Semantic locality-aware biclustering for brain functional network connectivity

Abstract

Functional connectivity (FC) has become central to understanding human brain dynamics and a reliable pursuit for investigating neuropsychiatric disorders. The human brain operates as a modular system, with distinct regions forming functional modules critical for neuronal processing. High-resolution modeling of these modules provides essential insights into the structural and functional basis of neural processing. However, subject heterogeneity–arising from individual variability and diverse symptom profiles–often obscures fine-grained neural patterns, limiting current methods in resolving disease-related alterations. To address this, we propose BrainBiC–a deep biclustering framework that jointly stratifies subjects and features, enabling effective navigation of the data manifold and meaningful knowledge discovery. It leverages semantic locality to preserve coherence in subgrouped neural patterns and jointly optimizes sample and attribute assignment probability distributions for novel bicluster retrieval. Comprehensive experiments on multiple neuroimaging datasets demonstrate that BrainBiC outperforms state-of-the-art methods in identifying neurologically meaningful brain connectivity substructures. The extracted connectivity signatures are highly modular, show strong associations with cognitive and behavioral variables, and reveal disruptions in functional integration within subcortical, sensorimotor, and visual circuits. These findings position BrainBiC as a robust framework for modeling disease heterogeneity and associated connectivity alterations, advancing data-driven precision psychiatry.

Introduction

In recent decades, neuroimaging has emerged as a transformative tool for understanding the structure, function, and pathology of the human brain. Through modalities such as functional magnetic resonance imaging (fMRI), positron emission tomography (PET), and diffusion tensor imaging (DTI), researchers have gained unprecedented access to the living brain’s architecture and dynamics. One of the most profound applications of these technologies is in the study of brain connectivity–how spatially distinct regions of the brain coordinate and communicate to support cognition, emotion, and behavior. A key concept arising from this research is functional connectivity (FC), which reflects statistical dependencies–typically temporal correlations–between signals from different brain regions. FC provides a window into the brain’s dynamic functional organization and offers critical insight into the mechanisms that underpin both typical and disordered mental functioning. Functional connectivity is conventionally modeled as a graph^1,2, where nodes represent anatomical regions of interest (ROIs) and edges correspond to statistical coupling between them. A more global perspective is captured through functional network connectivity (FNC), which examines interactions between broader functional components, often derived through data-driven decompositions such as independent component analysis (ICA). The human brain is a dynamic system, where regions interact through complex, nonlinear relationships that mediate cognition and behavior. The communication (FNC) among anatomically or functionally distinct brain regions that cooperate to support specific mental and behavioral functions generates brain networks³. Optimal communication among brain components scales the enormous neural processing required to support regular cognition^4,5. As such, disrupted brain links and incoherence in the neural community can potentially instigate poor neural responses and cognitive performance that are manifested in large part as symptoms of neuropsychiatric disorders (schizophrenia)^1,2,6.

The neuroimaging literature offers a comprehensive exploration of FC analysis, spanning a wide range of methodological approaches^7–12. In recent years, deep graph neural networks have been increasingly utilized to model their complex structure. For instance, BrainTGL¹³ for dynamic brain graph learning, BrainGNN¹⁴, which incorporates functional information in brain networks, and IBGNN¹⁵, designed to enhance interpretability. Other innovations include BN-GNN¹⁶, which applies reinforcement learning in graph neural networks, FBNetGen¹⁷, a generative model for functional brain networks, and transformer-based architectures^18,19 for learning high-level representations of brain connectivity. Although a few studies have applied biclustering to extract functional modules and connectivity signatures^20–22, its application to FC data remains limited. We propose a deep biclustering model that jointly learns feature and subject assignments while preserving complex, heterogeneous network topologies.

Although node-based clustering is commonly used in FC analysis^14,19, it overlooks the functional versatility of regions (ROIs), which often participate in multiple neural submodules through distinct connections^23–25. As such, grouping nodes can only obscure their functional diversity and ubiquitousness, limiting their granular presence in neuro-dynamics. Instead, we focus on edge-level analysis, enabling nodes to associate with multiple submodules through their functional links. This edge-centric approach yields a more flexible and granular representation of brain network dynamics, better suited for capturing heterogeneity in neuropsychiatric disorders. Beyond addressing population heterogeneity, deep biclustering offers a powerful means to explore the modular and dynamic structure of functional brain connectivity. The biclusters extracted by our model represent data-driven functional submodules, enabling targeted investigation of how specific neural circuits relate to cognition and neuropsychiatric dysfunction²⁶. This approach naturally extends to community detection, a key strategy in identifying cohesive subnetworks within brain graphs³. In schizophrenia, alterations in the network topology–such as reduced integration and segregation of brain communities–are well documented²⁷. By identifying distinct, functionally meaningful connectivity modules that distinguish healthy from diseased populations, deep biclustering provides a scalable and interpretable framework for advancing precision psychiatry.

A significant challenge in neuroimaging studies is subject heterogeneity, where individual variability in neural organization, disease progression, and cognitive function introduces substantial noise, making it difficult to extract meaningful biomarkers^28–31. This variability is particularly pronounced in psychiatric disorders such as schizophrenia, where symptomatology and neurobiological alterations vary widely in spatial and temporal progression across individuals⁶. Unleashing the variability in spatiotemporal progression patterns offers major benefits to patient stratification and disease understanding. This requires a granular exploration of the complex subspace with meticulously designed objectives to extract the most meaningful patterns in the data³². However, off-the-shelf resolution like clustering approaches, which rely on linear assumptions and population-averaged models, struggle to capture this fine-grained variability, leading to oversimplified subgrouping of the attributes. Therefore, a framework capable of more sophisticated navigation through the data manifolds is required. Recent advances in deep learning-based biclustering have emerged as powerful alternatives to traditional matrix factorization approaches, yet the field remains relatively underexplored compared to standard clustering methods due to the inherent complexity of simultaneously clustering both samples and features while maintaining biological interpretability^33,34. Contemporary deep learning approaches include variational autoencoders for biclustering³⁵, deep matrix factorization models^36,37, bayesian approaches like BGB , MCMC³⁸, Tensor Biclustering³⁹ and graph neural networks that exploit data relationships⁴⁰. While contrastive learning-based clustering methods such as SwAV⁴¹ and SimCLR⁴² have shown remarkable success in standard clustering by learning discriminative representations through positive and negative sample pairs, their application to biclustering faces fundamental limitations: contrastive approaches typically focus on sample-wise clustering and lack the dual clustering capability required for simultaneous feature and sample grouping inherent to biclustering problems. Here, we propose a deep biclustering framework that jointly stratifies subjects and neural features while capturing the underlying non-linearity in brain connectivity data. Deep learning enhances this process by mapping the complex, non-linear relationships inherent in brain connectivity and tracking informative data manifolds that traditional methods fail to capture⁴³.Our proposed semantic locality-enhanced framework addresses these limitations by incorporating contextual locality that preserves neighborhood structures in both sample and feature spaces, effectively capturing the semantic relationships, while simultaneously enabling the discovery of coherent biclusters through hierarchical sparsity constraints. Theoretically, our approach provides superior interpretability compared to concurrent methods by explicitly modeling the bipartite relationships between samples and features through the encoder-decoder bottleneck, while keeping the implementation light-weight and simple. Moreover, our method incorporates semantic relationships directly into the clustering objective, ensuring that biclusters not only exhibit statistical co-occurrence but also maintain semantic coherence within the feature and sample spaces. In addition, it empirically demonstrates competitive performance on neuroimaging datasets where preservation of biological relevance through a classification head ensures that discovered biclusters correspond to meaningful neurobiological modules rather than purely statistical associations. The limited adoption of deep learning in biclustering stems from the challenge of maintaining the dual clustering property while ensuring biological interpretability–a gap our method bridges by combining the representational power of deep architectures with domain-specific constraints that preserve neurobiological significance.

The connectivity disruptions captured by our model exhibit strong associations with clinical symptoms of schizophrenia (Fig. 3). Dysconnectivity within key regions–including the prefrontal cortex, hippocampus, and default mode network–has been previously linked to impairments in working memory, executive function, and social cognition⁴⁴. In parallel, the extracted connectivity signatures show significant correlations with cognitive performance measures (Fig. 2). Community-level analysis reveals distinct patterns of central and peripheral hub engagement across healthy and schizophrenia groups, reflecting altered information processing dynamics. Additionally, BrainBiC facilitates data-driven disease subtyping, capturing the broad spectrum of heterogeneity within schizophrenia. By integrating deep learning with network neuroscience, our framework offers a scalable approach for identifying disease-specific connectivity biomarkers, advancing computational neuroimaging and its clinical translation in precision psychiatry.

Fig. 3.

Association of bi-clustered connectivity with schizophrenia symptom (PANSS) scores. The correlation is computed between the average connectivity of SZ subjects in each bicluster and the symptom scores. The data is presented with a scatterplot with regression lines. The association is measured by Pearson correlation (r), adjusting for age and sex and false discovery rate correction at . Statistically significant associations are marked with (**).

Fig. 2.

Association between the brain connectivity subgraph extracted by the biclustering and distinct cognitive variables. For each subject, we compute the average of functional connectivity. The data is presented with a scatterplot with regression lines, and the association is measured by Pearson correlation (r), adjusting for age and sex and false discovery rate correction at . Statistically significant associations are marked with (**).

Results

Experimental settings for biclustering

Our model architecture comprises cascaded linear layers for both the encoder and decoder, with the bottleneck layer size empirically set to , consistent with the number of expected biclusters and optimized through validation. The dataset is partitioned into training (65%) and evaluation (35%) splits via random sampling. The evaluation set is further divided into validation (40%) and test (60%) subsets. We use a batch size of 32, and additional hyperparameter sensitivity analyses are provided in the supplementary material (Fig. S2). For benchmarking, we compare BrainBiC against a diverse set of models covering classical, deep learning, and graph-based methods. These include the k-means baseline, three statistical biclustering methods–FABIA⁴⁵, SAMBA⁴⁶, and N-BiC⁴⁷–as well as the auto-decoder model (AD)⁴⁸. Given the widespread application of graph neural networks (GNNs) in functional connectivity modeling, we also evaluate GNN-based approaches such as GAEBiC⁴⁹ and GraphMAE⁵⁰. Additionally, we include recent deep biclustering frameworks, including BCOT⁵¹, which leverages optimal transport on bipartite graphs, and a Bayesian deep biclustering model³⁸, Bayesian graph-guided biclustering (BGB)⁵², tensor biclustering (TB)³⁹ that uses a spectral tensor unfolding, and BnBiC²⁰. An ablation study assessing key components of our model is also reported. We run the models for 100 repetitive iterations and present the (mean ± standard deviation) of the performances across the runs. We maintain a consistent model order and experimental settings to ensure the reliability and fairness of the comparisons.

Performance evaluation metrics

We run our experiments on the real neuroimaging datasets described earlier, but we don’t have access to ground truth bicluster partitioning for the FC data. Thus, the evaluation metrics are centered around evaluating bicluster stability and quality. We adopt mean square residue (MSR)³³ that measures coherence within a bicluster. A low MSR indicates that features (values) in the bicluster vary minimally, implying strong local patterns. We also use average Pearson correlation coefficients (APCC)⁵³ for checking coherence in the bicluster attributes. For experimenting on bicluster community, connectedness, and modularity, we use a metric called the participation coefficient (PC)^54,55 - a graph-theoretic measure that quantifies how evenly a node’s connections are distributed across different modules within a network. We configure the participation coefficient to compare the connectedness within the community - connectivity among the attributes within a bicluster, and the interactions with the other parts of the system. In brain dynamics, it’s a measure of the interaction among a subset of brain networks and their communication with the rest of the brain. To evaluate a bicluster partitioning, we can measure the connectivity given by the edges among nodes within a bicluster - local connections () and edges between other modules of the system - global connections () of a bicluster b as follows,

1

2

where is the subset of edges connecting nodes in bicluster b and the rest of the system. So, the participation coefficient (PC) for each bicluster b is the ratio between local and global connectivity (Eq. 3).

3

To compare the biclustering performance across methods, we introduce an engagement index (EI) based on the normalized transformation of PC. For a bicluster b, the EI is given by Eq. 4

4

Here, and , if represents the similar local and global connectivity strength. Now, the average engagement index (AEI) for a biclustering run R with K biclusters is given by the Eq. 5.

5

Biclustering performance comparison

Table 1 presents a comprehensive evaluation of the proposed BrainBiC framework against a range of state-of-the-art clustering and biclustering methods. These include traditional statistical approaches (e.g., FABIA, SAMBA), baseline clustering (k-means), graph-based models (GAEBic, GraphMAE), and deep learning-based biclustering techniques (e.g., BCOT, Bayesian, BGB, TB, and BnBiC). BrainBiC consistently outperforms all compared methods in multiple performance metrics across four multi-site neuroimaging datasets (Table 1). Notably, it achieved the lowest MSR and highest APCC and AEI, confirming its ability to extract more coherent, semantically meaningful biclusters with rich modular structures. To assess the contribution of different architectural components, we conducted an ablation study by systematically removing key regularization terms: semantic locality, sparsity, and classification loss. The results confirm that each constraint plays a pivotal role in model effectiveness. Notably, the exclusion of semantic locality led to a marked decrease in the engagement index (EI), indicating a deviation in the modular structure of extracted biclusters. Similarly, removing sparsity or classification loss resulted in higher MSR and lower APCC, suggesting reduced subgroup discriminability. These results validate our architectural design choices and highlight the necessity of each regulatory term for effective bicluster retrieval.

Table 1.

Benchmarking the performance of the proposed method against state-of-the-art clustering and biclustering approaches. The highlighted row shows the performance of the proposed BrainBiC model.

Model Variant	Model	COBRE + fBIRN + MPRC			ABIDE
		MSR	APCC	AEI	MSR	APCC	AEI
Baseline	k-Means	0.721 ± 0.02	0.282 ± 0.04	0.381 ± 0.02	0.683 ± 0.06	0.327 ± 0.03	0.326 ± 0.02
Traditional Biclustering	N-BiC	0.557 ± 0.05	0.471 ± 0.05	0.401 ± 0.03	0.501 ± 0.04	0.356 ± 0.03	0.442 ± 0.03
	FABIA	0.601 ± 0.04	0.412 ± 0.05	0.502 ± 0.07	0.541 ± 0.05	0.482 ± 0.04	0.589 ± 0.04
	SAMBA	0.487 ± 0.06	0.285 ± 0.07	0.423 ± 0.07	0.462 ± 0.03	0.429 ± 0.04	0.436 ± 0.07
Auto-Encoder	AD	0.411 ± 0.04	0.423 ± 0.02	0.452 ± 0.04	0.393 ± 0.03	0.495 ± 0.03	0.488 ± 0.02
Graph Neural Network	GAEBic	0.378 ± 0.03	0.392 ± 0.02	0.523 ± 0.04	0.407 ± 0.05	0.423 ± 0.04	0.535 ± 0.05
	GraphMAE	0.345 ± 0.04	0.434 ± 0.05	0.582 ± 0.02	0.445 ± 0.03	0.478 ± 0.03	0.568 ± 0.04
Deep Biclustering	Bayesian	0.323 ± 0.04	0.426 ± 0.05	0.623 ± 0.06	0.429 ± 0.04	0.455 ± 0.03	0.603 ± 0.08
	BGB
	TB
	BCOT	0.315 ± 0.06	0.552 ± 0.05	0.645 ± 0.02	0.374 ± 0.09	0.502 ± 0.03	0.612 ± 0.08
	BnBiC						a
Proposed	BrainBiC	0.304 ± 0.05	0.568 ± 0.07	0.674 ± 0.05	0.348 ± 0.06	0.521 ± 0.02	0.652 ± 0.06
Ablation	w/o semantic locality	0.312 ± 0.04	0.523 ± 0.07	0.328 ± 0.09	0.368 ± 0.08	0.487 ± 0.02	0.417 ± 0.07
	w/o sparsity	0.308 ± 0.02	0.535 ± 0.02	0.602 ± 0.03	0.355 ± 0.03	0.487 ± 0.03	0.564 ± 0.04
	w/o classification loss	0.383 ± 0.02	0.527 ± 0.08	0.514 ± 0.04	0.436 ± 0.05	0.457 ± 0.09	0.423 ± 0.04

Bicluster analysis

Figure 1a illustrates representative functional connectivity subgraphs identified by BrainBiC. The resulting biclusters exhibit clear modular patterns, semantic coherence, and spatial localization within the brain network, capturing distinct neurofunctional themes. BiC 1 connects subcortical structures with visual-auditory-sensorimotor regions - highlights cerebellar integration with sensorimotor pathways⁵⁶. BiC 2 captures localized connectivity between the visual (VIS) and sensorimotor (SM) domains, suggesting perceptual-motor integration⁵⁷. BiC 3 is dominated by cognitive control circuits. BiC 4 and BiC 5 reveal distributed connectivity patterns across subcortical, auditory, visual, and sensorimotor domains – suggesting hybrid or overlapping subnetwork modules⁵⁸. Figure 1b, reveals distinct group-level differences between healthy controls (HC) and individuals with schizophrenia (SZ). Biclusters 1, 2, 4, and 5 display significant differences in connectivity strength across the visual (VS), subcortical (SC), and sensorimotor (SM) networks. In particular, BiC 1 and BiC 2 highlight alterations in connectivity strength, while BiC 4 and BiC 5 demonstrate a reversal in directionality between HC and SZ groups. Previous studies have implicated these regions–especially sensorimotor and visual pathways–in the manifestation of social and cognitive impairments in schizophrenia⁵⁹. The reduced connectivity in BiC 2 and the inverse pattern between the SM and VS regions in BiC 5 may underlie the deficits in social cognition and mentalization, key challenges faced by individuals with SZ^59,60.

Fig. 1.

The connectivity bicluster visualization. a Functional links on the BrainNet Viewer⁶¹. The edge color represents the connectivity strength, and the nodal color palette stands for the brain modules (SC Subcortical, AUD Auditory, SM Sensorimotor, VIS Visual, CC Cognitive control, DM Default mode, CB Cerebellum), summarized from group ICA. b Group-wise connectivity and their (HC-SZ) differences in functional connectivity. The top row is computed by averaging the HC subjects within a bicluster, the middle row for SZ, and the bottom row demonstrates the HC-SZ group differences. The color bar represents the strength of the functional connection. The differences are false discovery rate (FDR) corrected and statistically significant at .

Association with cognitive variables

Figure 2 demonstrates the statistical association between five connectivity subgraphs (BiC 1–5), extracted via our proposed biclustering algorithm, and four key cognitive domains: Attention, Working Memory, Verbal Learning, and Visual Learning. These relationships were evaluated using Pearson correlation coefficients (r), controlling for age and sex, and applying False Discovery Rate (FDR) correction for multiple comparisons. BiC 1 reveals a strong negative correlation with Attention (, ) and a strong positive correlation with Working Memory (, ), suggesting it encodes a subnetwork involved in executive function. In contrast, BiC 3 shows positive association with Attention and negative associations with both Working Memory and Verbal Learning (, ,, ), indicating its potential relevance to domain-specific functional trade-offs. BiC 5 exhibits a significant positive correlation with Visual Learning (, ), highlighting its relevance in visual cognitive processing - the association is more pronounced in SZ, suggesting a potential compensatory mechanism. exhibits a negative correlation with Working Memory (, ), indicating that increased connectivity in this subgraph corresponds to poorer memory performance, especially in SZ subjects. Bic 4 shows a significant positive correlation with Verbal Learning (, ), particularly in the HC group, suggesting selective involvement in language-related cognition. There are weak or non-significant associations, which may suggest selective or context-dependent engagement of the underlying subgraphs. Across several BiCs, the regression trends also vary between healthy controls (HC) and schizophrenia (SZ) groups, suggesting group-specific neural-cognitive relationships.

Association with schizophrenia symptoms (PANSS scores)

We examine how the connectivity patterns within each bicluster relate to clinical symptoms in SZ. Specifically, we investigated the correlation between biclustered connectivity and symptom severity as measured by the Positive and Negative Syndrome Scale (PANSS) ⁶². PANSS scores are widely used in psychiatric research to assess the symptom profile of schizophrenia across three domains: positive, negative, and general psychopathology. Figure 3 visualizes these associations for each bicluster based solely on SZ subjects. Connectivity patterns in BiC 1 exhibit strong negative correlations with all three PANSS domains: positive (), negative (), and general symptoms (). This indicates that subjects with more negative connectivity within this bicluster–which primarily involves subcortical, visual, and sensorimotor regions (see Fig. 1b)–tend to exhibit more severe clinical symptoms. These findings align with prior research implicating dysconnectivity in these circuits in schizophrenia-related dysfunctions in sensory processing and motivation.

BiC 5 also shows a statistically significant negative correlation with positive symptom severity (), suggesting a similar trend, where greater negative connectivity is associated with more pronounced psychotic symptoms. In contrast, BiC 2 is positively correlated with general symptom scores (), although it does not show significant associations with the positive or negative subscales. A similar association is observed for BiC 4 in the general domain (), though in the opposite direction. These results highlight distinct and potentially complementary roles of connectivity subgraphs in explaining heterogeneity in symptom dimensions.

Participation coefficient analysis

The Participation Coefficient (PC) is a widely used graph-theoretical metric that quantifies the extent to which a node is

connected across different modules in a network ⁵⁴. It is particularly relevant in brain network analysis, where it provides insight into whether a brain region (node) is specialized within a specific functional module or serves as an integrative hub interacting across multiple communities. PC is closely related to the concept of the clustering index (CI) ⁶³ and is defined mathematically in Eq. 4. A PC value greater than 1 within a bicluster suggests that nodes are strongly interconnected among themselves but weakly connected to the rest of the brain network–indicating modular segregation. In contrast, a PC value close to 1 implies more homogeneous and distributed connectivity. Higher PC values are indicative of brain regions acting as functionally coherent subnetworks. Figure 4 displays the participation coefficients for the HC and SZ groups across the five identified biclusters. Significant group differences were observed in BiC 2 and BiC 4, where HC subjects exhibited significantly higher PC values compared to SZ ( and , respectively). This suggests a loss of modular specificity in schizophrenia within these biclusters. BiC 2 primarily includes connections between the visual and sensorimotor regions, while BiC 4 captures subcortical, sensorimotor, and auditory interactions. The observed reduction in PC among SZ subjects in these biclusters potentially implies disrupted interregional communication in schizophrenia ^64,65.

Fig. 4.

Participation coefficient (PC) analysis. For each node, we estimate the average connectivity within the bicluster and connectivity with other modules (the rest of the network). We ignore the directionality while computing the connectedness by taking the absolute weight of the edges (connections). PC represents the ratio between these connectivity measures. Data are presented using a box plot (center line, median; box limits, upper and lower quartiles; whiskers, 1.5 inter-quartile range; points, outliers). The asterisks indicate significant differences between the two subgroups using two-sample t-tests (***; **; ns not significant; correction for multiple comparisons).

The group (HC/SZ) discriminative Biclusters

BiC 4 and BiC 5 exhibit the most prominent group-wise contrast in connectivity profiles between healthy controls (HC) and schizophrenia (SZ) subjects. These biclusters capture contextually homogeneous connectivity patterns of subgraphs that reflect diverse functional interactions in HC and SZ populations. Figure 5 visualizes these discriminative biclusters through two complementary perspectives: (a) The connectogram of average connectivity patterns within each group, and (b) The node-wise connectivity ranking, showing the relative contribution of each brain component (ICN) to the connectivity of the bicluster. In BiC 4, HC subjects show negative connectivity between subcortical and sensorimotor regions, while SZ subjects show more positive connectivity along these same links.

Fig. 5.

The most group discriminative biclusters (BiC, BiC 5). a HC and SZ connectogram for the biclusters. The color of the links represents the connectivity strength, and the brain modules are colored distinctively. b The components (ICN) associated with bicluster 4 & 5 are sorted using their average connectivity strength with other members of the bicluster. For each BiC, the left one is HC-sorted - the ranking of the components is organized using the connectivity strength computed across the HC subjects only, and SZ-sorted across SZ subjects only.

This shift in polarity may reflect aberrant integration of sensory and subcortical processing in schizophrenia, consistent with findings that associate thalamocortical and sensorimotor dysconnectivity with disrupted sensory gating and impaired integration in SZ ^66,67. In contrast, BiC 5 shows an inverse pattern. SZ subjects exhibit negative connectivity between sensorimotor, visual, and auditory regions, while HC subjects display relatively stronger integration among these domains. These disruptions may be linked to deficits in perceptual processing, audiovisual integration, and motor control that are frequently observed in schizophrenia ^68,69. The node-wise connectivity ranking in Fig. 5b further highlights the divergence in community structure between the groups. The components (ICNs) participating in these biclusters show different connectivity strength hierarchies across SZ and HC subjects. For instance, in BiC 4, regions like the thalamus, precuneus, and postcentral gyrus exhibit high connectivity in SZ but rank lower in HC, suggesting altered hubness and redistribution of functional roles.

Community structure: central and peripheral

To further investigate the functional architecture of group-discriminative biclusters, we perform a community-level analysis using the participation coefficient (PC). Nodes are categorized into two groups: central hubs (highly connected or ”rich club” nodes) and peripheral nodes (weakly coupled), based on the top-k and bottom-k connectivity magnitudes. Figure 6 illustrates the resulting central and peripheral communities in BiC 4 and BiC 5 for both healthy controls (HC) and schizophrenia (SZ) groups. Highlighted voxels are mapped onto the AAL anatomical brain template, reflecting the spatial distribution of each community. In BiC 4, the thalamus functions as a central hub in HC but shifts to a peripheral role in SZ. Conversely, the middle temporal gyrus (MTG) and putamen are peripheral in HC but become. central in SZ. This role reversal suggests a reconfiguration of subcortical and temporal structures in schizophrenia, consistent with previous findings implicating thalamic dysconnectivity and basal ganglia abnormalities in impaired sensorimotor and associative processing^66,70. In BiC 5, the MTG (62) and fusiform gyrus shift from peripheral in HC to central in SZ, suggesting altered visual-temporal integration and abnormal recruitment of these regions during social and facial processing tasks^71,72.

Fig. 6.

Community analysis of group (HC/SZ) distinctive biclusters - central and peripheral. We identify a set of incident nodes (ICNs) from the set of edges in the bicluster. For each node, we compute the average connectivity within the bicluster. Then, we form central (highly interconnected hub nodes) & peripheral (weakly interconnected) communities by selecting k nodes based on their connectivity strength. The relevant voxels of the community are overlaid on the AAL anatomical brain template. The static color solely depicts the presence in this scenario. The participating components are PCG_ R Right postcentral gyrus, SPL Superior parietal lobule, MTG Middle temporal gyrus, STG Superior temporal gyrus, PoCG Post central gyrus, SFG Superior frontal gyrus, PoCC Posterior cingulate cortex, PCL Para central lobule, CB Cerebellum.

Discussion

The human brain exhibits an organization of a small-world network, with segregated modular regions integrated by some hub nodes¹. The use of connectomes as biomarkers has gained significant momentum in recent years, particularly through the incorporation of clustering features that capture both functional connectivity patterns and structural network modifications characteristic of specific brain pathologies⁷³. In this study, we propose BrainBiC, a novel deep biclustering framework designed to uncover functional brain subgraphs with clinical and cognitive relevance, especially in the context of schizophrenia. Our model jointly stratifies subjects and connectivity features to overcome the limitations of traditional clustering and community detection methods that often fail to capture the granular heterogeneity present in neuroimaging data. This dual partitioning enables us to uncover nuanced subgroup-specific dysconnectivity patterns that are obscured in global or univariate analyses. By integrating semantic locality, sparsity, and class-specific objectives into a unified neural architecture (Fig.  7), BrainBiC reveals a modular and biologically meaningful subnetwork that is critical to neural dynamics and dysfunction. Our approach demonstrates superior performance in identifying meaningful subgraphs across multiple datasets and evaluation metrics (Table  1). The identified biclusters show distinct patterns of functional dysconnectivity between healthy controls (HC) and individuals with schizophrenia (SZ), particularly within sensorimotor, subcortical, and visual regions (Fig. 1b). These disruptions are consistent with long-standing findings of sensorimotor gating deficits⁷⁴, thalamocortical dysconnectivity⁶⁶, and perceptual processing impairments in schizophrenia⁶⁸.

Fig. 7.

The deep BrainBiC architecture for semantic locality preserving biclustering of brain functional connectivity. The model decomposes resting-state fMRI volumes using group ICA and generates static functional network connectivity (sFNC) using the sliding window correlation (SWC) technique. The sFNC matrix is distilled further for capturing the unique connections, constructing a connectivity vector. These vectors are encoded into a low-dimensional latent space using a neural encoder-decoder architecture. The objective function is comprised of reconstruction loss () and semantic locality preservation (). regulates the latent space for semantic coherence and makes the representation more suitable for biclustering. A classification branch powered by cross entropy () further enhances subject-level discriminability (e.g., HC, SZ, ASD), supporting subgroup discovery in heterogeneous neuroimaging data. The inference leverages the weight matrix and the hidden activations to generate biclusters.

BrainBiC establishes strong and interpretable links between connectivity patterns and cognitive performance. As shown in Fig.  2, BiC 1 is particularly sensitive to cognitive load and presents differential associations across domains - working memory, attention, and visual learning – domains often impaired in SZ⁷⁵. BiC 3 and BiC 5 are associated with attention and visual processing, respectively. Importantly, these associations exhibit group-specific trends, highlighting how neural signatures diverge between HC and SZ in clinically meaningful ways. These bicluster-cognition associations support the hypothesis that brain function is not globally impaired in schizophrenia but rather disrupted across specific subnetworks and domains⁷⁶. By isolating network-specific relationships, our findings highlight the functional specificity of connectivity motifs and underscore the importance of granular subnetwork analysis in understanding cognitive heterogeneity in SZ. This granular view complements prior research on connectome dysfunctions and supports precision psychiatry efforts aimed at targeting domain-specific impairments^77,78. The reduced integration observed in SZ may result from abnormal myelination, synaptic pruning, or neurotransmitter dysfunction, which collectively impair large-scale information flow across the brain^79,80.

The proposed framework effectively captures symptom-specific neural profiles, revealing the neurobiological basis of schizophrenia’s clinical diversity. As illustrated in Fig. 3, several biclusters exhibit statistically significant correlations with the positive, negative, and general symptom dimensions, as measured by the Positive and Negative Syndrome Scale (PANSS). These associations suggest a promising avenue for clinical phenotyping and stratified treatment planning. For example, BiC 1 shows distinct sensitivity in all three domains of symptoms, implicating disruptions in the subcortical and cerebellar regions, areas consistently linked to psychotic features and motor dysfunction in SZ^81,82. BiC 2 and BiC 4 are primarily associated with general symptoms such as anxiety and depression, with strong connectivity observed between visual, sensorimotor, and subcortical networks. These findings align with previous reports of widespread dysregulation in the thalamocortical and corticostriatal loops in affective and cognitive disorders^83,84. BiC 5 demonstrates a marked correlation with positive symptoms, including hallucinations and delusions, supporting the previous literature that associates hyperconnectivity in limbic and salience networks with the severity of positive symptoms^85,86. Together, these results highlight the critical role of subnetwork-level dysfunction in SZ, emphasizing that the disorder is not characterized by global network breakdown, but rather by distinct disruptions localized to functionally specific circuits. This bicluster-based analysis provides a fine-grained lens for identifying network-specific dysfunctions and symptom-linked profiles. Such granularity is essential for developing targeted interventions and supports the broader agenda of precision psychiatry, which seeks to tailor treatments to individual neural signatures and symptom trajectories.

A topological analysis of the brain networks (Figs. 4, 6) reveals altered participation coefficients and hub distributions in SZ. Specifically, SZ subjects exhibit reduced integrative connectivity (i.e., lower participation coefficients), along with a redistribution of central nodes from canonical integrative hubs (e.g., thalamus, postcentral gyrus) to less canonical regions (e.g., middle temporal gyrus, fusiform gyrus). These changes reflect a larger reorganization of the network hierarchy, consistent with disrupting the rich club and weak modular integration in schizophrenia^26,55. Moreover, disruptions in participation and modularity are commonly observed in Alzheimer’s disease and autism, where reduced inter-network integration impairs global coordination of cognitive and behavioral processes. Identifying nodes with atypical engagement in global communication may thus help elucidate the neurobiological underpinnings of these disorders. These topological disruptions echo findings in both neurodevelopmental (autism) and neurodegenerative (Alzheimer’s) disorders, which show similar reductions in rich-club architecture and global efficiency^87,88. This suggests that reduced network modularity and inter-network communication may be transdiagnostic features of brain disorders.

To further explore schizophrenia heterogeneity, we applied BrainBiC in a disease-specific subtyping analysis (supplementary Fig. S3). This unsupervised procedure revealed three different stable and distinct SZ subtypes, each defined by unique functional connectivity patterns, differential cognitive associations, and varying severity of symptoms. These findings align with recent literature emphasizing the need for personalized neurobiological subtyping in psychiatric disorders³⁰. Notably, compared to conventional clustering methods, biclustering offers enhanced granularity by allowing overlapping feature-subject assignments, uncovering more nuanced stratification aligned with recent efforts in precision psychiatry⁸⁹.

Our biclustering approach identified three neurobiologically distinct schizophrenia subtypes with unique pathophysiological signatures. ST1 exhibits preserved connectivity in sensorimotor-visual networks alongside better cognitive outcomes, consistent with compensatory neural mechanisms and maintained GABAergic function⁹⁰. ST2 demonstrates pervasive hypoconnectivity across functional domains, supporting thalamocortical dysconnectivity models and suggesting aberrant neurodevelopmental pruning processes^91,92. Furthermore, the negative correlation in ST2 with cognitive variables supports the glutamate hypofunction hypothesis, where NMDA receptor hypofunction leads to downstream effects on GABAergic interneurons, resulting in widespread cortical disinhibition and cognitive impairment^93,94. ST3 presents selective hyperconnectivity with elevated symptom burden (PANSS score), aligning with dopaminergic dysregulation and aberrant salience processing frameworks^95,96. These connectivity-defined subtypes map onto established neurobiological hypotheses of schizophrenia, potentially informing targeted therapeutic interventions based on distinct pathophysiological profiles. More discussion on subtypes’ neurobiological relevance is given in the supplementary section (6A).

BrainBiC offers a powerful and interpretable deep learning solution to uncover fine-grained connectivity subgraphs, stratify patient populations, and link neural phenotypes to clinical variables. The lightweight, modular architecture enables seamless integration across multiple data types, from neuroimaging and graph networks to behavioral assessments and multi-omics datasets, providing comprehensive biomedical insights. Its architecture not only facilitates granular subgroup discovery but also enhances interpretability, bridging the gap between data-driven findings and clinically actionable insights. Although demonstrated in the context of schizophrenia, BrainBiC’s generalizability and flexibility position it as a promising tool for precision diagnostics in a wide range of complex, multifactorial disorders such as depression, autism, and bipolar disorder.

Materials and methods

Datasets

We evaluate our deep biclustering framework using four resting-state fMRI (rs-fMRI) datasets. Three of these–COBRE⁹⁷, fBIRN⁹⁸, and MPRC⁹⁹–are widely used publicly available schizophrenia cohorts, which comply with the Institutional Review Board for this use of data. The experiments are performed following relevant named guidelines and regulations with informed consent from all participants and/or their legal guardians. The demographic characteristics and acquisition protocols are detailed in previous studies^100–102. From these sources, we construct a combined cohort of 856 subjects, comprising 490 healthy controls (HC) and 366 individuals with schizophrenia (SZ). These datasets include harmonized cognitive and symptom scores, enabling robust analysis of connectivity-cognition and connectivity-symptom associations. Data are corrected for effects at the acquisition site and other confounders such as gender, age, and demographics. To complement our evaluation, we include the Autism Brain Imaging Data Exchange (ABIDE) dataset¹⁰³, a widely used benchmark in neurodevelopmental disorder studies that can be accessed at https://fcon_1000.projects.nitrc.org/indi/abide/. ABIDE contains rs-fMRI data from 17 international sites, with a total of 1112 anonymized subjects - 539 diagnosed with autism spectrum disorder (ASD) and 573 typical controls. All datasets are preprocessed using the NeuroMark pipeline¹⁰⁴, ensuring consistency across sites and enabling reliable feature extraction for biclustering. Our choice of datasets reflects both domain relevance (schizophrenia and autism) and diversity, providing a comprehensive evaluation of the model across heterogeneous populations. We use the same model order and experimental setting for the consistency of the comparisons.

Data preprocessing and functional network connectivity (FNC)

Identifies the institutional and/or licensing committee that approved the experiments, including any relevant details. The functional magnetic resonance imaging (fMRI) data is preprocessed by statistical parametric mapping (SPM12, http://www.fil.ion.ucl.ac.uk/spm/). The preprocessing steps include head motion correction and slice-timing correction for timing differences in slice acquisition. The images are warped into standard Montreal Neurological Institute (MNI) space using an echo-planar imaging (EPI) template and slightly resampled to isotropic voxels. The smoothing uses a Gaussian kernel with a full width at half maximum (FWHM) = 6 mm. The detailed preprocessing steps are consistent with this study^102,105. In its general form, brain functional connectivity (FC) is represented as a graph or network composed of two main elements: (i) a set of nodes that characterize anatomical, functional, or computational brain units, and (ii) a set of edges that capture pairwise statistical dependencies or relationships between these nodes. When this network is constructed using data from functional imaging modalities such as functional magnetic resonance imaging (fMRI), it is commonly referred to as Functional Network Connectivity (FNC) in the neuroimaging literature ^102,106,107. In this study, we run spatially constrained group ICA (gICA) from the NeuroMark¹⁰⁴ pipeline on the fMRI scans using the GIFT toolbox. gICA followed by quality control decomposes the images into 53 intrinsic connectivity networks (ICNs) with their time courses (TCs), which are grouped into seven brain domains^100,101 (supplementary Fig. S11). The functional connection is usually estimated using the Pearson correlation between ICNs over time. The mean across the time course generates a symmetric square matrix popularly known as static functional network connectivity (sFNC)¹⁰⁸ (more details in supplementary). Mathematically, FNC is represented as a symmetric adjacency matrix of size , where V denotes the number of intrinsic connectivity networks (ICNs). The diagonal elements of this matrix are set to 1, corresponding to the correlation of a node with itself, which can also be interpreted as self-loops in the brain graph. Due to the symmetric nature of correlation, each connection appears twice–above and below the diagonal–resulting in redundancy. Consequently, we use only the upper or lower triangular portion of the matrix.

Problem definition

Let the static functional connectivity (FC) data be represented as , where N is the number of subjects and V is the number of brain regions or nodes (e.g., independent components or ICNs). The dataset is defined as, , where M denotes the number of edges in the upper triangular matrix of FC. The model optimizes two soft assignment probability matrices for biclustering. for feature-to-cluster assignments, and for subject-to-cluster assignments, where K is the number of biclusters. The final output of the model is a set of K biclusters defined as:

such that each bicluster captures a coherent subset of subjects y and a subset of functional connections x that jointly define a data-driven neural subgraph.

Biclustering framework

To this end, we propose a deep neural network framework named BrainBiC, designed to learn edge-level features and jointly optimize the assignment distributions for both samples and features, facilitating a novel biclustering retrieval. While our bicluster learning framework draws inspiration from the foundational work of Rahaman et al.²⁰, the present study substantially extends and enhances the original approach across multiple dimensions: methodological innovations, comprehensive experimental validation, and intuitive evaluation metrics that collectively advance the model’s neurobiological interpretability and domain adaptation capabilities. Our proposed architecture introduces three key methodological enhancements. First, we incorporate novel semantic locality constraints work as a learnable graph Laplacian regularization, which provides a principled mathematical framework for capturing the intrinsic geometric structure of brain functional connectivity networks. Second, we implement hierarchical sparsity constraints across the encoder-decoder layers, which serve multiple functions: enhancing representation learning for high-dimensional sparse data, acting as a regularizer to promote model convergence, and mitigating bias and overfitting issues. These constraints also enable multi-resolution bicluster discovery that naturally reflects the hierarchical organization of biological systems. Third, we integrate joint classification objectives specifically tailored for disease-relevant feature extraction. The integration of a supervised classification head represents a significant advancement, facilitating the discovery of clinically meaningful features from neuroimaging data and effectively bridging the gap between data-driven subgroup identification and neurobiologically interpretable disease subtyping. These enhancements collectively position our framework to address the critical need for explainable and clinically relevant machine learning models in neuroimaging applications. The model decomposes resting-state fMRI volumes using group ICA and generates static functional network connectivity (sFNC) using the sliding window correlation (SWC) technique. The sFNC matrix is distilled further for capturing the unique connections, constructing a connectivity vector. However, vectorization of the feature matrix inherently eliminates the spatial structure and connectivity semantics of the brain. Thus, BrainBiC incorporates learnable positional encoding to retain the spatial and topological context of the connections. The architecture is illustrated in Fig. 7. The framework is built upon an autoencoder (AE) model augmented with biclustering regularization. The core idea is to embed the data into a latent bottleneck layer whose dimensionality equals the number of expected biclusters (K). This design enables the bottleneck to capture joint structure across subjects and connectivity features. This formulation is inspired by the work of Sun et al. ⁴⁸, where the encoder’s weight matrix and hidden layer activations are used to estimate the contribution of samples and features to each latent factor.

From each subject, the vectorized functional connectivity features are represented as , where M denotes the number of unique connectivity edges. Each feature vector is enhanced with a learnable position embedding and passed through an encoder network , which projects the input into a lower-dimensional latent representation . A corresponding decoder network then reconstructs the input vector from this latent code. The complete dataset can be represented as a matrix , where N is the number of subjects and M is the number of connectivity features. To facilitate biclustering, we leverage the encoder weight matrix and the latent activation to model the soft assignment probabilities for both characteristics and subjects. The model is first pre-trained for input reconstruction and supervised classification and subsequently fine-tuned using bicluster-oriented constraints. Reconstruction loss is calculated between original and reconstructed inputs, while binary cross-entropy loss is used to predict disease labels at the subject level. To regularize the clustering process, the matrices and are transformed into soft assignment distributions for features and subjects, respectively, and their divergence from auxiliary target distributions is minimized to refine the bicluster structure.

6

where denotes the autoencoder’s reconstruction of the input element , and is the Euclidean norm.

7

where is the ground-truth label and is the predicted probability (e.g., from a softmax or sigmoid output) for the sample.

Semantic Locality refers to the principle that semantically similar attributes (e.g., with similar modules, roles, or labels) should be closely located in the learned representation. In the context of brain networks, particularly functional connectivity networks, semantic locality assumes a neurobiological interpretation: it refers to the tendency for functionally or cognitively related brain regions to exhibit strong, localized connectivity patterns, often within the same functional module or resting-state network (RSN). Learnable graph Laplacian regularization¹⁰⁹ is often used to enforce this smoothness by penalizing differences in representations between functionally connected regions. Nevertheless, its application requires careful consideration given the fully connected nature of functional connectivity graphs. Thus, the traditional degree matrix D becomes less informative since every node has the same degree, making the standard Laplacian less discriminative²⁷. However, the weighted adjacency matrix A, still contains crucial information about the relative importance of functional relationships. We develop a biclustering framework that accommodates flexible constraint integration, enabling domain experts to seamlessly incorporate custom regularization schemes and domain-specific knowledge into the training process. Our semantic locality implementation imposes constraints directly on the latent space instead of the reconstructed outputs, facilitating more principled control over the learned feature representations. This weight-level regularization indirectly shapes the latent space by ensuring that similar input features contribute similarly to each latent dimension, promoting smoother and more structured representations. Our proposed scheme achieves latent space regularization at the source of the transformation, potentially leading to more robust and interpretable embeddings. Such orchestration is particularly powerful because it transforms the continuous connectivity strengths into a meaningful neighborhood structure. Moreover, in brain connectivity analysis, it ensures that brain regions with strong functional coupling remain proximal in the learned embedding space, enabling the auto-encoder to discover biclusters that respect the hierarchical modular organization of brain networks¹¹⁰. This proximity-weighted approach is superior to binary thresholding methods commonly used in traditional graph-based brain network analysis, as it preserves the continuous nature of functional connectivity while maintaining computational tractability and biological interpretability. The formulation is described in 8,

8

where is the encoder’s weight matrix, and represents a similarity measure between features and , promoting local smoothness in the feature space. The similarity measure is defined as:

9

where and denote the feature vectors of the and connectivity edges across all subjects, and is a scaling parameter controlling the sensitivity to pairwise distances.

Equation (8) draws inspiration from the Gaussian kernel formulation, where the term denotes the distance between feature vectors and , and is a scaling hyperparameter that controls the sensitivity to this distance. To compute , we employ a custom variant of the Earth Mover’s Distance (EMD) tailored for one-dimensional vectors, as proposed in ⁷⁸. This adaptation is particularly suited for our data modality–static functional network connectivity (sFNC)–which is both vectorized and bounded in the range . The EMD-based similarity computation iteratively compares the two feature vectors and accumulates the absolute difference in amplitudes at each index position (see detailed formulation in the supplementary material Algorithm S1). Notably, for smaller values of both and , the similarity term becomes more concentrated, thereby enforcing the semantic locality constraint more strongly by encouraging neighboring features to be embedded closer together in the latent space.

A sparsity constraint is introduced to avoid the bias from larger weights. We use a revised L1 norm¹¹¹ on the W matrix for the sparsity however, since we adjust the sparsity on actual neuroimaging data using gICA, we reduce the effect by making it smaller than the usual L1 norm.

10

To enforce a biclustering structure, we introduce a regularization term based on the soft assignments of both features and subjects. Specifically, the encoder weight matrix is transformed into a probability distribution over bicluster assignments for each feature using a Softmax function across the latent dimension. The resulting feature assignment matrix is denoted as , where is given by:

11

Following the Deep Embedded Clustering (DEC) paradigm¹¹², we refine the cluster assignments by learning from confident predictions. Inspired by¹¹³, we define a target distribution , computed as:

12

For subject-wise clustering, we compute soft assignments from the latent activation matrix , where is the batch size. The corresponding assignment distribution is calculated via:

13

The target distribution for subject assignments, , is analogously defined as:

14

To optimize these assignments, we minimize the Kullback–Leibler divergence between the source and target distributions:

15

The complete training objective combines both pre-training (reconstruction and classification) and fine-tuning (biclustering and regularization) losses as:

16

Here, balances the reconstruction/classification and clustering objectives, while and are non-negative weights that regulate the impact of biclustering and structural constraints, respectively.

During inference, the absolute value of the encoder weight reflects the contribution of the feature to the bicluster. Similarly, the latent activation reflects the membership strength of the subject in the same bicluster. We define a meta-heuristic rule to determine bicluster membership,

• Include subject in bicluster if

• Include feature in bicluster if

Model Training. The overall training process is divided into two phases. First, we pre-train the autoencoder framework using the reconstruction error described in (6) and the classification loss (7). Then, we fine-tune using the semantic locality, biclustering (15), and sparsity constraints described in (10). Model optimization is driven by minimizing the objective function defined in (16). The model is initially trained on reconstruction loss with a large value for - a tuning parameter for balancing between the loss terms- until the model reaches a reasonable performance on reconstructing the input matrix. Then, we shift the gear to more cluster-oriented updates by reducing . The training cycle runs for 250 epochs using the Adam optimizer with a learning rate of in Pytorch.

Regularization and Validation. The model incorporates multiple complementary terms. The semantic locality constraint functions as a graph Laplacian regularization term, penalizing large differences between embeddings of functionally connected brain regions, thereby preserving the inherent topological structure of neural networks. Concurrently, hierarchical sparsity constraints applied to encoder-decoder weights serve dual purposes: promoting selective feature extraction and enhancing model interpretability by identifying the most informative connectivity patterns. The sparsity regularization creates a more favorable optimization landscape by reducing the effective parameter space, which mitigates overfitting while encouraging the model to concentrate on neurobiologically meaningful connectivity signatures¹¹⁴. Furthermore, sparse representations contribute to improved convergence properties by creating a more convex optimization surface and reducing gradient noise, thereby enhancing optimization stability¹¹⁵. Additionally, implementing early stopping based on validation reconstruction error provides robust model selection criteria that balance reconstruction fidelity with biological interpretability, ensuring that discovered biclusters represent genuine functional brain modules rather than overfitted noise patterns. To assess generalization performance, we employed stratified k-fold cross-validation (k=5) across diverse data splits, maintaining balanced representation of clinical groups and demographic characteristics.

Conclusion

This study introduces BrainBiC, a deep biclustering framework leveraging semantic locality constraints for learning meaningful latent representations that preserve coherent relationships between features and samples, ensuring that discovered biclusters maintain both statistical significance and interpretable structure. The application on brain functional connectivity uncovers clinically and cognitively relevant subgraphs in brain functional connectivity. By jointly stratifying subjects and neural features, BrainBiC addresses heterogeneity in schizophrenia and captures modular, interpretable connectivity signatures. Extensive experiments across multiple neuroimaging datasets demonstrate BrainBiC’s superior performance in identifying functional subgraphs that correlate with cognitive function and symptom severity and support biologically informed subtyping. These findings highlight the utility of biclustering as a scalable tool for neuroimaging analysis and offer a promising direction for data-driven precision psychiatry in schizophrenia and beyond. Future work will explore extending the framework to longitudinal datasets, integrating multi-modal imaging and genetic data, and applying the approach to early diagnosis, prognosis, and individualized treatment planning. As neuroimaging datasets expand in scale and complexity, such integrative, unsupervised learning approaches will be instrumental in unraveling the neural basis of complex brain disorders and informing personalized clinical interventions.

Author contributions

Md Abdur Rahaman and Vince Calhoun designed the framework for deep biclustering using an auto-encoder framework. Rogers Silva also helped with the idea of brain edge clustering and shaped the framework. Md Abdur Rahaman ran the experiments and drafted the manuscript. Zening Fu and Armin Iraji helped preprocess the datasets and edit the manuscript. Vince Calhoun supervised the progress of the project, thoroughly edited the paper, and gave valuable feedback on the results. All authors have approved the final version of the submission.

Data availability

In this study, we conducted experiments using four different datasets. Three of these–COBRE, fBIRN, and MPRC–are internal datasets available upon request from the respective study sites and corresponding authors. The details regarding data access can be found in the referenced studies. Additionally, we utilized a publicly available benchmark dataset, the Autism Brain Imaging Data Exchange (ABIDE), which can be accessed at https://fcon_1000.projects.nitrc.org/indi/abide/. The demographic characteristics and acquisition protocols for these datasets are described in prior studies mentioned in the data preprocessing section of the manuscript. The supplementary materials provide further methodological details, including spatial maps and general brain decomposition methods. The ”Data Preprocessing” section of the manuscript provides information regarding brain templates and preprocessing steps. For convenience, we have included the spatial maps used in generating sFNC in the supplementary materials. The codebase is implemented in Python 3.12.0, with deep learning models developed using PyTorch. The complete code, including scripts for model definition, training, and evaluation, is available at https://github.com/A-Rahaman/BrainBiC. Model training, evaluation, and inference were conducted on a high-performance computing cluster equipped with NVIDIA GeForce GTX TITAN X (12GB) GPUs. The corresponding author is available for further clarification for any inquiries regarding the dataset or methodology.

Declarations

Competing interests

The authors declare no competing interests.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-025-18007-9.