064
0.0069
Schaefer
1000
-0.0044
0.0065
A.7.3 Downstream task performance across atlases
Due space constraints, only subset of results included in the main text. Here, provide the complete evaluation on all 12 downstream tasks across 16 atlases (Table Results are reported mean + standard deviation, averaged over 10-fold cross-validation Within each resolution group, the best-performing atlas for each task is highlighted in bold.
subject-level evaluation.
30

---

DCA
500
0.702
0.537
0.895
1:0.054
0.459
0.661
0.459
0.603
2:0004
0.884
20.148
0.475
4:0.09
0.515
40..1
0.459
+0.111
0.638
2:0.1
Schacfer
500
0.694
0.565
0,876
0.456
0.653
0.440
20074
0.598
2005
0,886
20145
0.477
20.0
0,516
-0.002
0.428
-0.122
0,633
20014
Schacfer
400
0.726
0.527
1-0.099
0,893
1-005
0,462
+
0.668
0.444
20/000
0.609
20045
0,875
20.51
0.497
10.104
0.525
+00.00
0,458
+0.12
0,640
20.11
Table 12: Evaluation downstream task performance across atlases. Values are shown as mean + standard deviation.
DCA
360
0.710
0.535
0.887
2004
0.469
0.630
0.448
0.615
20045
0.852
-0104
2009
0.516
-0.17
+000S
0.69%
20.1%
MMP
360
0.740
10,065
0.513
10.06
0.859
10.063
0.427
+0.015
0.663
0.395
0.612
0.863
-00
0,515
100005
0.542
+0.092
+0.099
0.655
20.00
20
Schacfer
300
0.670
0.517
1-0,082
0.888
0.469
0.661
0.485
0.620
21H046
0.856
20.15
0.480
20.1
0.497
+0,100
0.463
+0.099
0.667
10000
DCA
200
0.687
140073
0,497
100074
0.900
1-0.04
0,479
#-0001
0,663
0,456
0.644
2004
0,776
10112
0.473
1008
0,505
+0,882
+0.10
0.635
1:000
Schacfer
200
0.668
0.505
0.885
0.459
0.660
0.418
0.635
0.7%
0.478
10.105
0.526
#0.997
0.467
+0.104
200066
166
0.606
0.488
0.740
1-0.00
0,243
0.632
0.405
0.689
20M53
0.527
-0.20
0.328
100059
0.483
+0008
0.439
+0.02
0,662
20.12
AAL
120
0.646
0.439
0.783
100.63
0. 1.308
0.660
0.410
20074
0.681
20045
-9.21
0.402
100059
+0.009
+0,094
0,680
100000
0.
16
0.6.36
0.431
0.783
0.322
0.656
0.413
0.682
20
0.570
-0.216
0.411
20.054
-0.00
-0. 102
0,679
20185
0.
DCA
100
0.666
0.491
0,869
10.002
0.452
0,655
0.387
0.650
0.696
20.00
0.452
10.3
0.472
+0.005
+0.104
0,662
220.06
Schaefer
100
0.628
0.474
0.879
00,02
0.469
0.643
0.451
0.643
20054
0.682
-0217
0.455
0.120
0.530
0.078
00,998
20007
Brodmann
0.659
0.456
20066
0,727
=0,058
0,315
0.609
0,410
2007
0,729
2004
0.424
202206
0.413
#0093
0.490
+0075
0,442
+0009
0.620
20113
41
17
0.620
10.06
0.433
1.0072
0,796
1-0052
0.373
+40.11
0.589
0.367
0.677
140008
0.230
100.006
0.386
1:0077
0.454
+00072
0.418
+-0.044
0,608
1:0000
Yeo
0.547
10.077
0.415
10.032
0.686
100042
0,237
0.598
0.363
0.696
0.069
0,260
1:0.047
+-0.440
+-0.80
0,560
20.1% 11
Adas
Cognitive task (24-way)
Age group classificatiion
Crystallized intelligence
Cognitive lask (7-way)
Gender classification
General intelligence
Fluid intelligence
Autism diagnosis
Autism cross- cross-site site
AD diagnosis
Fingerprinting
FC stability
Task
31

---

A.8 Effect of parcel number on downstream tasks
To examine whether downstream tasks prefer specific spatial resolutions, we varied the number of parcels for both DCA (41, 100, 200, 360, 400, 500) and Schaefer (100, 200, 300, 400, 500) atlases. For each resolution, we performed subject-level poos-validation and report accuracies in Tables Across both atlas families, three consistent patterns emerge:
and 14
Peak-shaped rrssolution-optiaal tasks. Cognitive decoding shows clear "rise-then- fall" profile: performance increases from coarse to intermediate resolutions and declines when parcels become excessively fine (c.g., DCA peaks around 200-360 parcels; Schaefer peaks typically at 300-400 for 7-way decoding), indicating optimal meso-scale. Intuitively, coarse parcellations underfit task-relevant heterogeneity, whereas wer-fragmentation re- duces SNR per parcel, inflates inter- inter-parcel edges, and amplifies misalignment across subjects, all which hurt generalization.
tasks. Several clinical endpoints (e.g., AD diagnosis) exhibit weak or no monotonic trend across resolutions for both DCA and Schaefer. These tasks likely rely on subcortical or global signals that cortex-only atlases do not explicitly model, so varying cortical granularity alone has limited effect. In such settings, choosing resolution can be or downstream interpretability rather than accuracy.
desolution-insensiie
guided by computational
Size-driven tasks. Metrics whose value is mechanically affected by parcel size show systematic behavior: FC stability decreases beyond intermediate resolutions (consistent with lower within- within-parce parcel SNR and shorter time series per parcel), whereas subject fingerprinting improves with finer parcellations (more idiosyncratic, high high-dimensional FC signatures), with the tendencies observed for both atlas families.
Table 13: Downstream task performance across atlas resolutions for DCA
DCA 41
DCA 100
DCA 200
DCA 360
DCA 400
DCA 500
Gender classification f
0.651
0.666
0.687
0.710
0.707
0.702
Fluid intelligence
0.429
0.491
0.497
0,535
0.543
0.537
Cognitive task (7-way) f
0.842
0.869
0.900
0.887
0.882
0.895
Cognitive task (24-way)
0.426
0.452
0.479
0.469
0.465
0,459
Autism diagnosis
0.633
0.655
0.663
0.680
0.665
0.661
AD diagnosis f
0,443
0.387
0.456
0,448
0,447
0.459
FC stability
0.642
0.650
0.644
0.615
0.609
0.603
Fingerprinting f
0.435
0.696
0.776
0.852
0.811
0.884
Age group classification f
0,408
0,452
0.473
0,433
0.512
0,475
Crystallized intelligence f
0.521
0.472
0.505
0.516
0.523
0.515
General intelligence t
0.439
0.442
0.461
0.446
0.448
0.459
Autism cross-site
0.636
0.662
0.635
0.696
0.696
0.638
Table 14: Downstream task performance across atlas resolutions for Schaefer
Schaefer 100
Schaefer 200
Schaefer 300
Schacfer 400
Schaefer 500
Gender classification
0.628
0.668
0.670
0.726
0,694
Fluid intelligence
0.474
0.505
0.517
0.527
0.565
Cognitive lask (7-way)
0.879
0.885
0.888
0.893
0.876
Cognitive task (24-way) f
0.469
0.459
0.469
0.462
0.456
Autism diagnosis
0.643
0.660
0.668
0,653
AD diagmosis T
0.451
0.418
0.485
0.444
0,440
FC stability 1
0.643
0,635
0.620
0.609
0.598
Fingerprinting t
0.682
0.796
0.856
0.875
0.886
Age group classification f
0.455
0.478
0.480
0.497
0.477
Crystallized intelligence
0.530
0.526
0.497
0.525
0.516
General intelligence
0.469
0.467
0.463
0.458
0.428
Autism cross-site 1
0.640
0.662
0.667
0.640
0.638
Taken together, there is no universally optimal parcel count. Intermediate resolutions (roughly 200-400 parcels) often strike favorable trade-off for cortex-driven cognitive decoding, whereas
32

---

resolution-insensitin clinical tasks are robust across scales, and size-driven metrics move predictably with parcel granularity. These findings are consistent across DCA and Schaefer (Tables [3] [4] and provide practical guidance for selecting atlas resolution by task type rather than adopting a single fixed setting.
A.9 Main task ablation
A.9.1 Regularization and reconstruction loss
We investigated whether incorporating an orthogonality regularizer or a reconstruction loss would further improve parcellation quality (Table [5).. Applying these augmented objectives the same 100 subjects used in our main experiments yielded no statistically significant gains in homogeneity or silhouette coefficient for 100 parcels, indicating that the core KL-based clustering loss sufficient to drive optimal voxel-level atlas generation.
The orthogonality regularizer is defined on the centroid matrix D E R xxd (with unit-norm rows) follows. Let
orthogonal loss
G = DD T
(E KxX)
be the Gram matrix of pairwise inner products. We zero out the diagonal to isolate off aff-diagonal similarities:
G = G Ix-
The orthogonality loss then penalizes the mean absolute off off-diagonal entry via
R. (D)
Σ (Ga))
V K(KK- - (
Minimizing R encourages the rows of D to remain mutually orthogonal.
masked reconstructed loss
We only consider the reconstruction of non-background voxels.
Ri=l -m;) (f. xx)²
if EN (1 m:) > 0,
Lmasked MSE
N ΣE m;)
0,
otherwise,
where è and x; are the predicted and target values at voxel i, respectively, and m, E {0, 1] is the binary mask indicating background (m, 1) or foreground (m, 0).
Table 15: Ablation study on orthogonality and masked reconstruction loss components.
Loss
Homogeneity
Silhouette
KL
Orthogonality
Reconstruction
0.100211.0214 0.0890=0.0091 0.10041:0.0215
0.030110.0066
0.0267+0.0045
0.030410.0067
A.9.2 Clustering different smoothing level
To improve signal quality and spatial coherence, we applied spatial smoothing using AFNI's BdBlurToFWHM [31], targeting 3 mm full width at half maximum (FWHM). The preprocessed volumetrie images were resampled to mm isotropic resolution. This follows the common practice of setting the smoothing kernel to approximately 1.5 times the image resolution. For comparison, we also present results under two additional conditions: no smoothing and mm FWHM smoothing. And there is significant difference (Table I6).
33

---

Table 16: Evaluation of similarity metrics across smoothing levels and parcel resolutions.
Raw
200
500
800
Metrics
0.1004
0.1127
0.1266
0.1363
0.1535
Homogeneity T
+ 0.0216
0.0225
0.0229
+ 0.0228
0.0226
0.0305
0.0422
0.0554
0.0647
0.0883
Silhouette ?
+ 0.0068
0.0094
0,0085
= 0.0090
0.0114
FWHM 3mm
100
200
360
500
800
Metries
0.1004
0.1127
0.1266
0.1364
0.1536
Homogeneity f
0.0216
+. 0.0225
0.0230
0.0229
0.0227
0.0304
0.0417
0.0545
0.0644
0.0866
Silhouctte f
+ 0.00668
+ 0.0078
1. 0.0080
+ 0.0086
1: 0.0114
FWHM 6mm
100
200
360
500
800
Metrics
0.1005
0.1128
0.1267
0.1364
0.1536
Homogeneity 1
0.0217
1: 0.0225
0.0229
1. 0.0229
1. 0.0227
0.0306
0.0419
0.0546
0.0642
0.0868
Silhouette f
+ 0.0069
+ 0.0078
+ 0.0081
+ 0.0083
+ 0.0102
A.9.3 Choice of graph cut method
In addition to spectral clustering, we evaluated several graph-cut algorithms (Fig. and Table 17p. However, most failed to guarantee that each resulting parcel forms a single connected subgraph, leading fragmented regions. Here, weighted UFF-connectter clustering algorithm begins by converting the input edge list and weights into undirected adjacency list, then randomly seeds initial clusters by assigning to each cluster. Each cluster maintains a max-heap of its unassigned neighboring nodes, prioritized by edge weight. Clusters then grow in parallel: each step, cluster pops the nighest-weght neighbor from its heap, claims that node (if unassigned), and pushes all of its unassigned neighbors onto the heap. To enforce roughly equal cluster sizes, each cluster stops growing once it reaches [N/k]] If any nodes remain unassigned after this frontier-driven expansion, they are absorbed into the smallest adjacent cluster. By always selecting the strongest edges first and only adding connected nodes, this method produces contiguous clusters that respect the underlying graph's 's weighted connectivity. Table 17: Evaluation of similarity metrics across graph methods and parcel resolutions.
breadth-firt first search (BFS) based algorithm. The
unique node
graph
100
200
360
500
800
Metrics
0.1004
0.1127
0.1266
0.1364
0.1536
Homogeneity ?
0.0216
+ 0.0225
0.0230
0.02229
+
0.0304
0.0417
0.0545
0.0644
0.0866
Silhouette
0.0068
+ 0.0078
+ 0.0080
0.0086
+ 0.0114
100
200
360
500
800
Metrics
0.0930
0.1026
0.1134
0.1210
0.1341
Homogeneity f
0.0204
+ 0.0220
+ 0.0215
+ 0.0219
+ 0.0222
0.0223
0,0308
0.0407
0.0479
0.0607
Silhouette
0.0052
+: 0.0061
0.0065
0.0069
+ 0.0072
A.9.4 Choice gray matter mask
In the main text, the corresponding ROT masks are extracted from FreeSurfer's aparc+aeeg.mp..
48
Here, we show the result (Table 18) by defining the ROI with the same mask to MMP Iand Schaefer
34

---

Homogeneity
0.10
1
200
300
600
Silhouette coefficient
0.100
0.075
0.025
6.000
300
600
Yea7
Yeo17
Brodmann
AALI
AAL2
Schaefer
Figure 10: Homogeneity and Silhouette coefficients for weighted BFS crn-econeetedd clustering and baselines, measured over 100 HCP subjects varying numbers of parcels.
et al 12] DCA still shows higher homogeneity and silhouette coefficients compared to corresponding atlas.
Table 18: Evaluation of Similarity Metrics on Schaefer, DCA, MMP, and DCA360 with Gray Matter Masks
Schacfer100
DCA100
MMP
DCA360
Homogeneity Silhouette
0.088510.0212 0.0091
0.001410.0216 0.03041000068
0.1212:10.021 0.0470=000006
0.1266=0.0230
0.054510.0080
A.9.5 Number neighbours
We adopt the standard 26 36-neigbbourhood in 3-D, which encompasses all voxels in 3 x 3 x 3 cube (excluding the centre) and thus captures both face- and diagonal interactions. To gauge its impact, we evaluated two reduced neighbourhoods- K 6 (face-connected voxels only) and K 18 (face edge axelss-alongsidee the full 26 setting. Table 19 shows that K and = 26 yield nearly indistinguishable performance > 0.05, -/U-test), whereas K = 18 produces
noticeably lower silhouette score (p < 0.05 ). Overall, the full 26-neighbourhood provides stable and competitive results.
Table 19: Ablation neighbourhood size.
K
Homogeneity t
Silhouette
6
0.1005+0.0016
0.0313+:00 0.0071
18
0.0010
0.0215+ 0.0068
26
0.1004+0.00155
0.030410.0067
35

---

A.9.6 Distribution-baser loss
We compared three common divergence objectives-Wasseestteee distance, Jensen- Sensen-Shannon diver- gence, and the KL. divergence used in the main paper. r0 virtually identical performance across all choices, with variations well within one standard deviation (p > 0.05 ). This suggests that the framework is largely insensitive to the specific distribution-matte matttiinnn-taiinn loss employed during clustering refinement.
Table 20: Reliability across distribution--ased loss functions.
Loss
Homogeneity
Silhouette 1
Wasserstein
0.1003 + 0.0215
(0306++00000
IS divergence
0.0308++0.000 0.021
KL divergence (used)
0.1004
0.0304+0.006
A.9.7 Centroid initialisation
Finally, we evaluated four initialisation schemes for the clustering centroids: random, random+norm (unit-normalised centroids), xavier+norm, and orthogonal+nore norm. As shown Table 21 orthogo-
nal+norm markedly lowers the first-epoch loss, indicating faster early convergence, yet all methods converge to nearly identical homogeneity and silhouette scores training completes (p 0.05 )
Table 21: Impact of centroid initialisation.
Initialisation
Ist-epoch loss +
Homogeneity 1
Silhouette
random
6.5578
0.1010
0.0312++0.000
random+norm
0.0150
0.1004
0.0307
xavier+norm
0.0207
0.1004++00025
0.0307+000067
orthogonal+norm
0.0022
0.1004
0.030410.0068
36

---

We systematically examined how three key hyperparameters in group Proup-level level atlas generation- voxel reliability threshold o, template distinctiveness threshold 8, and voxel inclusion threshold 7- afffect downstream task performance. The following four tables report performance across 12 tasks using atlases of innrressin resolution (100 to 500 pareels), under various parameter settings.
0.651
0.868- 0.002
0.43510 0.30
0.612: 00:0000030
0.48 10-01111000 10S
0.659 H0,06
0,092-0-211 211
0,437:10.08 0.00%
0,510--0. 108
0,460-200.088 0.004
0.637 102
0.677:100.08
0.493 105
0005 0.886-20.000 0..00055
0.461=00000 030
0.619110.033 10.081
1-450--0.008
0.652100000 0.33
0,768110 188
0.415100090
0.464--0.006
-0.000
0.421-40112 120
0.657-10.00 060
0.9
0.510
0.9
Table 22: Effect of group atlas generation parameters on performance (100 regions). Values are shown as mean d: standard deviation.
0
0.519-00,006
0.873-0055
0.55120018
0.17:000
10:0000
0-47711000)
0669 0,00
0:24::07099
0.516 100
0,452:10099
0,22110076
Table 23: Effect of group atlas generation parameters on performance (200 regions), Values are shown as mean + standard deviation.
0.678:10.00
0,896-10.00S
0-463-10053
0.646110006
0.432 10058
0.6511004
0.731 19.199
0.450100004
0.474:10.075
0.435+0.141
0.648:10.09 0.009
0.3
0.8
0--47
0.3
0.8
0.491
0.7
0.637
0.528 0,090)
0.363
0.36200019
06N
2007
0,22 102280008
06599
2004
0.80
0337200888
0,494 #0.00
0.459=0.091
0.61220.777
0.7
0.698 0.698:0.00
=0.000002
#0.091
0.8%6
0.472
0.61220066
1:41750.00
0655
0.70 189
0.41220.07
0.366
0.441=0.13
0.634 089
0,3
0.3
0.626 0.626:20.006
0.496 102
0.882
0:44620.0000
0.667-10.021
10.021
0.47
0.648
0.698
0.423 101
0.515++.009
0.452-0.074
0.65810.088
0.692:0.085
+0.092
0.861
0.463
0.661
0.429 40:144
0.639 1014
0.702 181
0.13620108
0.522
0.45710.055
0.645:0.073
0.9
0.9
0.627
n.475-0.094
0.877==0.050
0.457=0.031
0.668:20004
0.443-00007
0.649::0.45
0.690
0.412:0.108
0.507
0.448-00.06
0.662:20.085
0.686:=0.055
0.539 -..06-00003
0.878=00.046
0.473=00:228
0.6472000448
0.426--0132
0.640=00.44
0.759-10.88 10.12
0.422-0.085
5522:400994
0.57--0.080
0.657-0.100 108
0.2
0.8
0.2
0.8
0.542
0.640::0.00
0.473 -4.3
0.877100000
0,45810.025
0.6521000
0,428
0.699-00005
0,704
0.40%1-0102
0.503
0.4431-0.08)
0.637200084
0.6921-0.06
1.5.91-0.099
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A.10 Group atlas generation analysis
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Cognitive lask (7 (-wa))
Cognitive took (24 wmyy
Age group classification
Crystallized mecligennc
Cognitive tusk (7-way)
Cognitive lisk )
Age group classiiictioon
Crystallized inteligenne
Gender classification
Genneall intellignnce
Gender classification
Guneral intelligence
Huild inselligence
intss llognosis
Autism cross---- site
Fluid incllignne
Autismn diognosis
AD diagnosis
PC slabilty
Fingerprining
AD diagnosis
stubiiity
Fingeprrminng
Autism
37

---

1.691--00008
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Our results reveal several trends. When the number of parcels is small (e.g., 100), using a = 0.2 yields better performance, while a = 0.3 becomes more advantageous as the resolution increases, possibly because finer parcellations require more voxels capture individual variability- even if some voxels are less reliable. For B. a lower threshold (8 = 0.2) tends to offer a marginal performance benefit, possibly due to increased distinctiveness between parcels. Although ? = 0.7 yiclds slightly better performance overall, we choose y = 0.8 for group-leved atlas generation to match the voxel coverage of MMP 8] and ensure
0.699
Table 24: Effect of group atlas generation parameters on performance (360 regions). Values are shown as mean +: standard deviation.
002-10004
0.555:1000
0.896:00000
0.611:004
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0 500--00086
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Table 25: Effect of group atlas generation parameters on performance (500 regions). Values are shown as mean + standard deviation.
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comparability. Consequently, our final group atlas is generated using hypeparameters a = 0.2, 3 = 0.2, and y = 0.8.
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175
0.7
Cognitive (24-w0yy)
Age group classification
Crystallized intellience
Cognitive task (24- way)
Age group acaitiation
Crystalliedd melligence
Cognitive task (7-k7wawy)) (7-way)
Cognitive tosk (7-way)
Gender classfication
General imelligence
Gender classification
General imelligence
Fluid inselligence
Autism diagnoss
Autism cross- site
Fluid inseligence
Autisam diugnosss
FC stavility diagnosis
Fingerprincing rining
AD diagnosis
Fingerprinting
Autism cross-site
FC stubdliyy
38

---

A.11 Spatiotemporal masking strategy
To ensure that masked regions form contiguous blocks in the high- high-resolution volume, we first spatially downsample the original 96 x 96 x 96 grid by factor of 16 along each axis, yielding a coarse 6 x 6 6 volume (time dimension unchanged). We then sample two independent binary masks on this downsampled grid: a spatial mask with fraction of voxels ser to zero, and temporal mask with fraction 24 of frames set zero. We choose 7s and Iy so that the overall masking ratio satisfies
xx) σx)
(10)
where is the desired fraction of masked spatiotemporal volume (e.g. 0.8 for 80% masking (57) Finally, we upsample these binary masks back to the original resolution by expanding each down- sampled voxel mask to 16 block in space and each temporal mask entry to the corresponding contiguous frames. Applying the resulting mask to the full full-resolution data yields large, continuous spatiotemporal occlusions, encouraging the encoder to reconstruct missing patches using both local and long-range context.
Spatial mask rate X,
t=
t=1
t=
= n
Spatial mask rate X
fMRI
masked
Illustration of the spatiotemporal masking scheme. We first select fixed subset comprising 3g of spatial voxels and mask them to zero across all time steps; additionally, we mask all voxels at fraction 2, of temporal frames to zero.
Figure 11:
A.12 Train and validation loss
We select the encoder checkpoint at epoch and visualize the training losses, whose trajectories closely match those of other volumetric methods (58
Training & Validation
024
Validation Loss
922
1053
336
Epoch
Figure 12: Training losses. We use the epoch-8 encoder checkpoint.
39

---

A.13
Data organization
There are two parts our repository, DCA and ATlaScore. Please follow /ettps//githin com/ ncclab- sustech/Dooa for details.
A.13.1 DCA
The codes for pretraining and personalized clustering. One example subject provided. DCA/
data/
fmri/
mask/
sub_test. txt
data_prrppaatton.ipp ipynb
results/
demo/
calation_frril py
main.py
utils.pp
swin_ wwwur.eerr. py
A.13.2 AtlaScore
The codes for evaluating atlases. The volumetric Homogeneity and Silhouette evaluations, well as the surface-based DCBC evaluation, are provided. All 12 downstream tasks are implemented in downstream/ with FC features for DCA100 provided an example.
AtlaScore/
similarity/
compute_ady _aj -py
eva.py
eva_DCBC. py
downstream/
docs/
fc_data/
nii_data/
dosmstream.pp py
demo ipynb
40


Reviews:
[{"review_id": "VKFDjCb5cQ", "reviewer": "Reviewer_puq2", "summary": "The paper presents Deep Cluster Atlas (DCA), a graph-guided deep-embedding framework for generating individualized, voxel-level brain parcellations from resting-state fMRI. It begins by pre-training a Swin-UNETR auto-encoder on heavily masked 4-D fMRI blocks, producing rich spatiotemporal embeddings for every voxel. DCA then alternates among three steps---re-weighting graph edges via spectral clustering, updating K cluster centroids, and refining the embeddings---until it converges to generate parcels that are both spatially contiguous and functionally coherent. Tested on 1000 Human Connectome Project subjects and resolutions ranging from 100 to 800 parcels, DCA achieves about 74% higher homogeneity and 24% better silhouette scores than widely used atlases.", "questions": "See weaknesses.", "limitations": "Yes, the authors have adequately addressed the limitations and potential negative societal impact of their work.", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 4, "strengths_and_weaknesses": "## Strengths\n- The proposed method is explained in a clear and intuitive way, which facilitates the understanding. \n- The proposed method achieves about 74% higher homogeneity and 24% better silhouette scores, and the ablation study further demonstrates the effectiveness of each model component. \n- The problem of more individualized brain atlas construction is an important scientific question.  \n\n## Weaknesses\nThe full evaluation results on all 12 downstream tasks (as shown in Appendix Table 6) do not show consistent advantage of DCA against baseline methods. DCA 100 only outperforms 5 out of 12 tasks against the baselines, and DCA 400 only outperforms baselines on 2 out of 12 tasks. \n- This raises the question about whether DCA's gain in homogeneity and silhouette scores can be translated to practical performance improvement of downstream tasks. \n- The authors should clarify the criteria of how they decide which tasks are reported in the main paper to avoid the perception of cherrypicking the results. More detailed discussions on why the DCA have more advantages on certain tasks than others should also be included. \n- It is unclear what metrics the authors are reporting for the task performance in Fig. 4 and Table 6. Are these accuracy, F1 scores, or are they different from tasks to tasks? More details about the metrics should be added in Section 5 in the main paper.", "was_revised": true, "final_justification": "The authors rebuttal has sufficiently addressed 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.\n\nI think that the paper has reached the bar of NeurIPS acceptance, and the community would benefit from the ideas and approaches discussed in this paper.", "rebuttal": "> General response\n\nWe 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**).\n\nWe 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**).\n\n> DCA 400 performance\n\nWe 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.\n\nTo 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.\n\n**Table 1: Evaluation of similarity metrics across atlases**\n||MMP 360|DCA 360|Schaefer 400|DCA 400|\n|---|---|---|---|---|\n|Homogeneity ↑|0.0706±0.0208|0.1266±0.0229|0.0780±0.0222|**0.1294±0.0229**|\n|Silhouette ↑|0.0426±0.0059|0.0545±0.0080|0.0454±0.0066|**0.0572±0.0082**|\n\n**Table 2: Evaluation of downstream task performance across atlases**\n||MMP 360|DCA 360|Schaefer 400|DCA 400|\n|---|---|---|---|---|\n|Gender classification ↑|**0.740±0.065**|0.710±0.059|0.726±0.066|0.707±0.051|\n|Fluid intelligence ↑|0.513±0.087|0.535±0.084|0.527±0.089|**0.543±0.101**|\n|Cognitive task (7-way) ↑|0.859±0.063|0.887±0.042|**0.893±0.051**|0.882±0.048|\n|Cognitive task (24-way) ↑|0.427±0.018|**0.469±0.037**|0.462±0.031|0.465±0.035|\n|Autism diagnosis ↑|0.662±0.035|**0.680±0.044**|0.668±0.045|0.665±0.069|\n|AD diagnosis ↑|0.395±0.109|**0.448±0.131**|0.444±0.040|0.447±0.035|\n|FC stability ↑|0.612±0.044|**0.615±0.043**|0.609±0.045|0.609±0.044|\n|Fingerprinting ↑|0.863±0.150|0.852±0.164|**0.875±0.151**|0.811±0.210|\n|Age group classification ↑|**0.515±0.075**|0.433±0.079|0.497±0.104|0.512±0.086|\n|Crystallized intelligence ↑|**0.542±0.092**|0.516±0.117|0.525±0.101|0.523±0.113|\n|General intelligence ↑|0.417±0.099|0.446±0.085|**0.458±0.121**|0.448±0.104|\n|Autism cross-site ↑|0.655±0.092|**0.696±0.136**|0.640±0.110|**0.696±0.146**|\n\n> Weakness 1: Transferability of similarity metrics\n\nWe believe that the observed gains in homogeneity and silhouette scores likely translate into improved downstream performance. Below, we present supporting evidence.\n\nIn 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. \n\nTo 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.\n\n**Table 3: Classification results (low resolution)**\n||Age accuracy ↑|Age F1 (macro) ↑|Age F1 (weighted) ↑|Gender accuracy ↑|Gender F1 (macro) ↑|Gender F1 (weighted) ↑|\n|---|---|---|---|---|---|---|\n|Yeo 17|0.45|0.40|0.40|**0.65**|0.56|0.58|\n|Brodmann 41|**0.55**|0.41|0.53|**0.65**|**0.65**|**0.65**|\n|GIANT 50|**0.55**|**0.51**|0.54|0.60|0.56|0.57|\n|Watershed 100|0.50|0.36|0.47|**0.65**|0.56|0.58|\n|Schaefer 100|0.50|0.37|0.47|0.60|0.52|0.54|\n|**DCA 100 (group)**|**0.55**|**0.51**|**0.55**|**0.65**|0.60|0.62|\n|**DCA 100 (individual)**|**0.55**|0.41|0.50|**0.65**|0.64|**0.65**|\n\n**Table 4: Classification results (medium resolution)**\n||Age accuracy ↑|Age F1 (macro) ↑|Age F1 (weighted) ↑|Gender accuracy ↑|Gender F1 (macro) ↑|Gender F1 (weighted) ↑|\n|---|---|---|---|---|---|---|\n|Allen 141|0.40|0.33|0.41|0.65|0.65|0.65|\n|MUSE 149|0.50|0.44|0.44|0.55|0.54|0.55|\n|AAL 166|0.50|**0.45**|0.45|0.65|0.64|0.65|\n|Schaefer 200|0.50|0.38|0.48|0.65|0.56|0.58|\n|**DCA 200 (group)**|0.55|0.40|0.51|**0.70**|**0.67**|**0.68**|\n|**DCA 200 (individual)**|**0.60**|0.43|**0.55**|**0.70**|**0.67**|**0.68**|\n\n**Table 5: Classification results (high resolution)**\n||Age accuracy ↑|Age F1 (macro) ↑|Age F1 (weighted) ↑|Gender accuracy ↑|Gender F1 (macro) ↑|Gender F1 (weighted) ↑|\n|---|---|---|---|---|---|---|\n|MMP 360|0.55|0.50|0.55|**0.75**|**0.73**|**0.74**|\n|**DCA 360 (group)**|0.60|0.43|0.54|0.70|0.70|0.70|\n|**DCA 360 (individual)**|**0.70**|**0.51**|**0.65**|**0.75**|0.72|**0.74**|\n\n> Weakness 2: Task selection criteria\n\nWe 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.\n\n> Weakness 2: Task performance inconsistency\n\nDCA 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.\n\nFurthermore, 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.\n\n> Weakness 3: Evaluation metric clarity\n\nWe 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**).\n\n---\n\nReference:\n\n[1] A genetically informed brain atlas for enhancing brain imaging genomics. Nature Communications 2025.\n\n[2] The frontoparietal network: function, electrophysiology, and importance of individual precision mapping. Dialogues in Clinical Neuroscience 2018.\n\n[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.\n\n[4] Predictive models demonstrate age‐dependent association of subcortical volumes and cognitive measures. Human Brain Mapping 2023."}, {"review_id": "HOV9Jn3mR0", "reviewer": "Reviewer_o9NK", "summary": "This paper introduces Deep Cluster Atlas (DCA), a novel framework for generating individualized and group-level voxel-wise brain parcellations. DCA leverages a pretrained Swin-UNETR encoder combined with spatially regularized deep clustering to create high-resolution brain atlases that are both functionally coherent and anatomically contiguous. It overcomes limitations of traditional brain atlases, which are often fixed, group-level templates with limited flexibility. DCA allows flexible control over parcellation granularity and anatomical scope, and it outperforms existing methods in terms of homogeneity, silhouette coefficient, and performance on downstream tasks like autism diagnosis and cognitive decoding.", "questions": "1. Regarding the Voxel-level atlas evaluation platform, how is functional connectivity derived? Is it different from the standard method, which computes the Pearson correlation coefficient between average time series of different brain regions? \n2. In line 154, the cluster centroids are initialized with orthogonal rows and L2-normalized. What are the advantages of this initialization method? \n3. In line 160, for the KNN graph, why is the number of neighbors K fixed at 26? Is there a specific reason for choosing this value rather than others? \n4. Since the method relies on clustering, which can be sensitive to various factors, how can the stability of the generated atlas and FC connectivity be ensured?\n5. The impact of K on downstream task performance should be explored. Is there an optimal K for the best results, or does it vary across tasks?", "limitations": "1. Technically, this is a multi-objective clustering task, a common approach in clustering methods, so the technical novelty is not particularly significant.\n2. The proposed atlas is evaluated using only SVC. Comparing the results with other brain atlases using a variety of advanced models, especially graph-based deep learning methods, would provide a more robust validation of the atlas's performance.", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\n1. Innovative Framework. DCA introduces an advanced deep learning model for brain atlas construction, utilizing graph-guided deep clustering. This method combines functionally coherent brain regions with spatial continuity, which has been a challenge in previous methods.\n2. High Flexibility. The approach supports flexible control over parcellation granularity, allowing users to generate atlases tailored to their specific needs.\n3. Extensive Experiments. The paper presents extensive experiments demonstrating that DCA consistently outperforms state-of-the-art atlases (e.g., Yeo, Brodmann, Schaefer) across various metrics, including homogeneity, silhouette score, and performance on downstream tasks such as autism diagnosis and cognitive decoding.\n4. Comprehensive Evaluation. The authors develop a benchmarking platform to evaluate the quality of atlases, using both internal metrics (homogeneity, silhouette score) and external metrics based on downstream tasks.\n5. Well-Presented. The paper is well-organized and easy to understand. The presentation of the methodology and experimental results is clear, and the use of figures enhances the paper's readability.\n\nWeaknesses\n1. Modest Technical Innovation. The main contribution of the paper lies in designing individualized and group-level brain atlases with a focus on maintaining functionally coherent and anatomically contiguous regions. The paper also provides a platform for evaluating these atlases and presents extensive experimental validation. From a technical perspective, the approach essentially relies on a deep clustering model, using a pre-trained encoder with two clustering objectives: one based on prototypes and the other based on a graph, which correspond to the two goals of functionally coherent and anatomically contiguous regions, and aligns these clustering objectives. Technically, this is a multi-objective clustering and alignment task, which is a fairly common approach in clustering methods, and thus, the innovation in terms of technical novelty is not particularly significant.\n2. Unclear Technical Details. (1) In Figure 2(C), regarding the Voxel-level atlas evaluation platform, how is functional connectivity derived? Is it different from the standard method, which computes the Pearson correlation coefficient between average time series of different brain regions? This should be clarified. (2) In line 154, the cluster centroids are initialized with orthogonal rows and L2-normalized. What are the advantages of this initialization method? The rationale behind this choice needs further explanation. (3) In line 160, for the KNN graph, why is the number of neighbors K fixed at 26? Is there a specific reason for choosing this value rather than others? A more detailed explanation of this choice is needed.\n3. Not Sufficiently Convincing Evaluation. The paper primarily evaluates the proposed atlas using a single classification method (SVC) across all downstream tasks. However, to more comprehensively assess the performance, it would be beneficial to compare the results with other existing brain atlases using a variety of established models and algorithms, including more advanced techniques such as graph-based deep learning models and other state-of-the-art machine learning methods. This would provide a more robust validation of whether the proposed atlas consistently outperforms other atlases across different models and tasks.\n4. Method Stability. In the supplementary material, on page 11, Table 6 shows that the proposed method performs poorly on FC stability compared to other methods. Since the proposed method is based on clustering, which is often sensitive to various factors, the results might be unstable. How can the stability of the generated atlas and FC connectivity be guaranteed? Furthermore, in Table 6, the proposed method underperforms on several metrics compared to other atlases. The reasons for these results should be explained, and how the method can be made more stable should be clarified.\n5. Choice of Number of Parcels K. The paper mentions that different values of K provide different resolutions, but it would be interesting to explore how K influences downstream task performance. Is there an optimal K that yields the best experimental results, or is the impact of K on downstream tasks unstable? This needs further investigation.\n6. Computational and Storage Demands. The high computational and storage requirements of the method are mentioned, but the actual demands are not explicitly detailed in the paper. It would be helpful for readers if the practical computational cost of voxel-based methods, in terms of memory and execution time, were provided.\n7. On open access. The code has been released. However, in terms of data, more commonly used datasets should be provided with the generated atlas outputs, so that the community can conveniently conduct follow-up research.", "was_revised": true, "final_justification": "All my concerns have been addressed during the rebuttal. The authors have put considerable effort into addressing the raised concerns, both through additional experiments and thoughtful clarifications. I appreciate their thoroughness.", "rebuttal": "> General response\n\nWe 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.\n\n> Weakness 1: Technical innovation\n\nWe 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:\n\n(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**).\n\n(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.\n\n> Weakness 2: Functional connectivity method\n\nWe 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.\n\n> Weakness 2: Initialization method\n\nWe 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 ($p>0.05$).\n\n> Weakness 2: Number of neighbors\n\nWe 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**).\n\n> Weakness 3: Downstream evaluation\n\nWe 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.\n\nWe 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**).\n\n> Weakness 4: Method stability\n\nWe 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.\n\n1) 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.\n\n**Table 1: Intra- and inter-subject atlas similarity**\n||Dice ↑|IoU ↑|\n|---|---|---|\n|Inter-subject - null|0.497|0.349|\n|Inter-subject|**0.614**|**0.481**|\n|Intra-subject - null|0.506|0.358|\n|Intra-subject|**0.789**|**0.707**|\n\n2) 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**).\n\n3) 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.\n\n> Weakness 5: Choice of number of parcels\n\nWe 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:\n\n1) 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.\n\n2) 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.\n\n3) 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.\n\n**Table 2: Downstream task performance across atlas resolutions for DCA**\n||DCA 41|DCA 100|DCA 200|DCA 360|DCA 400|DCA 500|\n|---|---|---|---|---|---|---|\n|Gender classification ↑|0.651|0.666|0.687|**0.710**|0.707|0.702|\n|Fluid intelligence ↑|0.429|0.491|0.497|0.535|**0.543**|0.537|\n|Cognitive task (7-way) ↑|0.842|0.869|**0.900**|0.887|0.882|0.895|\n|Cognitive task (24-way) ↑|0.426|0.452|**0.479**|0.469|0.465|0.459|\n|Autism diagnosis ↑|0.633|0.655|0.663|**0.680**|0.665|0.661|\n|AD diagnosis ↑|0.443|0.387|0.456|0.448|0.447|**0.459**|\n|FC stability ↑|0.642|**0.650**|0.644|0.615|0.609|0.603|\n|Fingerprinting ↑|0.435|0.696|0.776|0.852|0.811|**0.884**|\n|Age group classification ↑|0.408|0.452|0.473|0.433|**0.512**|0.475|\n|Crystallized intelligence ↑|0.521|0.472|0.505|0.516|**0.523**|0.515|\n|General intelligence ↑|0.439|0.442|**0.461**|0.446|0.448|0.459|\n|Autism cross-site ↑|0.636|0.662|0.635|**0.696**|**0.696**|0.638|\n\n**Table 3: Downstream task performance across atlas resolutions for Schaefer**\n||Schaefer 100|Schaefer 200|Schaefer 300|Schaefer 400|Schaefer 500|\n|---|---|---|---|---|---|\n|Gender classification ↑|0.628|0.668|0.670|**0.726**|0.694|\n|Fluid intelligence ↑|0.474|0.505|0.517|0.527|**0.565**|\n|Cognitive task (7-way) ↑|0.879|0.885|0.888|**0.893**|0.876|\n|Cognitive task (24-way) ↑|**0.469**|0.459|**0.469**|0.462|0.456|\n|Autism diagnosis ↑|0.643|0.660|0.661|**0.668**|0.653|\n|AD diagnosis ↑|0.451|0.418|**0.485**|0.444|0.440|\n|FC stability ↑|**0.643**|0.635|0.620|0.609|0.598|\n|Fingerprinting ↑|0.682|0.796|0.856|0.875|**0.886**|\n|Age group classification ↑|0.455|0.478|0.480|**0.497**|0.477|\n|Crystallized intelligence ↑|**0.530**|0.526|0.497|0.525|0.516|\n|General intelligence ↑|**0.469**|0.467|0.463|0.458|0.428|\n|Autism cross-site ↑|0.640|0.662|**0.667**|0.640|0.638|\n\nTaken 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.\n\n> Weakness 6: Computational and storage demands\n\nOur 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.\n\nFor 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.\n\n> Weakness 7: Open access\n\nWe acknowledge this oversight. The group-level  DCA 100 atlas (HCP-based) is available at AtlaScore/downstream/docs/ as a **demo**. \n\nModel weights, individual-level atlases and other resolutions (from 100 to 1000) based on different datasets will be released upon acceptance.\n\n---\n\nReference:\n\n[1] A hierarchical atlas of the human cerebellum for functional precision mapping. Nature Communications 2024.\n\n[2] Benchmarking methods for mapping functional connectivity in the brain. Nature Methods 2025.\n\n[3] Provable Benefit of Orthogonal Initialization in Optimizing Deep Linear Networks. ICLR 2020.\n\n[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.\n\n[5] Predictive models demonstrate age‐dependent association of subcortical volumes and cognitive measures. Human Brain Mapping 2023.\n\n[6] SwiFT: Swin 4D fMRI Transformer. NeurIPS 2023."}, {"review_id": "5PGfMMxMKl", "reviewer": "Reviewer_uHxM", "summary": "This paper proposes Deep Cluster Atlas (DCA), a novel deep learning framework for generating individualized, voxel-wise brain atlases from resting-state fMRI data. Unlike traditional atlases that are predefined and group-level, DCA uses graph-guided deep embedding clustering to create functionally coherent and spatially contiguous brain parcellations with controllable resolution and anatomical coverage. The method supports both group-level and subject-specific atlas construction and generalizes across different brain regions.", "questions": "1. I noticed that the Related Work section includes several recent approaches on MRI-based brain atlas construction and brain segmentation published in the past two to three years. However, these methods are not included in the comparative experiments. Could the authors clarify whether this omission is due to the lack of publicly available implementations or other reasons?\n2. In addition to the KL divergence loss, it would be interesting to know whether the authors have experimented with other distribution-based loss functions, and how those choices might impact the model's performance.", "limitations": "Please see the weakness.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1. The paper identifies critical limitations of existing brain atlases: fixed resolution, group-level averaging, and lack of flexibility and individual specificity, convincingly argues for the need for individualized, voxel-level, and flexible parcellation methods that better reflect both functional and anatomical information.\n2. The proposed DCA framework has good flexibility and generalizability; the standardized benchmarking platform provides quantitative evidence of DCA's superiority over several state-of-the-art atlases across a range of tasks and spatial scales.\n3. The author provided the source code and corresponding results.\n\nWeakness:\n1. The comparative methods included in the main experiments are relatively outdated, lacking any recent approaches proposed after 2020, which may weaken the relevance and rigor of the evaluation.\n2. The figures in the main text suffer from low resolution (the appendix is good), and enhancing their clarity would significantly improve the readability and presentation quality of the paper.\n3. The ablation analysis in the main paper lacks depth, focusing solely on coarse-grained, modular ablations without exploring finer-grained factors that could provide deeper insights into the contribution of each component.", "was_revised": false, "final_justification": "", "rebuttal": "> General response\n\nWe 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**). \n\nWe 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**).\n\n> Weakness 1: Outdated comparative baselines\n\nThank 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.\n\nRecent 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`. \nSpecifically, 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.\n\n**Table 1: Evaluation of similarity metrics across atlases at low (≤ 100 parcels) and medium (> 100 parcels) resolution**\n||GIANT 50|Watershed 100|DCA 100|Allen 141|MUSE 149|DCA 200|\n|---|---|---|---|---|---|---|\n|Homogeneity ↑|0.0148±0.0073|0.0143±0.0070|**0.1004±0.0216**|0.0230±0.0106|0.0208±0.0080|**0.1127±0.0225**|\n|Silhouette ↑|0.0079±0.0023|0.0078±0.0020|**0.0304±0.0068**|0.0164±0.0055|0.0149±0.0035|**0.0417±0.0078**|\n\n**Table 2: Evaluation of downstream task performance across atlases at low (≤ 100 parcels) and medium (> 100 parcels) resolution**\n||GIANT 50|Watershed 100|DCA 100|Allen 141|MUSE 149|DCA 200|\n|---|---|---|---|---|---|---|\n|Gender classification ↑|0.654±0.073|0.646±0.052|**0.666±0.080**|0.645±0.109|0.681±0.041|**0.687±0.073**|\n|Fluid intelligence ↑|0.384±0.098|0.425±0.053|**0.491±0.082**|0.434±0.095|0.456±0.071|**0.497±0.074**|\n|Cognitive task (7-way) ↑|0.670±0.065|0.383±0.050|**0.869±0.062**|0.622±0.053|0.749±0.038|**0.900±0.044**|\n|Cognitive task (24-way) ↑|0.266±0.024|0.104±0.013|**0.452±0.030**|0.171±0.018|0.261±0.030|**0.479±0.031**|\n|Autism diagnosis ↑|0.610±0.038|0.561±0.046|**0.655±0.054**|0.646±0.062|0.636±0.057|**0.663±0.040**|\n|AD diagnosis ↑|**0.459±0.064**|0.403±0.083|0.387±0.077|**0.467±0.090**|0.425±0.085|0.456±0.107|\n|FC stability ↑|**0.733±0.048**|0.731±0.053|0.650±0.045|0.664±0.066|**0.684±0.058**|0.644±0.043|\n|Fingerprinting ↑|0.358±0.205|0.347±0.216|**0.696±0.201**|0.493±0.248|0.539±0.256|**0.776±0.172**|\n|Age group classification ↑|0.343±0.047|0.349±0.058|**0.452±0.136**|0.394±0.072|0.353±0.051|**0.473±0.048**|\n|Crystallized intelligence ↑|0.462±0.089|0.447±0.076|**0.472±0.095**|0.488±0.046|**0.505±0.069**|**0.505±0.082**|\n|General intelligence ↑|0.381±0.091|0.406±0.082|**0.442±0.104**|0.375±0.050|**0.465±0.116**|0.461±0.108|\n|Autism cross-site ↑|0.611±0.066|0.568±0.114|**0.662±0.068**|0.595±0.166|0.609±0.107|**0.635±0.091**|\n\n> Weakness 2: Low-resolution figures in main text\n\nThank you for pointing this out. We will improve the resolution of the figures in the main text to enhance clarity and overall presentation quality.\n\n> Weakness 3: Coarse ablation and Loss analysis\n\nDue 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.\n\n1. Model architecture – removing key components degrades performance and breaks spatial continuity (**Appendix 6.1**);\n\n2. Regularization options and SimMIM loss – adding these has a negligible impact on final metrics (**Appendix 6.2**);\n\n3. Pretraining data preprocessing – different preprocessing strategies do not affect model performance (**Appendix 6.3**);\n\n4. Data smoothing – all smoothed variants evaluated with DCA outperform baseline atlases (**Appendix 5.1**);\n\n5. Graph segmentation methods – spectral clustering consistently outperforms alternative approaches (**Appendix 6.4**);\n\n6. Tissue segmentation templates – results remain superior to baselines regardless of template choice (**Appendix 6.5**);\n\n7. Hyperparameters for group-level atlas generation – Impact of different hyperparameters on downstream tasks (**Appendix 7**).\n\nAnd following the reviewers’ suggestions, we have now included additional ablation studies to further validate our design choices.\n\n**(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.\n\nAs 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.\n\n**Table 3: Ablation study on neighborhood size selection**\n||Homogeneity ↑|Silhouette ↑|\n|---|---|---|\n|6|0.1005±0.0216|0.0313±0.0071|\n|18|0.1005±0.0310|0.0215±0.0068|\n|26|0.1004±0.0215|0.0304±0.0067|\n\n**(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.\n\n**Table 4: Reliability on distribution-based loss functions**\n||Homogeneity ↑|Silhouette ↑|\n|---|---|---|\n|Wasserstein Loss|0.1003±0.0215|0.0306±0.0069|\n|JS Divergence|0.1005±0.0216|0.0308±0.0069|\n|KL Divergence (used)|0.1004±0.0216|0.0304±0.0068|\n\n**(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).\n\n**Table 5: Comparisons on different initialization methods**\n||First epoch loss ↓|Homogeneity ↑|Silhouette ↑|\n|---|---|---|---|\n|random|6.5578±0.0774|0.1010±0.0218|0.0312±0.0070|\n|random+norm|4.6205±0.0151|0.1004±0.0215|0.0307±0.0068|\n|xavier+norm|4.6185±0.0207|0.1004±0.0215|0.0307±0.0067|\n|orthogonal+norm (used)|**4.6062±0.0027**|0.1004±0.0216|0.0304±0.0068|\n\n---\n\nReference:\n\n[1] A hierarchical Bayesian brain parcellation framework for fusion of functional imaging datasets. Imaging Neuroscience 2025.\n\n[2] A hierarchical atlas of the human cerebellum for functional precision mapping. Nature Communications 2024.\n\n[3] A genetically informed brain atlas for enhancing brain imaging genomics. Nature Communications 2025."}, {"review_id": "MceSSYj7Xw", "reviewer": "Reviewer_zwAk", "summary": "The paper suggests a method to derive personalized atlases for fMRI by learning the clustering jointly with finetuning the pretrained SWIN encoder backbone. Inspired by deep embedding clustering, clustering is learn by matching the learnt cluster centers with the results of spectral clustering of a 26-nearest neighbour graph derived from SWIN embedding outputs, where the adjacency is constructed with the cosine similarity between output embeddings.\nTo evaluate the atlases the paper uses homogeneity (averaged within parcel voxels correlation averaged across parcels later), silhouette score, and downstream tasks (eg age classification) performance.", "questions": "* Is there a conceptual reason not to replace Swin Transformer with Hiera [1] backbone, which is also hierarchical and is supposed to be simpler and better performing?\n* In why in plot 3b there are no points for DCA below 100 to compare, for example to compare with Yeo 7 and Yeo 17 ?\n* Do you have an explanation why homogeneity and silhouette score values are so low in general? How do you interpret it?\n* Сould you provide the comparison of your predicted atlases with Schaefer et al [3] using intersection over union or similar metrics. It might be helpful to see how actually different are the atlases in terms of space and be more interpretable than homogeneity or silhouette score, especially for the people not familiar with the fMRI data. Are there any fully human labeled datasets for the atlases? Would [2] be helpful?\n* In [3] they used metric close to homogeneity but also with accounting for the parcel size (see equation (2) from [3]). Why have you decided not to account for the parcel size here? Could we add the comparison between atlases using metric from [3]?\n* In appendix Fig 4 and Table 5 - What is your explanation that DCA is worse with the DCBC metric than the other methods?\n\n\nMinor\n* In lines 129-130 you write *\"In parallel, we build a 26-nearest-neighbour graph over the ROI masked voxels, weighting edges by pairwise embedding correlations. \"*. Why 26? How sensitive is the network for the change of $k$ here (eg 20 instead of 26)? Does it come from some biological motivation or some previous research? \n* In equation 2 (lines 163-164) you truncate the cosine similarity at 0. One could just keep $k$ edges with biggest absolute values. If its because inside the single region of interest everything should be only positively correlated, it might be worth adding an explicit explanation.\n\n[1] Ryali, C., Hu, Y. T., Bolya, D., Wei, C., Fan, H., Huang, P. Y., ... & Feichtenhofer, C. (2023, July). Hiera: A hierarchical vision transformer without the bells-and-whistles. In International conference on machine learning (pp. 29441-29454). PMLR.  \n[2] Hermosillo, R. J., Moore, L. A., Feczko, E., Miranda-Domínguez, Ó., Pines, A., Dworetsky, A., ... & Fair, D. A. (2024). A precision functional atlas of personalized network topography and probabilities. Nature neuroscience, 27(5), 1000-1013.  \n[3] Schaefer, A., Kong, R., Gordon, E. M., Laumann, T. O., Zuo, X. N., Holmes, A. J., ... & Yeo, B. T. (2018). Local-global parcellation of the human cerebral cortex from intrinsic functional connectivity MRI. Cerebral cortex, 28(9), 3095-3114.", "limitations": "yes, though I would add a sentence that the number of parcels are hard fixed right now and the model does not have a capability to adjust it now", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths\n* DCA shows an improvement on homogeneity and silhouette score compared to the common atlases\n* Adopting silhouette score for using correlations as a distance function is a neat idea as its not vulnerable for the arbitrary shapes of curse of dimensionality problems this way\n* Paper provides the code and the plots contain error bars\n\nWeaknesses\n* DEC implies a specified number of clusters $k$ as input for the model, however, a discussion on what happens if $k$ is defined incorrectly is missing. [1-2] could be helpful for this. (varying $k$ could be interesting, especially if *\"discover novel parcellations\"*, lines 102-103, is the goal). \n* The metric performance (homogeneity and silhouette score) seems to be poor for all of the methods, including the proposed DCA. \n* Some crucial design choices (eg number of neighbours for the kNN graph for spectral clustering) are not explained and their impact is not experimentally explored\n\n[1] Leiber, C., Strauß, N., Schubert, M., & Seidl, T. (2024). Dying Clusters Is All You Need--Deep Clustering With an Unknown Number of Clusters. arXiv preprint arXiv:2410.09491.   \n[2] Ronen, M., Finder, S. E., & Freifeld, O. (2022). Deepdpm: Deep clustering with an unknown number of clusters. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (pp. 9861-9870).", "was_revised": true, "final_justification": "The authors have addressed my concerns during the review period, hence, I updated the score towards more positive", "rebuttal": "> General response\n\nWe 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**). \n\nWe 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**).\n\n> Q1: Choice of Swin-UNETR\n\nWe 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**).\n\nWe 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.\n\n**Table 1: Backbone comparison: Classification for age and gender**\n||Age accuracy ↑|Age F1 (macro) ↑|Gender accuracy ↑|Gender F1 (macro) ↑|\n|---|---|---|---|---|\n|Brain-JEPA [1]|0.419|0.151|0.663|0.657|\n|BrainLM [2]|0.373|0.179|0.528|0.485|\n|**Swin-UNETR**|**0.445**|**0.373**|**0.816**|**0.813**|\n\n> Q2: DCA 7/17/41 performance\n\nIn 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**).\n\nDCA 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.\n\n**Table 2: Evaluation of similarity metrics across atlases**\n||Yeo 7|DCA 7|Yeo 17|DCA 17|Brodmann 41|DCA 41|\n|---|---|---|---|---|---|---|\n|Homogeneity ↑|0.0329±0.0174|0.0764±0.0186|0.0392±0.0186|0.0819±0.0193|0.0251±0.0120|**0.0892±0.0203**|\n|Silhouette ↑|0.0193±0.0062|0.0081±0.0038|**0.0228±0.0066**|0.0139±0.0045|0.0128±0.0037|0.0198±0.0053|\n\n**Table 3: Evaluation of downstream task performance across atlases**\n||Yeo 7|DCA 7|Yeo 17|DCA 17|Brodmann 41|DCA 41|\n|---|---|---|---|---|---|---|\n|Gender classification ↑|0.547±0.077|0.619±0.052|0.620±0.063|**0.666±0.040**|0.659±0.078|0.651±0.045|\n|Fluid intelligence ↑|0.415±0.032|0.318±0.080|0.433±0.072|0.355±0.095|**0.456±0.046**|0.429±0.070|\n|Cognitive task (7-way) ↑|0.686±0.042|0.551±0.053|0.796±0.052|0.734±0.041|0.727±0.058|**0.842±0.060**|\n|Cognitive task (24-way) ↑|0.237±0.022|0.176±0.021|0.373±0.019|0.321±0.031|0.315±0.026|**0.426±0.046**|\n|Autism diagnosis ↑|0.598±0.030|0.617±0.051|0.589±0.071|0.617±0.040|0.609±0.055|**0.633±0.041**|\n|AD diagnosis ↑|0.363±0.081|0.371±0.087|0.367±0.089|**0.443±0.096**|0.410±0.079|**0.443±0.081**|\n|FC stability ↑|0.696±0.085|0.631±0.104|0.677±0.068|0.696±0.054|**0.729±0.044**|0.642±0.052|\n|Fingerprinting ↑|0.069±0.083|0.134±0.129|0.230±0.166|0.218±0.149|0.424±0.206|**0.435±0.220**|\n|Age group classification ↑|0.260±0.047|0.284±0.049|0.386±0.077|0.363±0.069|**0.413±0.093**|0.408±0.101|\n|Crystallized intelligence ↑|0.376±0.040|0.431±0.069|0.454±0.072|0.428±0.068|0.490±0.075|**0.521±0.069**|\n|General intelligence ↑|0.396±0.080|0.350±0.068|0.418±0.064|0.407±0.071|**0.442±0.079**|0.439±0.070|\n|Autism cross-site ↑|0.560±0.118|0.600±0.076|0.608±0.069|0.617±0.095|0.620±0.113|**0.636±0.083**|\n\n> Q3: Homogeneity and silhouette performance interpretation\n\nWe 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**).\n\n> Q4: Comparison with Schaefer atlases\n\nTo 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.\n\nWhile 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.\n\n> Q5: Homogeneity metric definition\n\nWe 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.\n\n> Q6: DCBC metric performance interpretation\n\nWhile 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.\n\n> Q7: Choice of number of neighbors\n\nWe 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**).\n\n> Q8: Cosine similarity truncation\n\nWe 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.\n\n> Weakness 1: Choice of number of parcels $K$\n\nWhen $K$ 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.\n\nVarying $K$ 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.\n\n---\n\nReference:\n\n[1] Brain-JEPA: Brain Dynamics Foundation Model with Gradient Positioning and Spatiotemporal Masking. NeurIPS 2024.\n\n[2] BrainLM: A foundation model for brain activity recordings. ICLR 2024.\n\n[3] Atlas-guided parcellation: Individualized functionally-homogenous parcellation in cerebral cortex. Computers in Biology and Medicine 2022.\n\n[4] A precision functional atlas of personalized network topography and probabilities. Nature Neuroscience 2024.\n\n[5] Local-global parcellation of the human cerebral cortex from intrinsic functional connectivity MRI. Cerebral Cortex 2018.\n\n[6] Neuromaps: structural and functional interpretation of brain maps. Nature Methods 2022."}]

Author rebuttal:

Meta-review: The paper introduces a graph-guided deep-embedding framework for generating individualized, voxel-level brain parcellations from resting-state fMRI. The introduced method outperforms existing methods in terms of homogeneity, silhouette coefficient, and performance on downstream tasks like autism diagnosis and cognitive decoding.

Initially, the reviewers highlighted good paper presentation, innovative framework and extensive validation. On the negative side, the reviewers were bringing up unclear practicality of the solution, missing points of comparisons and were requesting additional clarifications.The authors rebuttal has addressed all of the reviewers concerns and in the discussion phase all reviewers recommended the paper for acceptance (3x5 and 4). AC agrees with the reviewers and recommends to accept.
Decision: Accept (poster)