Learning meaningful latent representations from nonlinear fMRI data remains a fundamental challenge in neuroimaging analysis. Traditional independent component analysis, widely used due to its ability to estimate interpretable functional brain networks, relies on a linear mixing assumption for latent sources, limiting its ability to capture the inherently nonlinear and complex organization of brain dynamics. More recently, deep representation learning methods have emerged as promising alternatives for modeling nonlinear latent structure. However, many of these approaches have been evaluated primarily on simulated datasets or natural image benchmarks, with comparatively limited validation on real-world neuroimaging data such as fMRI. In this work, we are motivated by the β-TCVAE (Total Correlation Variational Autoencoder), a refinement of the β-VAE framework for learning latent representations without introducing additional hyperparameters during training. We adapt and modify this model to fMRI data for nonlinear source disentanglement, aiming to separate mixed spatial and temporal brain signals into interpretable components. We show that the β-TCVAE framework can recover meaningful nonlinear spatial components with biological relevance, including well-established intrinsic connectivity networks such as the default mode network. Furthermore, we evaluate the learned representations using functional network connectivity, showing that the latent structure captures coherent and interpretable brain organization patterns. This study provides a pilot investigation that bridges nonlinear representation learning and fMRI analysis.

Low-dimensional manifolds underlie mental and cognitive representations, and characterizing individual differences is critical to neuropsychiatric research. Existing manifold learning methods either distort subject-specific features through population-level alignment or limit cross-subject comparisons with individualized models. We introduce a scalable, subject-specific manifold learning framework with two modules: one capturing individual spatial variation via individualized spatial weights, and an efficient variant reducing computational cost with minimal performance loss. Simulations show that population-level alignment distorts manifold geometry, whereas our approach preserves subject-specific structure. Applied to movie-watching fMRI, our modules improve behavioral label recovery and reconstruction accuracy. In clinical resting-state fMRI, the efficient module identifies individualized spatial activation patterns highlighting sensorimotor, learning, and emotion-related regions. Further validation on an independent resting-state dataset demonstrates 95% test-retest identification accuracy. Together, these results show our framework is robust, reproducible, and broadly applicable across computational neuroscience and clinical research. Individualized manifold learning for neuroimaging enables subject-specific optimization while preserving cross-subject correspondence, capturing individual neural variation within a shared modeling space for meaningful group comparison.

Individual brain parcellation is vital for understanding individual variability and advancing precision neuroscience. However, existing deep learning parcellation methods often lack principled seed selection and overlook neuroscientific priors such as inter-hemispheric homotopy. To address these limitations, we propose a submodular-homotopic atlas parcellation encoder (SHAPE) with contrastive learning. To address seed selection, SHAPE applies submodular optimization on supervoxels to identify homotopic seed pairs, ensuring cross-subject correspondence. To integrate neuroscientific priors, SHAPE introduces a homotopic contrastive learning strategy within a graph convolutional network, embedding inter-hemispheric symmetry into node representations. A competitive region growing algorithm is used to generate the final individualized parcellations. Results show that SHAPE outperforms existing methods in functional homogeneity, clustering validity, and sensitivity to individual variability across multiple parcellation scales. Ablation studies confirm the contributions of key components. Overall, SHAPE establishes a principled and neuroscientifically grounded framework for individualized brain parcellation, bridging the gap between data-driven learning and biological plausibility.

Analyzing multi-subject functional magnetic resonance imaging (fMRI) data requires methods that can jointly capture shared and individual patterns of brain activity across participants. Joint blind source separation (JBSS) techniques, such as independent vector analysis (IVA), provide a principled framework for this purpose by modeling dependencies across subjects while identifying distinct functional networks. Constrained IVA variants, including adaptive-reverse cIVA-G (ar-cIVA-G) and threshold-free cIVA-G (tf-cIVA-G), further enhance interpretability through the use of reference templates and inter-subject correlation constraints. Alternatively, regression-based methods like IVA-G regression (regIVA-G) and reference-guided component analysis (RGCA) process subjects individually, aligning their components to references with improved computational efficiency. Despite their potential, systematic evaluations of reference-based JBSS approaches for fMRI analysis remain limited. In this work, we present a comparative study of these methods to assess their capacity for identifying schizophrenia-related biomarkers using real fMRI data from subjects with schizophrenia and healthy controls. Our results demonstrate that both constrained IVA and regression-based methods effectively extract meaningful biomarkers while the latter achieve comparable performance at substantially reduced computational cost.

Multimodal neuroimaging has shown promise for improving the diagnosis of brain disorders. However, its clinical applicability is often limited by incomplete data due to high acquisition costs, equipment constraints, or patient compliance. Existing strategies, such as data imputation and knowledge distillation, suffer from noise propagation and poor adaptability to diverse missing modality scenarios. To overcome these challenges, we propose a novel MultiBranch and Multi-Task Learning (MBMT) framework that leverages hard parameter sharing (HPS) to enhance knowledge transfer and incorporates feature disentanglement (FD) to effectively separate specific and common representations, reducing redundancy and noise while enabling complementary multimodal integration. Results showed that MBMT achieved superior performance on autism diagnostic tasks with varying levels of modality incompleteness, demonstrating its effectiveness and robustness. Ablation studies further confirmed that both HPS and FD contributed to the overall model performance. Collectively, MBMT provides a reliable and effective solution for handling incomplete data in multimodal fusion.

The brain exhibits dynamic coordination of amplitude across networks that supports emerging cognitive abilities and may drive overall cognitive development, yet how these dynamics differ by sex and relate to cognition in late childhood remains unclear. Using resting-state fMRI from 2,000 healthy 9- to 11-year-olds in the ABCD study, we applied time-resolved dynamic time warping to quantify network amplitude disparity. Clustering revealed three recurring network states: convergent with uniform amplitude distribution, divergent with heterogeneous distribution, and mixed, representing a flexible intermediate balance. Females more often occupied the flexible mixed state, whereas males remained longer in convergent and divergent states. Better cognitive performance was linked to greater time in the mixed state, higher transition rates, and shorter dwell times within individual states, indicating more flexible neural dynamics. These findings suggest that neural flexibility supports cognition in late childhood and that sex differences in dynamic timescale-aligned amplitude coordination emerge before adolescence.

Functional magnetic resonance imaging (fMRI) is widely used in neurobiology studies to investigate brain networks, and large-scale fMRI studies increasingly rely on data pooled from multiple imaging sites to increase sample sizes and statistical power. However, site-related biases from scanner hardware and software can distort functional connectivity measures, inflate false positives, and obscure genuine group differences. While most data preprocessing pipelines ignore this issue, we introduce a framework for detecting the extent of site effects for fMRI data based on the Grassmannian kernel (GK) and correct them through a mean-rotation transformation. The GK quantifies the alignment of datasets’ linear subspaces, that is, the span of possible components within each dataset, thereby capturing systematic site-related variability. We first characterize site-related effect through the distribution of the GK, then apply the mean-rotation transformation to remove site-specific biases. We validate the performance of our site harmonization method using withinsite GK distributions and by performing two-sample t-tests on functional network connectivity (FNC) matrices derived from threshold-free constrained independent vector analysis (tf-cIVA). The GK-based correction improves cross-site consistency and enables more reliable detection of biologically meaningful group differences.

Joint matrix decompositions are widely used to extract useful features from multiple datasets. Multiset Canonical Correlation Analysis (mCCA) is one of the oldest and most established methods among those. Prior work claimed that Independent Vector Analysis (IVA), an extension of Independent Component Analysis (ICA) to multiple datasets, generalizes mCCA and that, under the assumption of orthogonality, the objective function of IVA with a Gaussian model (IVA-G) coincides with that of mCCA using the genvar criterion. We revisit this connection and demonstrate that the main difference between these methods is in fact not orthogonality but deflation, which is inherent to most mCCA objective functions, including genvar. To show this, we introduce orthogonal IVA-G (o-IVA-G) and deflationary orthogonal IVA-G (d-o-IVA-G) and compare them with IVA-G and mCCA-genvar in simulations inspired by the functional Magnetic Resonance Imaging (fMRI) subgroup identification problem. Our results suggest that the all-at-once methods can successfully perform Joint Blind Source Separation (JBSS) in more difficult scenarios and are more statistically efficient than deflationary methods.

A key challenge in neuroscience is inferring relationships between brain structure and function from high-dimensional, multimodal neuroimaging data. While conventional multivariate approaches often simplify statistical assumptions and estimate one-dimensional independent sources shared across modalities, the true relationships between latent sources are likely more complex-statistical dependence may exist both within and between modalities and span more than one dimension per modality. Here, we introduce Multimodal Subspace Independent Vector Analysis (MSIVA), a method for capturing both joint and unique vector sources from multiple data modalities by defining cross-modal and unimodal subspaces with variable dimensions. MSIVA enables flexible estimation of varying-size independent subspaces within modalities and their one-to-one linkage to corresponding subspaces across modalities. Crucially, it captures subject-level variability at the voxel level within independent subspaces, in contrast to traditional methods that share identical independent components across subjects. We evaluated three initialization workflows with five candidate subspace structures in multiple synthetic datasets and two large multimodal neuroimaging datasets, including structural MRI (sMRI) and functional MRI (fMRI). After confirming that MSIVA successfully recovered ground-truth subspace structures in synthetic data, we applied MSIVA to identify latent subspace structures in neuroimaging data. Subsequent subspace-specific canonical correlation analysis, brain-phenotype prediction, and voxelwise brain-age delta analysis revealed that MSIVA sources were strongly associated with multiple phenotype variables, including age, sex, schizophrenia, lifestyle factors, and cognitive functions. Further, we identified modality- and group-specific brain regions related to age (for example, cerebellum, precentral gyrus, and cingulate gyrus in sMRI; occipital lobe and superior frontal gyrus in fMRI), sex (for example, cerebellum in sMRI, frontal lobe in fMRI, and precuneus in both sMRI and fMRI), and schizophrenia (for example, cerebellar, frontal, and insular cortices in sMRI; occipital pole, lingual gyrus, and precuneus in fMRI), shedding light on linked phenotypic and neuropsychiatric biomarkers of brain structure and function.

Independent vector analysis (IVA) has emerged as a powerful tool for fusing and analyzing functional magnetic resonance imaging (fMRI) data. Applying IVA to multi-task fMRI data enhances analytical power by capturing the relationships across different tasks in order to discover their underlying multivariate relationship to one another. Incorporation of prior information into IVA enhances the separability and interpretability of estimated components. In this paper, we demonstrate successful fusion of multi-task fMRI feature data under two settings: constrained IVA and constrained transposed IVA (tIVA). We show that using these methods for fusing multi-task fMRI feature data offers novel ways to improve the quality and interpretability of the analysis. While constrained IVA extracts components linked to distinct brain networks, tIVA reverses the roles of spatial components and subject profiles, enabling flexible analysis of behavioral effects. We apply both methods to a multi-task fMRI dataset of 247 subjects. We demonstrate that for task-based fMRI, structural MRI (sMRI) references provide a better match for task data than resting-state fMRI (rs-fMRI) references, and using sMRI priors improves identification of group differences in task-related networks, such as the sensory-motor network during the Auditory Oddball (AOD) task. Additionally, constrained tIVA allows for targeted investigation of the effects of behavioral variables by applying them individually during the analysis. For instance, by using the letter number sequence subtest, a measure of working memory, as a behavioral constraint in tIVA, we observed significant group differences in the auditory and sensory-motor networks during the AOD task. Results show that the use of two constrained approaches, guided by well-aligned structural and behavioral references, enables a more comprehensive analysis of underlying brain function as modulated by task.

Large-scale functional magnetic resonance imaging (fMRI) datasets provide exciting opportunities for understanding and improving brain health. Data-driven techniques such as independent component analysis (ICA) and independent vector analysis (IVA) have been attractive solutions for multisubject fMRI analysis, as the extraction of functional connectivity networks is the key step in many studies. Constrained versions of ICA and IVA help significantly improve performance and interpretability, but their comparative advantages and the practical impact of their different formulations remain unclear. This work addresses this gap by conducting a comprehensive comparison of three state-of-the-art constrained algorithms: threshold-free constrained IVA (tf-cIVA), adaptive-reverse constrained IVA (ar-cIVA), and adaptive-reverse constrained ICA (ar-cEBM). These methods differ significantly in how they leverage the cross-subject information (joint processing of IVA versus the subject-wise approach of constrained ICA) and in their definitions of the closeness with the references (Lagrangian-based adaptive thresholding versus a threshold-free regularization term). We perform a multidimensional comparison among these methods using multiple metrics such as reproducibility, scalability, alignment with references, connectivity, and consistency on a multi-site fMRI dataset of 429 subjects. Our results reveal replicability across the three methods regarding their spatial correlation with the references and identification of biomarkers, as well as distinct trade-offs in other aspects: tf-cIVA excels in reproducibility and produces highly structured temporal functional network connectivity (FNC), making it a strong candidate for dynamic or connectivity-based analyses. Meanwhile, ar-cIVA demonstrates the greatest sensitivity to group differences in spatial FNC, suggesting its utility for identifying spatial biomarkers. Finally, ar-cEBM, via its subject-wise approach, offers superior computational scalability for large datasets. Surprisingly, despite not jointly modeling cross-subject information, ar-cEBM produces more stable spatial maps across subjects, suggesting its flexible density matching may be more critical for group consistency than the joint-processing framework itself. Therefore, besides providing a complete picture, the work provides practical guidance, indicating that the algorithm choice might depend on the specific research question.

Modeling shared and subject-specific structure in multisubject spatiotemporal data remains challenging, particularly in neuroimaging, where both spatial and temporal patterns exhibit rich variability across subjects. Existing matrix and tensor decompositions provide interpretable factorizations, but rely on fixed multilinear structures or coupling schemes that may limit their flexibility in capturing complex variability. In this work, we introduce a spatiotemporal variational tensor decomposition (ST-VTD) framework that combines a tensor factorization generative model with structured priors to jointly represent spatial maps and temporal dynamics. Spatial factors are regularized to promote a low-rank structure inspired by the LL1 decomposition, while temporal factors are modeled using a learned Long short-term memory (LSTM)-based prior, enabling flexible and adaptive dynamics. Posterior inference is performed using an amortized variational formulation by unrolling iterations of an optimization algorithm, leading to an interpretable and parameter-efficient architecture. The proposed inference framework employs a warm-start strategy based on group independent component analysis, which we found to improve optimization performance. Experiments on a realistic synthetic functional MRI (fMRI) dataset demonstrate that the proposed approach significantly improves latent factor recovery compared with representative classical and probabilistic decomposition benchmarks.

Fine-scale spatial dynamics within functional brain networks manifest as high spatial-frequency variations that conventional independent component analysis (ICA) methods fail to capture. These subtle changes may carry critical information about transient connectivity and disordered brain function. We developed NeuroMark-DyFICA (dynamic frequency-informed ICA), a novel framework to enhance detection of spatiotemporal variability in fMRI data. It integrates three stages: dynamic NeuroMark ICA across sliding windows to estimate time-varying, spatially constrained networks; high-pass spatial filtering to emphasize fine-scale spatial features; and group-level ICA to extract refined dynamic components with subject-specific mixing weights. Unlike prior NeuroMark applications or conventional dynamic ICA, NeuroMark-DyFICA establishes a reproducible latent space of high-frequency dynamics, uniquely capturing transient, fine-scale reconfigurations of network topography. Validation using a controlled 2D simulation demonstrated reliable detection of subtle spatial shifts mimicking pathology, which conventional ICA failed to recover. Applying to resting-state fMRI from schizophrenia patients and healthy controls, multiple networks were estimated. We highlight six representative systems (thalamus, auditory, visual/fusiform, middle frontal, default mode, cerebellum). Results revealed two complementary abnormalities in schizophrenia: an imbalance between inactive and hyper-engaged states and altered convergence among dynamic states. NeuroMark-DyFICA reveals fine-grained spatiotemporal disruptions in brain networks, offering mechanistic insights and potential biomarkers for psychiatric disorders.

Independent Vector Analysis (IVA) is a widely used technique for multi-subject fMRI analysis. To guide the decomposition and increase the interpretability of the extracted components, constrained IVA methods incorporate prior information, also known as references, into the model to guide the solution towards those. In this context, threshold-free constrained IVA (tf-cIVA) avoids the difficult issue of threshold selection by leveraging the structure of IVA and using a regularization term to encourage correlation with the corresponding component and penalize all cross-component correlations. Although it is shown to provide desirable performance, the strategy in tf-cIVA can suppress correlations between brain networks within the same functional domain, contrary to the expected neurobiological behavior. In this work, we propose a domain-informed tf-cIVA (ditf-cIVA) that defines a regularization term to selectively preserve the correlation within brain domains. We compare our method with tf-cIVA on a resting-state fMRI dataset of 58 healthy controls and 58 schizophrenia patients. Our findings demonstrate that ditfcIVA produces a more modular spatial functional network connectivity structure, yields more consistent component estimations as measured by higher one-sample t-values, and shows increased sensitivity in detecting significant group differences between the two cohorts.

Blind source separation, particularly through independent component analysis (ICA), is widely utilized across various signal processing domains for disentangling underlying components from observed mixed signals, owing to its fully data-driven nature that minimizes reliance on prior assumptions. However, conventional ICA methods rely on an assumption of linear mixing, limiting their ability to capture complex nonlinear relationships and to maintain robustness in noisy environments. In this work, we present deep deterministic nonlinear independent component analysis (DDICA), a novel deep neural network-based framework designed to address these limitations. DDICA leverages a matrix-based entropy function to directly optimize the independence criterion via stochastic gradient descent, bypassing the need for variational approximations or adversarial schemes. This results in a streamlined training process and improved resilience to noise. We validated the effectiveness and generalizability of DDICA across a range of applications, including simulated signal mixtures, hyperspectral image unmixing, modeling of primary visual receptive fields, and resting-state functional magnetic resonance imaging (fMRI) data analysis. Experimental results demonstrate that DDICA effectively separates independent components with high accuracy across a range of applications. These findings suggest that DDICA offers a robust and versatile solution for blind source separation in diverse signal processing tasks.

Multiset Canonical Correlation Analysis (mCCA), also called Generalized Canonical Correlation Analysis (GCCA), is a technique to identify correlated variables across multiple datasets, which can be used for feature extraction in fields like neuroscience, cross-language information retrieval, and recommendation systems, among others. Besides its wide use, there is still a lack of comprehensive understanding of its theory and implementation with different objective functions all under one umbrella. In this paper, we review the five main mCCA methods: sumcor, maxvar, minvar, genvar, and ssqcor. We provide a concise overview of their optimization problems along with their solutions and pseudocodes. After this, we discuss the application of mCCA for estimating underlying latent components in the Joint Blind Source Separation (JBSS) problem and propose the source identification conditions of the different mCCA methods, i.e., the conditions under which they are able to achieve JBSS. We substantiate the proposed theoretical conditions with numerical results and test the statistical efficiency of the methods for finite samples. We observe in our experiments that genvar appears to have the least restrictive source identification conditions and to be more statistically efficient than the other methods. This suggests that genvar is generally the best-performing mCCA method for JBSS except for special cases, which is an important finding, as the most commonly used mCCA methods are maxvar and sumcor.

Resting-state fMRI has been widely used to investigate the neurobiology of psychiatric disorders. However, analyzing large-scale fMRI data poses significant challenges due to data complexity and subject heterogeneity. Independent vector analysis (IVA) has been effectively utilized to identify biomarkers and detect homogeneous subgroups in resting-state fMRI data. Compared to other joint blind source separation methods like group ICA, IVA preserves subject variability by incorporating multivariate information across subjects. However, the computational cost of IVA increases exponentially with the number of subjects, limiting its applicability to large-scale datasets. In this paper, we propose a regression-assisted framework for large-scale resting-state fMRI analysis. This framework addresses the computational limitations of traditional blind source separation algorithms, such as IVA, by leveraging results from multilinear regression as an initialization for constrained IVA, while maintaining strong source separation performance. Additionally, we introduce the coreset selection method, which enables efficient and deterministic selection of a representative subset of data. We apply the proposed framework to 352 subjects from the B-SNIP study. The results demonstrate its advantages in preserving subject variability, reducing computational costs, and producing more reproducible estimation results. Clinically, the framework detects significant and reproducible differences in functional network interactions between healthy controls and schizophrenia patients across multiple brain regions. Notably, it identifies abnormal interactions between the dorsolateral prefrontal cortex and the dorsal posterior cingulate cortex, aligning with previous clinical research. These findings suggest that the proposed framework has the potential to serve as a valuable biomarker detection tool for various psychiatric disorders.