Estimation of connectional brain templates using selective multi-view network normalization

The brain connectome encodes different facets of the brain construct such as function and structure in a network. Noting that a brain network captures the individual signature of a particular subject, it remains a formidable challenge to extract a shared and representative brain signature across a population of brain networks, let alone multi-view brain networks. In this paper, we propose netNorm, a method that can meet this challenge by normalizing a population of multi-view brain networks, where each brain network represents a particular view of the brain, acquired using a neuroimaging technique. While conventional methods integrate the network views equally at a global scale, we propose a selective technique which unfolds the fusion process at a local scale by first selecting for each local pairwise connectivity between two anatomical regions of interest the most representative cross-view feature vector in the population. By combining the selected cross-view feature vectors, we then estimate a population representative tensor. Such multi-view representation captures the most shared traits across all subjects and thereby occupies a centered location compared to all views. In the final step, netNorm non-linearly fuses the frontal views of the estimated representative population tensor into a single network depicting the final brain connectional template. We demonstrate the broad applicability of our method on four connectomic datasets and we show that netNorm (i) produces the most centered and representative connectional brain template (CBT) that consistently captures the unique and distinctive traits of a population of multi-view brain networks, and (ii) identifies disordered brain connections by comparing templates estimated using disordered and healthy brains, respectively, demonstrating the discriminative power of the estimated CBTs. This allows to rapidly and efficiently spot atypical deviations from the normal brain connectome for comparative studies, circumventing the need to use machine learning techniques for discriminative feature identification.     

Comparative survey of multigraph integration methods for holistic brain connectivity mapping

One of the greatest scientific challenges in network neuroscience is to create a representative map of a population of heterogeneous brain networks, which acts as a connectional fingerprint. The connectional brain template (CBT), also named network atlas, presents a powerful tool for capturing the most representative and discriminative traits of a given population while preserving its topological patterns. The idea of a CBT is to integrate a population of heterogeneous brain connectivity networks, derived from different neuroimaging modalities or brain views (e.g., structural and functional), into a unified holistic representation. Here we review current state-of-the-art methods designed to estimate well-centered and representative CBT for populations of single-view and multi-view brain networks. We start by reviewing each CBT learning method, then we introduce the evaluation measures to compare CBT representativeness of populations generated by single-view and multigraph integration methods, separately, based on the following criteria: Centeredness, biomarker-reproducibility, node-level similarity, global-level similarity, and distance-based similarity. We demonstrate that the deep graph normalizer (DGN) method significantly outperforms other multi-graph and all single-view integration methods for estimating CBTs using a variety of healthy and disordered datasets in terms of centeredness, reproducibility (i.e., graph-derived biomarkers reproducibility that disentangle the typical from the atypical connectivity variability), and preserving the topological traits at both local and global graph-levels.     

Joint functional brain network atlas estimation and feature selection for neurological disorder diagnosis with application to autism

Image-based brain maps, generally coined as ‘intensity or image atlases’, have led the field of brain mapping in health and disease for decades, while investigating a wide spectrum of neurological disorders. Estimating representative brain atlases constitute a fundamental step in several MRI-based neurological disorder mapping, diagnosis, and prognosis. However, these are strikingly lacking in the field of brain connectomics, where connectional brain atlases derived from functional MRI (fRMI) or diffusion MRI (dMRI) are almost absent. On the other hand, conventional connectomic-based classification methods traditionally resort to feature selection methods to decrease the high-dimensionality of connectomic data for learning how to diagnose new patients. However, these are generally limited by high computational cost and a large variability in performance across different datasets, which might hinder the identification of reproducible biomarkers. To address both limitations, we unprecedentedly propose a brain network atlas-guided feature selection (NAG-FS) method to disentangle the healthy from the disordered connectome. To this aim, given a population of brain connectomes, we propose to learn how estimate a centered and representative functional brain network atlas (i.e., a population center) to reliably map the functional connectome and its variability across training individuals, thereby capturing their shared traits (i.e., connectional fingerprint of a population). Essentially, we first learn the pairwise similarities between connectomes in the population to map them into different subspaces. Next, we non-linearly diffuse and fuse connectomes living in each subspace, respectively. By integrating the produced subspace-specific network atlases we ultimately estimate the population network atlas. Last, we compute the difference between healthy and disordered network atlases to identify the most discriminative features, which are then used to train a predictive learner. Our method boosted the classification performance by 6% in comparison to state-of-the-art FS methods when classifying autistic and healthy subjects.     

Signed graph representation learning for functional-to-structural brain network mapping

MRI-derived brain networks have been widely used to understand functional and structural interactions among brain regions, and factors that affect them, such as brain development and diseases. Graph mining on brain networks can facilitate the discovery of novel biomarkers for clinical phenotypes and neurodegenerative diseases. Since brain functional and structural networks describe the brain topology from different perspectives, exploring a representation that combines these cross-modality brain networks has significant clinical implications. Most current studies aim to extract a fused representation by projecting the structural network to the functional counterpart. Since the functional network is dynamic and the structural network is static, mapping a static object to a dynamic object may not be optimal. However, mapping in the opposite direction (i.e., from functional to structural networks) are suffered from the challenges introduced by negative links within signed graphs. Here, we propose a novel graph learning framework, named as Deep Signed Brain Graph Mining or DSBGM, with a signed graph encoder that, from an opposite perspective, learns the cross-modality representations by projecting the functional network to the structural counterpart. We validate our framework on clinical phenotype and neurodegenerative disease prediction tasks using two independent, publicly available datasets (HCP and OASIS). Our experimental results clearly demonstrate the advantages of our model compared to several state-of-the-art methods.     

Reproducibility and intercorrelation of graph theoretical measures in structural brain connectivity networks

Diffusion-weighted magnetic resonance imaging can be used to non-invasively probe the brain microstructure. In addition, recent advances have enabled the identification of complex fiber configurations present in most of the white matter. This has improved the investigation of structural connectivity with tractography methods. Whole-brain structural connectivity networks, or connectomes, are reconstructed by parcellating the gray matter and performing tractography to determine connectivity between these regions. These complex networks can be analyzed with graph theoretical methods, which measure their global and local properties. However, as these tools have only recently been applied to structural brain networks, there is little information about the reproducibility and intercorrelation of network properties, connectivity weights and fiber tractography reconstruction parameters in the brain. We studied the reproducibility and correlation in structural brain connectivity networks reconstructed with constrained spherical deconvolution based probabilistic streamlines tractography. Diffusion-weighted data from 19 subjects were acquired with b = 2800 s/mm² and 75 gradient orientations. Intrasubject variability was computed with residual bootstrapping. Our findings indicate that the reproducibility of graph theoretical metrics is generally excellent with the exception of betweenness centrality. A reconstruction density of approximately one million streamlines is necessary for excellent reproducibility, but the reproducibility increases further with higher densities. The reproducibility decreases, but only slightly, when switching to a higher order in constrained spherical deconvolution. Moreover, in binary networks, using sufficiently high threshold values improves the reproducibility. We show that multiple network properties and connectivity weights are highly intercorrelated. The experiments were replicated by using a test-retest dataset of 44 healthy subjects provided by the Human Connectome Project. In conclusion, our results provide guidelines for reproducible investigation of structural brain networks.     

Disease prediction with edge-variational graph convolutional networks

The need for computational models that can incorporate imaging data with non-imaging data while investigating inter-subject associations arises in the task of population-based disease analysis. Although off-the-shelf deep convolutional neural networks have empowered representation learning from imaging data, incorporating data of different modalities complementarily in a unified model to improve the disease diagnostic quality is still challenging. In this work, we propose a generalizable graph-convolutional framework for population-based disease prediction on multi-modal medical data. Unlike previous methods constructing a static affinity population graph in a hand-crafting manner, the proposed framework can automatically learn to build a population graph with variational edges, which we show can be optimized jointly with spectral graph convolutional networks. In addition, to estimate the predictive uncertainty related to the constructed graph, we propose Monte–Carlo edge dropout uncertainty estimation. Experimental results on four multi-modal datasets demonstrate that the proposed method can substantially improve the predictive accuracy for Autism Spectrum Disorder, Alzheimer’s disease, and ocular diseases. A sufficient ablation study with in-depth discussion is conducted to evaluate the effectiveness of each component and the choice of algorithmic details of the proposed method. The results indicate the potential and extendability of the proposed framework in leveraging multi-modal data for population-based disease prediction.     

Adversarial brain multiplex prediction from a single brain network with application to gender fingerprinting

Brain connectivity networks, derived from magnetic resonance imaging (MRI), non-invasively quantify the relationship in function, structure, and morphology between two brain regions of interest (ROIs) and give insights into gender-related connectional differences. However, to the best of our knowledge, studies on gender differences in brain connectivity were limited to investigating pairwise (i.e., low-order) relationships across ROIs, overlooking the complex high-order interconnectedness of the brain as a network. A few recent works on neurological disorders addressed this limitation by introducing the brain multiplex which is composed of a source network intra-layer, a target intra-layer, and a convolutional interlayer capturing the high-level relationship between both intra-layers. However, brain multiplexes are built from at least two different brain networks hindering their application to connectomic datasets with single brain networks (e.g., functional networks). To fill this gap, we propose Adversarial Brain Multiplex Translator (ABMT), the first work for predicting brain multiplexes from a source network using geometric adversarial learning to investigate gender differences in the human brain. Our framework comprises: (i) a geometric source to target network translator mimicking a U-Net architecture with skip connections, (ii) a conditional discriminator which distinguishes between predicted and ground truth target intra-layers, and finally (iii) a multi-layer perceptron (MLP) classifier which supervises the prediction of the target multiplex using the subject class label (e.g., gender). Our experiments on a large dataset demonstrated that predicted multiplexes significantly boost gender classification accuracy compared with source networks and unprecedentedly identify both low and high-order gender-specific brain multiplex connections. Our ABMT source code is available on GitHub at https://github.com/basiralab/ABMT.     

Enhanced neuroimaging genetics using multi-view non-negative matrix factorization with sparsity and prior knowledge

Neuroimaging genetics is a powerful approach to jointly explore genetic features with rich brain imaging phenotypes for neurodegenerative diseases. Conventional imaging genetics approaches based on canonical correlation analysis cannot accommodate multimodal inputs effectively and have limited interpretability. We propose a novel imaging genetics approach based on non-negative matrix factorization (NMF). By leveraging the parsimonious property known as topic modeling in multi-view NMF, we add sparsity constraints and prior information to identify a sparse set of biologically related features across modalities. Thus, our approach incorporates prior knowledge and improves multimodal integration capabilities and interpretability. We applied our algorithm to simulated and real imaging genetics datasets of Parkinson's disease (PD) for performance evaluation. Our algorithm could identify important associated features mapped to interpretable distinct topics more robustly than other methods. It revealed promising features of single-nucleotide polymorphisms and brain regions related to a subset of PD-related clinical scores in a few topics using a real imaging genetic dataset. The proposed imaging genetics approach can reveal novel associations between genetic and neuroimaging features to improve understanding of various neurodegenerative diseases.     

Weight-conserving characterization of complex functional brain networks

Complex functional brain networks are large networks of brain regions and functional brain connections. Statistical characterizations of these networks aim to quantify global and local properties of brain activity with a small number of network measures. Important functional network measures include measures of modularity (measures of the goodness with which a network is optimally partitioned into functional subgroups) and measures of centrality (measures of the functional influence of individual brain regions). Characterizations of functional networks are increasing in popularity, but are associated with several important methodological problems. These problems include the inability to characterize densely connected and weighted functional networks, the neglect of degenerate topologically distinct high-modularity partitions of these networks, and the absence of a network null model for testing hypotheses of association between observed nontrivial network properties and simple weighted connectivity properties. In this study we describe a set of methods to overcome these problems. Specifically, we generalize measures of modularity and centrality to fully connected and weighted complex networks, describe the detection of degenerate high-modularity partitions of these networks, and introduce a weighted-connectivity null model of these networks. We illustrate our methods by demonstrating degenerate high-modularity partitions and strong correlations between two complementary measures of centrality in resting-state functional magnetic resonance imaging (MRI) networks from the 1000 Functional Connectomes Project, an open-access repository of resting-state functional MRI datasets. Our methods may allow more sound and reliable characterizations and comparisons of functional brain networks across conditions and subjects.     

Modeling the outcome of structural disconnection on resting-state functional connectivity

A growing body of experimental evidence suggests that functional connectivity at rest is shaped by the underlying anatomical structure. Furthermore, the organizational properties of resting-state functional networks are thought to serve as the basis for an optimal cognitive integration. A disconnection at the structural level, as occurring in some brain diseases, would then lead to functional and presumably cognitive impairments. In this work, we propose a computational model to investigate the role of a structural disconnection (encompassing putative local/global and axonal/synaptic mechanisms) on the organizational properties of emergent functional networks. The brain's spontaneous neural activity and the corresponding hemodynamic response were simulated using a large-scale network model, consisting of local neural populations coupled through white matter fibers. For a certain coupling strength, simulations reproduced healthy resting-state functional connectivity with graph properties in the range of the ones reported experimentally. When the structural connectivity is decreased, either globally or locally, the resultant simulated functional connectivity exhibited a network reorganization characterized by an increase in hierarchy, efficiency and robustness, a decrease in small-worldness and clustering and a narrower degree distribution, in the same way as recently reported for schizophrenia patients. Theoretical results indicate that most disconnection-related neuropathologies should induce the same qualitative changes in resting-state brain activity.     

Nucleus classification in histology images using message passing network

Identification of nuclear components in the histology landscape is an important step towards developing computational pathology tools for the profiling of tumor micro-environment. Most existing methods for the identification of such components are limited in scope due to heterogeneous nature of the nuclei. Graph-based methods offer a natural way to formulate the nucleus classification problem to incorporate both appearance and geometric locations of the nuclei. The main challenge is to define models that can handle such an unstructured domain. Current approaches focus on learning better features and then employ well-known classifiers for identifying distinct nuclear phenotypes. In contrast, we propose a message passing network that is a fully learnable framework build on classical network flow formulation. Based on physical interaction of the nuclei, a nearest neighbor graph is constructed such that the nodes represent the nuclei centroids. For each edge and node, appearance and geometric features are computed which are then used for the construction of messages utilized for diffusing contextual information to the neighboring nodes. Such an algorithm can infer global information over an entire network and predict biologically meaningful nuclear communities. We show that learning such communities improves the performance of nucleus classification task in histology images. The proposed algorithm can be used as a component in existing state-of-the-art methods resulting in improved nucleus classification performance across four different publicly available datasets.     

Modeling spatio-temporal patterns of holistic functional brain networks via multi-head guided attention graph neural networks (Multi-Head GAGNNs)

Mounting evidence has demonstrated that complex brain function processes are realized by the interaction of holistic functional brain networks which are spatially distributed across specific brain regions in a temporally dynamic fashion. Therefore, modeling spatio-temporal patterns of holistic functional brain networks plays an important role in understanding brain function. Compared to traditional modeling methods such as principal component analysis, independent component analysis, and sparse coding, superior performance has been achieved by recent deep learning methodologies. However, there are still two limitations of existing deep learning approaches for functional brain network modeling. They either (1) merely modeled a single targeted network and ignored holistic ones at one time, or (2) underutilized both spatial and temporal features of fMRI during network modeling, and the spatial/temporal accuracy was thus not warranted. To address these limitations, we proposed a novel Multi-Head Guided Attention Graph Neural Network (Multi-Head GAGNN) to simultaneously model both spatial and temporal patterns of holistic functional brain networks. Specifically, a spatial Multi-Head Attention Graph U-Net was first adopted to model the spatial patterns of multiple brain networks, and a temporal Multi-Head Guided Attention Network was then introduced to model the corresponding temporal patterns under the guidance of modeled spatial patterns. Based on seven task fMRI datasets from the public Human Connectome Project and resting state fMRI datasets from the public Autism Brain Imaging Data Exchange I of 1448 subjects, the proposed Multi-Head GAGNN showed superior ability and generalizability in modeling both spatial and temporal patterns of holistic functional brain networks in individual brains compared to other state-of-the-art (SOTA) models. Furthermore, the modeled spatio-temporal patterns of functional brain networks via the proposed Multi-Head GAGNN can better predict the individual cognitive behavioral measures compared to the other SOTA models. This study provided a novel and powerful tool for brain function modeling as well as for understanding the brain-cognitive behavior associations.     

Anatomical insights into disrupted small-world networks in schizophrenia

Schizophrenia is characterized by lowered efficiency in distributed information processing, as indicated by research that identified a disrupted small-world functional network. However, whether the dysconnection manifested by the disrupted small-world functional network is reflected in underlying anatomical disruption in schizophrenia remains unresolved. This study examined the topological properties of human brain anatomical networks derived from diffusion tensor imaging in patients with schizophrenia and in healthy controls. We constructed the weighted brain anatomical network for each of 79 schizophrenia patients and for 96 age and gender matched healthy subjects using diffusion tensor tractography and calculated the topological properties of the networks using a graph theoretical method. The topological properties of the patients' anatomical networks were altered, in that global efficiency decreased but local efficiency remained unchanged. The deleterious effects of schizophrenia on network performance appear to be localized as reduced regional efficiency in hubs such as the frontal associative cortices, the paralimbic/limbic regions and a subcortical structure (the left putamen). Additionally, scores on the Positive and Negative Symptom Scale correlated negatively with efficient network properties in schizophrenia. These findings suggest that complex brain network analysis may potentially be used to detect an imaging biomarker for schizophrenia.     

Groupwise registration with global-local graph shrinkage in atlas construction

Graph-based groupwise registration methods are widely used in atlas construction. Given a group of images, a graph is built whose nodes represent the images, and whose edges represent a geodesic path between two nodes. The distribution of images on an image manifold is explored through edge traversal in a graph. The final atlas is a mean image at the population center of the distribution on the manifold. The procedure of warping all images to the mean image turns to dynamic graph shrinkage in which nodes become closer to each other. Most conventional groupwise registration frameworks construct and shrink a graph without considering the local distribution of images on the dataset manifold and the local structure variations between image pairs. Neglecting the local information fundamentally decrease the accuracy and efficiency when population atlases are built for organs with large inter-subject anatomical variabilities. To overcome the problem, this paper proposes a global-local graph shrinkage approach that can generate accurate atlas. A connected graph is constructed automatically based on global similarities across the images to explore the global distribution. A local image distribution obtained by image clustering is used to simplify the edges of the constructed graph. Subsequently, local image similarities refine the deformation estimated through global image similarity for each image warping along the graph edges. Through the image warping, the overall simplified graph shrinks gradually to yield the atlas with respecting both global and local features. The proposed method is evaluated on 61 synthetic and 20 clinical liver datasets, and the results are compared with those of six state-of-the-art groupwise registration methods. The experimental results show that the proposed method outperforms non-global-local method approaches in terms of accuracy.     

RA-GCN: Graph convolutional network for disease prediction problems with imbalanced data

Disease prediction is a well-known classification problem in medical applications. Graph Convolutional Networks (GCNs) provide a powerful tool for analyzing the patients’ features relative to each other. This can be achieved by modeling the problem as a graph node classification task, where each node is a patient. Due to the nature of such medical datasets, class imbalance is a prevalent issue in the field of disease prediction, where the distribution of classes is skewed. When the class imbalance is present in the data, the existing graph-based classifiers tend to be biased towards the major class(es) and neglect the samples in the minor class(es). On the other hand, the correct diagnosis of the rare positive cases (true-positives) among all the patients is vital in a healthcare system. In conventional methods, such imbalance is tackled by assigning appropriate weights to classes in the loss function which is still dependent on the relative values of weights, sensitive to outliers, and in some cases biased towards the minor class(es). In this paper, we propose a Re-weighted Adversarial Graph Convolutional Network (RA-GCN) to prevent the graph-based classifier from emphasizing the samples of any particular class. This is accomplished by associating a graph-based neural network to each class, which is responsible for weighting the class samples and changing the importance of each sample for the classifier. Therefore, the classifier adjusts itself and determines the boundary between classes with more attention to the important samples. The parameters of the classifier and weighting networks are trained by an adversarial approach. We show experiments on synthetic and three publicly available medical datasets. Our results demonstrate the superiority of RA-GCN compared to recent methods in identifying the patient’s status on all three datasets. The detailed analysis of our method is provided as quantitative and qualitative experiments on synthetic datasets.     

On characterizing population commonalities and subject variations in brain networks

Brain networks based on resting state connectivity as well as inter-regional anatomical pathways obtained using diffusion imaging have provided insight into pathology and development. Such work has underscored the need for methods that can extract sub-networks that can accurately capture the connectivity patterns of the underlying population while simultaneously describing the variation of sub-networks at the subject level. We have designed a multi-layer graph clustering method that extracts clusters of nodes, called ‘network hubs’, which display higher levels of connectivity within the cluster than to the rest of the brain. The method determines an atlas of network hubs that describes the population, as well as weights that characterize subject-wise variation in terms of within- and between-hub connectivity. This lowers the dimensionality of brain networks, thereby providing a representation amenable to statistical analyses. The applicability of the proposed technique is demonstrated by extracting an atlas of network hubs for a population of typically developing controls (TDCs) as well as children with autism spectrum disorder (ASD), and using the structural and functional networks of a population to determine the subject-level variation of these hubs and their inter-connectivity. These hubs are then used to compare ASD and TDCs. Our method is generalizable to any population whose connectivity (structural or functional) can be captured via non-negative network graphs.     

Test-retest reliability of resting-state connectivity network characteristics using fMRI and graph theoretical measures

Characterizing the brain connectome using neuroimaging data and measures derived from graph theory emerged as a new approach that has been applied to brain maturation, cognitive function and neuropsychiatric disorders. For a broad application of this method especially for clinical populations and longitudinal studies, the reliability of this approach and its robustness to confounding factors need to be explored. Here we investigated test-retest reliability of graph metrics of functional networks derived from functional magnetic resonance imaging (fMRI) recorded in 33 healthy subjects during rest. We constructed undirected networks based on the Anatomic-Automatic-Labeling (AAL) atlas template and calculated several commonly used measures from the field of graph theory, focusing on the influence of different strategies for confound correction. For each subject, method and session we computed the following graph metrics: clustering coefficient, characteristic path length, local and global efficiency, assortativity, modularity, hierarchy and the small-worldness scalar. Reliability of each graph metric was assessed using the intraclass correlation coefficient (ICC).Overall ICCs ranged from low to high (0 to 0.763) depending on the method and metric. Methodologically, the use of a broader frequency band (0.008-0.15 Hz) yielded highest reliability indices (mean ICC = 0.484), followed by the use of global regression (mean ICC = 0.399). In general, the second order metrics (small-worldness, hierarchy, assortativity) studied here, tended to be more robust than first order metrics.In conclusion, our study provides methodological recommendations which allow the computation of sufficiently robust markers of network organization using graph metrics derived from fMRI data at rest.     

Multiple Lesions Insertion: boosting diabetic retinopathy screening through Poisson editing

Deep neural networks have made incredible progress in many computer vision tasks, owing to access to a great amount of data. However, collecting ground truth for large medical image datasets is extremely inconvenient and difficult to implement in practical applications, due to high professional requirements. Synthesizing can generate meaningful supplement samples to enlarge the insufficient medical image dataset. In this study, we propose a new data augmentation method, Multiple Lesions Insertion (MLI), to simulate new diabetic retinopathy (DR) fundus images based on the healthy fundus images that insert real lesions, such as exudates, hemorrhages, microaneurysms templates, into new healthy fundus images with Poisson editing. The synthetic fundus images can be generated according to the clinical rules, i.e., in different DR grading fundus images, the number of exudates, hemorrhages, microaneurysms are different. The generated DR fundus images by our MLI method are realistic with the real texture features and rich details, without black spots, artifacts, and discontinuities. We first demonstrate the feasibility of this method in a DR computer-aided diagnosis (CAD) system, which judges whether the patient has transferred treatment or not. Our results indicate that the MLI method outperforms most of the traditional augmentation methods, i.e, oversampling, under-sampling, cropping, rotation, and adding other real sample methods in the DR screening task.     

Manifold learning on brain functional networks in aging

We propose a new analysis framework to utilize the full information of brain functional networks for computing the mean of a set of brain functional networks and embedding brain functional networks into a low-dimensional space in which traditional regression and classification analyses can be easily employed. For this, we first represent the brain functional network by a symmetric positive matrix computed using sparse inverse covariance estimation. We then impose a Log-Euclidean Riemannian manifold structure on brain functional networks whose norm gives a convenient and practical way to define a mean. Finally, based on the fact that the computation of linear operations can be done in the tangent space of this Riemannian manifold, we adopt Locally Linear Embedding (LLE) to the Log-Euclidean Riemannian manifold space in order to embed the brain functional networks into a low-dimensional space. We show that the integration of the Log-Euclidean manifold with LLE provides more efficient and succinct representation of the functional network and facilitates regression analysis, such as ridge regression, on the brain functional network to more accurately predict age when compared to that of the Euclidean space of functional networks with LLE. Interestingly, using the Log-Euclidean analysis framework, we demonstrate the integration and segregation of cortical–subcortical networks as well as among the salience, executive, and emotional networks across lifespan.