Functional connectivity analysis of fMRI data based on regularized multiset canonical correlation analysis

Contrastive voxel clustering for multiscale modeling of brain network

Resting-state functional magnetic resonance imaging (fMRI) provides an efficient way to analyze the functional connectivity between brain regions. A comprehensive understanding of brain functionality requires a unified description of multi-scale layers of neural structure. However, existing brain network modeling methods often simplify this property by averaging Blood oxygen level dependent (BOLD) signals at the brain region level for fMRI-based analysis with the assumption that BOLD signals are homogeneous within each brain region, which ignores the heterogeneity of voxels within each Region of Interest (ROI). This study introduces a novel multi-stage self-supervised learning framework for multiscale brain network analysis, which effectively delineates brain functionality from voxel to ROIs and up to sample level. A Contrastive Voxel Clustering (CVC) module is proposed to simultaneously learn the voxel-level features and clustering assignments, which ensures the retention of informative clustering features at the finest voxel-level and concurrently preserves functional connectivity characteristics. Additionally, based on the extracted features and clustering assignments at the voxel level by CVC, a Brain ROI-based Graph Neural Network (BR-GNN) is built to extract functional connectivity features at the brain ROI-level and used for sample-level prediction, which integrates the functional clustering maps with the pre-established structural ROI maps and creates a more comprehensive and effective analytical tool. Experiments are performed on two datasets, which illustrate the effectiveness and generalization ability of the proposed method by analyzing voxel-level clustering results and brain ROIs-level functional characteristics. The proposed method provides a multiscale modeling framework for brain functional connectivity analysis, which will be further used for other brain disease identification. Code is available at https://github.com/yanliugroup/fmri-cvc.

fMRI-based spatio-temporal parcellations of the human brain

PURPOSE OF REVIEW

Human brain parcellation based on functional magnetic resonance imaging (fMRI) plays an essential role in neuroscience research. By segmenting vast and intricate fMRI data into functionally similar units, researchers can better decipher the brain's structure in both healthy and diseased states. This article reviews current methodologies and ideas in this field, while also outlining the obstacles and directions for future research.

RECENT FINDINGS

Traditional brain parcellation techniques, which often rely on cytoarchitectonic criteria, overlook the functional and temporal information accessible through fMRI. The adoption of machine learning techniques, notably deep learning, offers the potential to harness both spatial and temporal information for more nuanced brain segmentation. However, the search for a one-size-fits-all solution to brain segmentation is impractical, with the choice between group-level or individual-level models and the intended downstream analysis influencing the optimal parcellation strategy. Additionally, evaluating these models is complicated by our incomplete understanding of brain function and the absence of a definitive "ground truth".

SUMMARY

While recent methodological advancements have significantly enhanced our grasp of the brain's spatial and temporal dynamics, challenges persist in advancing fMRI-based spatio-temporal representations. Future efforts will likely focus on refining model evaluation and selection as well as developing methods that offer clear interpretability for clinical usage, thereby facilitating further breakthroughs in our comprehension of the brain.

Homogeneous-Multiset-CCA-Based Brain Covariation and Contravariance Connectivity Network Modeling

Brain connectivity networks based on functional magnetic resonance imaging (fMRI) have expanded our understanding of brain functions in both healthy and diseased states. However, most current studies construct connectivity networks using averaged regional time courses with the strong assumption that the activities of voxels contained in each brain region are similar, ignoring their possible variations. Additionally, pairwise correlation analysis is often adopted with more attention to positive relationships, while joint interactions at the network level as well as anti-correlations are less investigated. In this paper, to provide a new strategy for regional activity representation and brain connectivity modeling, a novel homogeneous multiset canonical correlation analysis (HMCCA) model is proposed, which enforces sign constraints on the weights of voxels to guarantee homogeneity within each brain region. It is capable of obtaining regional representative signals and constructing covariation and contravariance networks simultaneously, at both group and subject levels. Validations on two sessions of fMRI data verified its reproducibility and reliability when dealing with brain connectivity networks. Further experiments on subjects with and without Parkinson's disease (PD) revealed significant alterations in brain connectivity patterns, which were further associated with clinical scores and demonstrated superior prediction ability, indicating its potential in clinical practice.

Structured sparse multiset canonical correlation analysis of simultaneous fNIRS and EEG provides new insights into the human action-observation network

The action observation network (AON) is a network of brain regions involved in the execution and observation of a given action. The AON has been investigated in humans using mostly electroencephalogram (EEG) and functional magnetic resonance imaging (fMRI), but shared neural correlates of action observation and action execution are still unclear due to lack of ecologically valid neuroimaging measures. In this study, we used concurrent EEG and functional Near Infrared Spectroscopy (fNIRS) to examine the AON during a live-action observation and execution paradigm. We developed structured sparse multiset canonical correlation analysis (ssmCCA) to perform EEG-fNIRS data fusion. MCCA is a generalization of CCA to more than two sets of variables and is commonly used in medical multimodal data fusion. However, mCCA suffers from multi-collinearity, high dimensionality, unimodal feature selection, and loss of spatial information in interpreting the results. A limited number of participants (small sample size) is another problem in mCCA, which leads to overfitted models. Here, we adopted graph-guided (structured) fused least absolute shrinkage and selection operator (LASSO) penalty to mCCA to conduct feature selection, incorporating structural information amongst the variables (i.e., brain regions). Benefitting from concurrent recordings of brain hemodynamic and electrophysiological responses, the proposed ssmCCA finds linear transforms of each modality such that the correlation between their projections is maximized. Our analysis of 21 right-handed participants indicated that the left inferior parietal region was active during both action execution and action observation. Our findings provide new insights into the neural correlates of AON which are more fine-tuned than the results from each individual EEG or fNIRS analysis and validate the use of ssmCCA to fuse EEG and fNIRS datasets.

Extracting BOLD signals based on time-constrained multiset canonical correlation analysis for brain functional network estimation and classification

Brain functional network (BFN), usually estimated from blood oxygen level dependent (BOLD) functional magnetic resonance imaging (fMRI), has been proven to be a powerful tool to study the organization of the brain and discover biomarkers for diagnosis of brain disorders. Prior to BFN estimation and classification, extracting representative BOLD signals from brain regions of interest (ROIs) is a critical step. Traditional extraction methods include averaging, peaking operation and dimensionality reduction, often leading to signal cancellation and information loss. In this paper, we propose a novel method, namely time-constrained multiset canonical correlation analysis (TMCCA), to extract representative BOLD signals for subsequent BFN estimation and classification. Different from traditional methods that equally treat all BOLD signals in a ROI, the proposed method assigns weights to different BOLD signals, and learns the optimal weights to make the extracted representative signals jointly maximize the multiple correlations between ROIs. Importantly, time-constraint is incorporated into our proposed method, which can effectively encode nonlinear relationship among BOLD signals. To evaluate the effectiveness of the proposed method, the extracted BOLD signals is used to estimate BFN and, in turn, identify brain disorders, including mild cognitive impairment (MCI) and autistic spectrum disorder (ASD). Experimental results demonstrate that our proposed TMCCA can lead to better performance than traditional methods.

A technical review of canonical correlation analysis for neuroscience applications

Collecting comprehensive data sets of the same subject has become a standard in neuroscience research and uncovering multivariate relationships among collected data sets have gained significant attentions in recent years. Canonical correlation analysis (CCA) is one of the powerful multivariate tools to jointly investigate relationships among multiple data sets, which can uncover disease or environmental effects in various modalities simultaneously and characterize changes during development, aging, and disease progressions comprehensively. In the past 10 years, despite an increasing number of studies have utilized CCA in multivariate analysis, simple conventional CCA dominates these applications. Multiple CCA-variant techniques have been proposed to improve the model performance; however, the complicated multivariate formulations and not well-known capabilities have delayed their wide applications. Therefore, in this study, a comprehensive review of CCA and its variant techniques is provided. Detailed technical formulation with analytical and numerical solutions, current applications in neuroscience research, and advantages and limitations of each CCA-related technique are discussed. Finally, a general guideline in how to select the most appropriate CCA-related technique based on the properties of available data sets and particularly targeted neuroscience questions is provided.

Independent vector analysis for common subspace analysis: Application to multi-subject fMRI data yields meaningful subgroups of schizophrenia

The extraction of common and distinct biomedical signatures among different populations allows for a more detailed study of the group-specific as well as distinct information of different populations. A number of subspace analysis algorithms have been developed and successfully applied to data fusion, however they are limited to joint analysis of only a couple of datasets. Since subspace analysis is very promising for analysis of multi-subject medical imaging data as well, we focus on this problem and propose a new method based on independent vector analysis (IVA) for common subspace extraction (IVA-CS) for multi-subject data analysis. IVA-CS leverages the strength of IVA in identification of a complete subspace structure across multiple datasets along with an efficient solution that uses only second-order statistics. We propose a subset analysis approach within IVA-CS to mitigate issues in estimation in IVA due to high dimensionality, both in terms of components estimated and the number of datasets. We introduce a scheme to determine a desirable size for the subset that is high enough to exploit the dependence across datasets and is not affected by the high dimensionality issue. We demonstrate the success of IVA-CS in extracting complex subset structures and apply the method to analysis of functional magnetic resonance imaging data from 179 subjects and show that it successfully identifies shared and complementary brain patterns from patients with schizophrenia (SZ) and healthy controls group. Two components with linked resting-state networks are identified to be unique to the SZ group providing evidence of functional dysconnectivity. IVA-CS also identifies subgroups of SZs that show significant differences in terms of their brain networks and clinical symptoms.

Major depressive disorder identification by referenced multiset canonical correlation analysis with clinical scores

A novel method based on multiset canonical correlation analysis (mCCA) and linear discriminant analysis (LDA) is presented to identify the major depressive disorder (MDD). The new method comprises two parts, namely, the mCCA-rreg and sparse LDA models. The mCCA-rreg model extends the classical canonical correlation model to calculate functional connections by restricting the references to a reference space and adding a spatial regularization term. The reference space is used to ensure that the model extracts important components first from several datasets simultaneously by decreasing the importance of the components in which we are uninterested. The spatial regularization term helps in avoiding the multicollinearity and overfitting problems under the low signal-to-noise ratio circumstance. The sparse LDA model extends the classical LDA model to extract a small subset of discriminative classification features by fusing clinical scores. In the real data experiment, we extract two functional connection modes from 45 subjects by the mCCA-rreg model. Then, we construct classifiers to identify the patients with MDD based on the connections selected by the sparse LDA model. The best accuracy is higher than 95%. The results show that the mCCA-rreg model can retrieve the important components characterized by a preassigned reference space and exclude the noise or components of no interest. The sparse LDA model can extract discriminative classification features related to clinical scores.

Analysing linear multivariate pattern transformations in neuroimaging data

Most connectivity metrics in neuroimaging research reduce multivariate activity patterns in regions-of-interests (ROIs) to one dimension, which leads to a loss of information. Importantly, it prevents us from investigating the transformations between patterns in different ROIs. Here, we applied linear estimation theory in order to robustly estimate the linear transformations between multivariate fMRI patterns with a cross-validated ridge regression approach. We used three functional connectivity metrics that describe different features of these voxel-by-voxel mappings: goodness-of-fit, sparsity and pattern deformation. The goodness-of-fit describes the degree to which the patterns in an input region can be described as a linear transformation of patterns in an output region. The sparsity metric, which relies on a Monte Carlo procedure, was introduced in order to test whether the transformation mostly consists of one-to-one mappings between voxels in different regions. Furthermore, we defined a metric for pattern deformation, i.e. the degree to which the transformation rotates or rescales the input patterns. As a proof of concept, we applied these metrics to an event-related fMRI data set consisting of four subjects that has been used in previous studies. We focused on the transformations from early visual cortex (EVC) to inferior temporal cortex (ITC), fusiform face area (FFA) and parahippocampal place area (PPA). Our results suggest that the estimated linear mappings explain a significant amount of response variance in the three output ROIs. The transformation from EVC to ITC shows the highest goodness-of-fit, and those from EVC to FFA and PPA show the expected preference for faces and places as well as animate and inanimate objects, respectively. The pattern transformations are sparse, but sparsity is lower than would have been expected for one-to-one mappings, thus suggesting the presence of one-to-few voxel mappings. The mappings are also characterised by different levels of pattern deformations, thus indicating that the transformations differentially amplify or dampen certain dimensions of the input patterns. While our results are only based on a small number of subjects, they show that our pattern transformation metrics can describe novel aspects of multivariate functional connectivity in neuroimaging data.

A Novel Multilayer Correlation Maximization Model for Improving CCA-Based Frequency Recognition in SSVEP Brain-Computer Interface

Multiset canonical correlation analysis (MsetCCA) has been successfully applied to optimize the reference signals by extracting common features from multiple sets of electroencephalogram (EEG) for steady-state visual evoked potential (SSVEP) recognition in brain-computer interface application. To avoid extracting the possible noise components as common features, this study proposes a sophisticated extension of MsetCCA, called multilayer correlation maximization (MCM) model for further improving SSVEP recognition accuracy. MCM combines advantages of both CCA and MsetCCA by carrying out three layers of correlation maximization processes. The first layer is to extract the stimulus frequency-related information in using CCA between EEG samples and sine-cosine reference signals. The second layer is to learn reference signals by extracting the common features with MsetCCA. The third layer is to re-optimize the reference signals set in using CCA with sine-cosine reference signals again. Experimental study is implemented to validate effectiveness of the proposed MCM model in comparison with the standard CCA and MsetCCA algorithms. Superior performance of MCM demonstrates its promising potential for the development of an improved SSVEP-based brain-computer interface.

Quantifying the Interaction and Contribution of Multiple Datasets in Fusion: Application to the Detection of Schizophrenia

The extraction of information from multiple sets of data is a problem inherent to many disciplines. This is possible by either analyzing the data sets jointly as in data fusion or separately and then combining as in data integration. However, selecting the optimal method to combine and analyze multiset data is an ever-present challenge. The primary reason for this is the difficulty in determining the optimal contribution of each data set to an analysis as well as the amount of potentially exploitable complementary information among data sets. In this paper, we propose a novel classification rate-based technique to unambiguously quantify the contribution of each data set to a fusion result as well as facilitate direct comparisons of fusion methods on real data and apply a new method, independent vector analysis (IVA), to multiset fusion. This classification rate-based technique is used on functional magnetic resonance imaging data collected from 121 patients with schizophrenia and 150 healthy controls during the performance of three tasks. Through this application, we find that though optimal performance is achieved by exploiting all tasks, each task does not contribute equally to the result and this framework enables effective quantification of the value added by each task. Our results also demonstrate that data fusion methods are more powerful than data integration methods, with the former achieving a classification rate of 73.5 % and the latter achieving one of 70.9 %, a difference which we show is significant when all three tasks are analyzed together. Finally, we show that IVA, due to its flexibility, has equivalent or superior performance compared with the popular data fusion method, joint independent component analysis.

Structured and Sparse Canonical Correlation Analysis as a Brain-Wide Multi-Modal Data Fusion Approach

Multi-modal data fusion has recently emerged as a comprehensive neuroimaging analysis approach, which usually uses canonical correlation analysis (CCA). However, the current CCA-based fusion approaches face problems like high-dimensionality, multi-collinearity, unimodal feature selection, asymmetry, and loss of spatial information in reshaping the imaging data into vectors. This paper proposes a structured and sparse CCA (ssCCA) technique as a novel CCA method to overcome the above problems. To investigate the performance of the proposed algorithm, we have compared three data fusion techniques: standard CCA, regularized CCA, and ssCCA, and evaluated their ability to detect multi-modal data associations. We have used simulations to compare the performance of these approaches and probe the effects of non-negativity constraint, the dimensionality of features, sample size, and noise power. The results demonstrate that ssCCA outperforms the existing standard and regularized CCA-based fusion approaches. We have also applied the methods to real functional magnetic resonance imaging (fMRI) and structural MRI data of Alzheimer's disease (AD) patients (n = 34) and healthy control (HC) subjects (n = 42) from the ADNI database. The results illustrate that the proposed unsupervised technique differentiates the transition pattern between the subject-course of AD patients and HC subjects with a p-value of less than 1×10^-6 . Furthermore, we have depicted the brain mapping of functional areas that are most correlated with the anatomical changes in AD patients relative to HC subjects.

A CCA and ICA-Based Mixture Model for Identifying Major Depression Disorder

The fMRI signals are usually filtered before processing and analyzing. This process can result in the loss of information carried by the higher frequency in the low frequency fluctuation. ICA and CCA are two classical methods in fMRI. ICA finds the statistically independent components of the observed data, however these components are usually physiologically uninterpretable without auxiliary procedures. CCA decomposes two sets of data into component pairs in some order, however these components may be mixtures of real signals and noise. In order to obtain statistically independent components and avoid the loss of information in the process of filtering, we propose a mixed model based on ICA and CCA, which does not need to filter the data. It is shown by the experiments that the new model has some advantages compared with the classical ICA and CCA. The components obtained by the new model is statistically independent. The useful information included in the low frequency fluctuation can be preserved. Experiments on synthetic data show satisfying results. As an application, this new model is used to design an algorithm to discriminate the major depressions from normal controls, with encouraging experimental results.

Group Factor Analysis

Factor analysis (FA) provides linear factors that describe the relationships between individual variables of a data set. We extend this classical formulation into linear factors that describe the relationships between groups of variables, where each group represents either a set of related variables or a data set. The model also naturally extends canonical correlation analysis to more than two sets, in a way that is more flexible than previous extensions. Our solution is formulated as a variational inference of a latent variable model with structural sparsity, and it consists of two hierarchical levels: 1) the higher level models the relationships between the groups and 2) the lower models the observed variables given the higher level. We show that the resulting solution solves the group factor analysis (GFA) problem accurately, outperforming alternative FA-based solutions as well as more straightforward implementations of GFA. The method is demonstrated on two life science data sets, one on brain activation and the other on systems biology, illustrating its applicability to the analysis of different types of high-dimensional data sources.

FREQUENCY RECOGNITION IN SSVEP-BASED BCI USING MULTISET CANONICAL CORRELATION ANALYSIS

Canonical correlation analysis (CCA) has been one of the most popular methods for frequency recognition in steady-state visual evoked potential (SSVEP)-based brain–computer interfaces (BCIs). Despite its efficiency, a potential problem is that using pre-constructed sine-cosine waves as the required reference signals in the CCA method often does not result in the optimal recognition accuracy due to their lack of features from the real electro-encephalo-gram (EEG) data. To address this problem, this study proposes a novel method based on multiset canonical correlation analysis (MsetCCA) to optimize the reference signals used in the CCA method for SSVEP frequency recognition. The MsetCCA method learns multiple linear transforms that implement joint spatial filtering to maximize the overall correlation among canonical variates, and hence extracts SSVEP common features from multiple sets of EEG data recorded at the same stimulus frequency. The optimized reference signals are formed by combination of the common features and completely based on training data. Experimental study with EEG data from 10 healthy subjects demonstrates that the MsetCCA method improves the recognition accuracy of SSVEP frequency in comparison with the CCA method and other two competing methods (multiway CCA (MwayCCA) and phase constrained CCA (PCCA)), especially for a small number of channels and a short time window length. The superiority indicates that the proposed MsetCCA method is a new promising candidate for frequency recognition in SSVEP-based BCIs.

Canonical Granger causality between regions of interest

Estimating and modeling functional connectivity in the brain is a challenging problem with potential applications in the understanding of brain organization and various neurological and neuropsychological conditions. An important objective in connectivity analysis is to determine the connections between regions of interest in the brain. However, traditional functional connectivity analyses have frequently focused on modeling interactions between time series recordings at individual sensors, voxels, or vertices despite the fact that a single region of interest will often include multiple such recordings. In this paper, we present a novel measure of interaction between regions of interest rather than individual signals. The proposed measure, termed canonical Granger causality, combines ideas from canonical correlation and Granger causality analysis to yield a measure that reflects directed causality between two regions of interest. In particular, canonical Granger causality uses optimized linear combinations of signals from each region of interest to enable accurate causality measurements from substantially less data compared to alternative multivariate methods that have previously been proposed for this scenario. The optimized linear combinations are obtained using a variation of a technique developed for optimization on the Stiefel manifold. We demonstrate the advantages of canonical Granger causality in comparison to alternative causality measures for a range of different simulated datasets. We also apply the proposed measure to local field potential data recorded in a macaque brain during a visuomotor task. Results demonstrate that canonical Granger causality can be used to identify causal relationships between striate and prestriate cortexes in cases where standard Granger causality is unable to identify statistically significant interactions.