Analyzing Dynamical Brain Functional Connectivity as Trajectories on Space of Covariance Matrices

Bayesian estimation of covariate assisted principal regression for brain functional connectivity

This paper presents a Bayesian reformulation of covariate-assisted principal regression for covariance matrix outcomes to identify low-dimensional components in the covariance associated with covariates. By introducing a geometric approach to the covariance matrices and leveraging Euclidean geometry, we estimate dimension reduction parameters and model covariance heterogeneity based on covariates. This method enables joint estimation and uncertainty quantification of relevant model parameters associated with heteroscedasticity. We demonstrate our approach through simulation studies and apply it to analyze associations between covariates and brain functional connectivity using data from the Human Connectome Project.

Tensor-CSPNet: A Novel Geometric Deep Learning Framework for Motor Imagery Classification

Deep learning (DL) has been widely investigated in a vast majority of applications in electroencephalography (EEG)-based brain-computer interfaces (BCIs), especially for motor imagery (MI) classification in the past five years. The mainstream DL methodology for the MI-EEG classification exploits the temporospatial patterns of EEG signals using convolutional neural networks (CNNs), which have been particularly successful in visual images. However, since the statistical characteristics of visual images depart radically from EEG signals, a natural question arises whether an alternative network architecture exists apart from CNNs. To address this question, we propose a novel geometric DL (GDL) framework called Tensor-CSPNet, which characterizes spatial covariance matrices derived from EEG signals on symmetric positive definite (SPD) manifolds and fully captures the temporospatiofrequency patterns using existing deep neural networks on SPD manifolds, integrating with experiences from many successful MI-EEG classifiers to optimize the framework. In the experiments, Tensor-CSPNet attains or slightly outperforms the current state-of-the-art performance on the cross-validation and holdout scenarios in two commonly used MI-EEG datasets. Moreover, the visualization and interpretability analyses also exhibit the validity of Tensor-CSPNet for the MI-EEG classification. To conclude, in this study, we provide a feasible answer to the question by generalizing the DL methodologies on SPD manifolds, which indicates the start of a specific GDL methodology for the MI-EEG classification.

Accounting for temporal variability in functional magnetic resonance imaging improves prediction of intelligence

Neuroimaging-based prediction methods for intelligence have seen a rapid development. Among different neuroimaging modalities, prediction using functional connectivity (FC) has shown great promise. Most literature has focused on prediction using static FC, with limited investigations on the merits of such analysis compared to prediction using dynamic FC or region-level functional magnetic resonance imaging (fMRI) times series that encode temporal variability. To account for the temporal dynamics in fMRI, we propose a bi-directional long short-term memory (bi-LSTM) approach that incorporates feature selection mechanism. The proposed pipeline is implemented via an efficient algorithm and applied for predicting intelligence using region-level time series and dynamic FC. We compare the prediction performance using different fMRI features acquired from the Adolescent Brain Cognitive Development (ABCD) study involving nearly 7000 individuals. Our detailed analysis illustrates the consistently inferior performance of static FC compared to region-level time series or dynamic FC for single and combined rest and task fMRI experiments. The joint analysis of task and rest fMRI leads to improved intelligence prediction under all models compared to using fMRI from only one experiment. In addition, the proposed bi-LSTM pipeline based on region-level time series identifies several shared and differential important brain regions across fMRI experiments that drive intelligence prediction. A test-retest analysis of the selected regions shows strong reliability across cross-validation folds. Given the large sample size of ABCD study, our results provide strong evidence that superior prediction of intelligence can be achieved by accounting for temporal variations in fMRI.

A Similarity Measure-Based Approach Using RS-fMRI Data for Autism Spectrum Disorder Diagnosis

Autism spectrum disorder (ASD) is a lifelong neurological disease, which seriously reduces the patients' life quality. Generally, an early diagnosis is beneficial to improve ASD children's life quality. Current methods based on samples from multiple sites for ASD diagnosis perform poorly in generalization due to the heterogeneity of the data from multiple sites. To address this problem, this paper presents a similarity measure-based approach for ASD diagnosis. Specifically, the few-shot learning strategy is used to measure potential similarities in the RS-fMRI data distributions, and, furthermore, a similarity function for samples from multiple sites is trained to enhance the generalization. On the ABIDE database, the presented approach is compared to some representative methods, such as SVM and random forest, in terms of accuracy, precision, and F1 score. The experimental results show that the experimental indicators of the proposed method are better than those of the comparison methods to varying degrees. For example, the accuracy on the TRINITY site is more than 5% higher than that of the comparison method, which clearly proves that the presented approach achieves a better generalization performance than the compared methods.

Uncovering shape signatures of resting-state functional connectivity by geometric deep learning on Riemannian manifold

Functional neural activities manifest geometric patterns, as evidenced by the evolving network topology of functional connectivities (FC) even in the resting state. In this work, we propose a novel manifold‐based geometric neural network for functional brain networks (called “Geo‐Net4Net” for short) to learn the intrinsic low‐dimensional feature representations of resting‐state brain networks on the Riemannian manifold. This tool allows us to answer the scientific question of how the spontaneous fluctuation of FC supports behavior and cognition. We deploy a set of positive maps and rectified linear unit (ReLU) layers to uncover the intrinsic low‐dimensional feature representations of functional brain networks on the Riemannian manifold taking advantage of the symmetric positive‐definite (SPD) form of the correlation matrices. Due to the lack of well‐defined ground truth in the resting state, existing learning‐based methods are limited to unsupervised methodologies. To go beyond this boundary, we propose to self‐supervise the feature representation learning of resting‐state functional networks by leveraging the task‐based counterparts occurring before and after the underlying resting state. With this extra heuristic, our Geo‐Net4Net allows us to establish a more reasonable understanding of resting‐state FCs by capturing the geometric patterns (aka. spectral/shape signature) associated with resting states on the Riemannian manifold. We have conducted extensive experiments on both simulated data and task‐based functional resonance magnetic imaging (fMRI) data from the Human Connectome Project (HCP) database, where our Geo‐Net4Net not only achieves more accurate change detection results than other state‐of‐the‐art counterpart methods but also yields ubiquitous geometric patterns that manifest putative insights into brain function.

Constructing Multi-view High-order Functional Connectivity Networks for Diagnosis of Autism Spectrum Disorder

Brain functional connectivity network (FCN) based on resting-state functional magnetic resonance imaging (rs-fMRI) has been widely used to identify neuropsychiatric disorders such as autism spectrum disorder (ASD). Most existing FCN-based methods only estimate the correlation between brain regions of in terest (ROIs), without exploring more informative higher-level inter actions among multiple ROIs which could be beneficial to disease diagnosis. To fully explore the discriminative information provided by different brain networks, a cluster-based multi-view high-order FCN (Ho-FCN) framework is proposed in this paper. Specifically, we first group the functional connectivity (FC) time series into different clusters and compute the multi-order central moment series for the FC time series in each cluster. Then we utilize the correlation of central moment series between different clusters to reveal the high-order FC relationships among multiple ROIs. In addition, to address the phase mismatch issue in conventional FCNs, we also adopt the central moments of the correlation time series as the temporal-invariance features to capture the dynamic characteristics of low-order dynamic FCN (Lo-D-FCN). Experimental results on the ABIDE dataset validate that: 1) the proposed multi-view Ho-FCNs is able to explore rich discriminative information for ASD diagnosis; 2) the phase mismatch issue can be well circumvented by using central moments; and 3) the combination of different types of FCNs can significantly improve the diagnostic accuracy of ASD (86.2%).

Learning Brain Functional Networks with Latent Temporal Dependency for MCI Identification

AbstractResting-state functional magnetic resonance imaging (rs-fMRI) has become a popular non-invasive way of diagnosing neurological disorders or their early stages by probing functional connectivity between different brain regions of interest (ROIs) across subjects. In the past decades, researchers have proposed many methods to estimate brain functional networks (BFNs) based on blood-oxygen-level-dependent (BOLD) signals captured by rs-fMRI. However, most of the existing methods estimate BFNs under the assumption that signals are independently sampled, which ignores the temporal dependency and sequential order of different time points (or volumes). To address this problem, in this paper, we first propose a novel BFN estimation model by introducing a latent variable to control the sequence of volumes for encoding the temporal dependency and sequential information of signals into the estimated BFNs. Then, we develop an efficient learning algorithm to solve the proposed model by the alternating optimization scheme. To verify the effectiveness of the proposed method, the estimated BFNs are used to identify subjects with mild cognitive impairment (MCIs) from normal controls (NCs). Experimental results show that our method outperforms the baseline methods in the sense of classification performance.

Learning Common Harmonic Waves on Stiefel Manifold - A New Mathematical Approach for Brain Network Analyses

Converging evidence shows that disease-relevant brain alterations do not appear in random brain locations, instead, their spatial patterns follow large-scale brain networks. In this context, a powerful network analysis approach with a mathematical foundation is indispensable to understand the mechanisms of neuropathological events as they spread through the brain. Indeed, the topology of each brain network is governed by its native harmonic waves, which are a set of orthogonal bases derived from the Eigen-system of the underlying Laplacian matrix. To that end, we propose a novel connectome harmonic analysis framework that provides enhanced mathematical insights by detecting frequency-based alterations relevant to brain disorders. The backbone of our framework is a novel manifold algebra appropriate for inference across harmonic waves. This algebra overcomes the limitations of using classic Euclidean operations on irregular data structures. The individual harmonic differences are measured by a set of common harmonic waves learned from a population of individual Eigen-systems, where each native Eigen-system is regarded as a sample drawn from the Stiefel manifold. Specifically, a manifold optimization scheme is tailored to find the common harmonic waves, which reside at the center of the Stiefel manifold. To that end, the common harmonic waves constitute a new set of neurobiological bases to understand disease progression. Each harmonic wave exhibits a unique propagation pattern of neuropathological burden spreading across brain networks. The statistical power of our novel connectome harmonic analysis approach is evaluated by identifying frequency-based alterations relevant to Alzheimer's disease, where our learning-based manifold approach discovers more significant and reproducible network dysfunction patterns than Euclidean methods.

Re-visiting Riemannian geometry of symmetric positive definite matrices for the analysis of functional connectivity

Common representations of functional networks of resting state fMRI time series, including covariance, precision, and cross-correlation matrices, belong to the family of symmetric positive definite (SPD) matrices forming a special mathematical structure called Riemannian manifold. Due to its geometric properties, the analysis and operation of functional connectivity matrices may well be performed on the Riemannian manifold of the SPD space. Analysis of functional networks on the SPD space takes account of all the pairwise interactions (edges) as a whole, which differs from the conventional rationale of considering edges as independent from each other. Despite its geometric characteristics, only a few studies have been conducted for functional network analysis on the SPD manifold and inference methods specialized for connectivity analysis on the SPD manifold are rarely found. The current study aims to show the significance of connectivity analysis on the SPD space and introduce inference algorithms on the SPD manifold, such as regression analysis of functional networks in association with behaviors, principal geodesic analysis, clustering, state transition analysis of dynamic functional networks and statistical tests for network equality on the SPD manifold. We applied the proposed methods to both simulated data and experimental resting state fMRI data from the human connectome project and argue the importance of analyzing functional networks under the SPD geometry. All the algorithms for numerical operations and inferences on the SPD manifold are implemented as a MATLAB library, called SPDtoolbox, for public use to expediate functional network analysis on the right geometry.