Riemannian Regression and Classification Models of Brain Networks Applied to Autism

Capturing functional connectomics using Riemannian partial least squares

For neurological disorders and diseases, functional and anatomical connectomes of the human brain can be used to better inform targeted interventions and treatment strategies. Functional magnetic resonance imaging (fMRI) is a non-invasive neuroimaging technique that captures spatio-temporal brain function through change in blood-oxygen-level-dependent (BOLD) signals over time. FMRI can be used to study the functional connectome through the functional connectivity matrix; that is, Pearson's correlation matrix between time series from the regions of interest of an fMRI image. One approach to analysing functional connectivity is using partial least squares (PLS), a multivariate regression technique designed for high-dimensional predictor data. However, analysing functional connectivity with PLS ignores a key property of the functional connectivity matrix; namely, these matrices are positive definite. To account for this, we introduce a generalisation of PLS to Riemannian manifolds, called R-PLS, and apply it to symmetric positive definite matrices with the affine invariant geometry. We apply R-PLS to two functional imaging datasets: COBRE, which investigates functional differences between schizophrenic patients and healthy controls, and; ABIDE, which compares people with autism spectrum disorder and neurotypical controls. Using the variable importance in the projection statistic on the results of R-PLS, we identify key functional connections in each dataset that are well represented in the literature. Given the generality of R-PLS, this method has the potential to investigate new functional connectomes in the brain, and with future application to structural data can open up further avenues of research in multi-modal imaging analysis.

An Explainable Geometric-Weighted Graph Attention Network for Identifying Functional Networks Associated with Gait Impairment

One of the hallmark symptoms of Parkinson's Disease (PD) is the progressive loss of postural reflexes, which eventually leads to gait difficulties and balance problems. Identifying disruptions in brain function associated with gait impairment could be crucial in better understanding PD motor progression, thus advancing the development of more effective and personalized therapeutics. In this work, we present an explainable, geometric, weighted-graph attention neural network (xGW-GAT) to identify functional networks predictive of the progression of gait difficulties in individuals with PD. xGW-GAT predicts the multi-class gait impairment on the MDS-Unified PD Rating Scale (MDS-UPDRS). Our computational- and data-efficient model represents functional connectomes as symmetric positive definite (SPD) matrices on a Riemannian manifold to explicitly encode pairwise interactions of entire connectomes, based on which we learn an attention mask yielding individual- and group-level explainability. Applied to our resting-state functional MRI (rs-fMRI) dataset of individuals with PD, xGW-GAT identifies functional connectivity patterns associated with gait impairment in PD and offers interpretable explanations of functional subnetworks associated with motor impairment. Our model successfully outperforms several existing methods while simultaneously revealing clinically-relevant connectivity patterns. The source code is available at https://github.com/favour-nerrise/xGW-GAT.

Tangent functional connectomes uncover more unique phenotypic traits

Functional connectomes (FCs) containing pairwise estimations of functional couplings between pairs of brain regions are commonly represented by correlation matrices. As symmetric positive definite matrices, FCs can be transformed via tangent space projections, resulting into tangent-FCs. Tangent-FCs have led to more accurate models predicting brain conditions or aging. Motivated by the fact that tangent-FCs seem to be better biomarkers than FCs, we hypothesized that tangent-FCs have also a higher fingerprint. We explored the effects of six factors: fMRI condition, scan length, parcellation granularity, reference matrix, main-diagonal regularization, and distance metric. Our results showed that identification rates are systematically higher when using tangent-FCs across the "fingerprint gradient" (here including test-retest, monozygotic and dizygotic twins). Highest identification rates were achieved when minimally (0.01) regularizing FCs while performing tangent space projection using Riemann reference matrix and using correlation distance to compare the resulting tangent-FCs. Such configuration was validated in a second dataset (resting-state).

An Explainable Geometric-Weighted Graph Attention Network for Identifying Functional Networks Associated with Gait Impairment

One of the hallmark symptoms of Parkinson's Disease (PD) is the progressive loss of postural reflexes, which eventually leads to gait difficulties and balance problems. Identifying disruptions in brain function associated with gait impairment could be crucial in better understanding PD motor progression, thus advancing the development of more effective and personalized therapeutics. In this work, we present an explainable, geometric, weighted-graph attention neural network (xGW-GAT) to identify functional networks predictive of the progression of gait difficulties in individuals with PD. xGW-GAT predicts the multi-class gait impairment on the MDS-Unified PD Rating Scale (MDS-UPDRS). Our computational- and data-efficient model represents functional connectomes as symmetric positive definite (SPD) matrices on a Riemannian manifold to explicitly encode pairwise interactions of entire connectomes, based on which we learn an attention mask yielding individual- and group-level explain-ability. Applied to our resting-state functional MRI (rs-fMRI) dataset of individuals with PD, xGW-GAT identifies functional connectivity patterns associated with gait impairment in PD and offers interpretable explanations of functional subnetworks associated with motor impairment. Our model successfully outperforms several existing methods while simultaneously revealing clinically-relevant connectivity patterns. The source code is available at https://github.com/favour-nerrise/xGW-GAT.

Discovering functional connectivity features characterizing multiple sclerosis phenotypes using explainable artificial intelligence

Multiple sclerosis (MS) is a neurological condition characterized by severe structural brain damage and by functional reorganization of the main brain networks that try to limit the clinical consequences of structural burden. Resting-state (RS) functional connectivity (FC) abnormalities found in this condition were shown to be variable across different MS phases, according to the severity of clinical manifestations. The article describes a system exploiting machine learning on RS FC matrices to discriminate different MS phenotypes and to identify relevant functional connections for MS stage characterization. To this end, the system exploits some mathematical properties of covariance-based RS FC representation, which can be described by a Riemannian manifold. The classification performance of the proposed framework was significantly above the chance level for all MS phenotypes. Moreover, the proposed system was successful in identifying relevant RS FC alterations contributing to an accurate phenotype classification.

Exploring high-order correlations with deep-broad learning for autism spectrum disorder diagnosis

Recently, a lot of research has been conducted on diagnosing neurological disorders, such as autism spectrum disorder (ASD). Functional magnetic resonance imaging (fMRI) is the commonly used technique to assist in the diagnosis of ASD. In the past years, some conventional methods have been proposed to extract the low-order functional connectivity network features for ASD diagnosis, which ignore the complexity and global features of the brain network. Most deep learning-based methods generally have a large number of parameters that need to be adjusted during the learning process. To overcome the limitations mentioned above, we propose a novel deep-broad learning method for learning the higher-order brain functional connectivity network features to assist in ASD diagnosis. Specifically, we first construct the high-order functional connectivity network that describes global correlations of the brain regions based on hypergraph, and then we use the deep-broad learning method to extract the high-dimensional feature representations for brain networks sequentially. The evaluation of the proposed method is conducted on Autism Brain Imaging Data Exchange (ABIDE) dataset. The results show that our proposed method can achieve 71.8% accuracy on the multi-center dataset and 70.6% average accuracy on 17 single-center datasets, which are the best results compared with the state-of-the-art methods. Experimental results demonstrate that our method can describe the global features of the brain regions and get rich discriminative information for the classification task.

A Riemannian Revisiting of Structure-Function Mapping Based on Eigenmodes

Understanding the link between brain structure and function may not only improve our knowledge of brain organization, but also lead to better quantification of pathology. To quantify this link, recent studies have attempted to predict the brain's functional connectivity from its structural connectivity. However, functional connectivity matrices live in the Riemannian manifold of the symmetric positive definite space and a specific attention must be paid to operate on this appropriate space. In this work we investigated the implications of using a distance based on an affine invariant Riemannian metric in the context of structure-function mapping. Specifically, we revisit previously proposed structure-function mappings based on eigendecomposition and test them on 100 healthy subjects from the Human Connectome Project using this adapted notion of distance. First, we show that using this Riemannian distance significantly alters the notion of similarity between subjects from a functional point of view. We also show that using this distance improves the correlation between the structural and functional similarity of different subjects. Finally, by using a distance appropriate to this manifold, we demonstrate the importance of mapping function from structure under the Riemannian manifold and show in particular that it is possible to outperform the group average and the so-called glass ceiling on the performance of mappings based on eigenmodes.

rs-fMRI and machine learning for ASD diagnosis: a systematic review and meta-analysis

Autism Spectrum Disorder (ASD) diagnosis is still based on behavioral criteria through a lengthy and time-consuming process. Much effort is being made to identify brain imaging biomarkers and develop tools that could facilitate its diagnosis. In particular, using Machine Learning classifiers based on resting-state fMRI (rs-fMRI) data is promising, but there is an ongoing need for further research on their accuracy and reliability. Therefore, we conducted a systematic review and meta-analysis to summarize the available evidence in the literature so far. A bivariate random-effects meta-analytic model was implemented to investigate the sensitivity and specificity across the 55 studies that offered sufficient information for quantitative analysis. Our results indicated overall summary sensitivity and specificity estimates of 73.8% and 74.8%, respectively. SVM stood out as the most used classifier, presenting summary estimates above 76%. Studies with bigger samples tended to obtain worse accuracies, except in the subgroup analysis for ANN classifiers. The use of other brain imaging or phenotypic data to complement rs-fMRI information seems promising, achieving higher sensitivities when compared to rs-fMRI data alone (84.7% versus 72.8%). Finally, our analysis showed AUC values between acceptable and excellent. Still, given the many limitations indicated in our study, further well-designed studies are warranted to extend the potential use of those classification algorithms to clinical settings.

TE-HI-GCN: An Ensemble of Transfer Hierarchical Graph Convolutional Networks for Disorder Diagnosis

Accurate diagnosis of psychiatric disorders plays a critical role in improving the quality of life for patients and potentially supports the development of new treatments. Graph convolutional networks (GCNs) are shown to be successful in modeling applications with graph structures. However, training an accurate GCNs model for brain networks faces several challenges, including high dimensional and noisy correlation in the brain networks, limited labeled training data, and depth limitation of GCN learning. Generalization and interpretability are important in developing predictive models for clinical diagnosis. To address these challenges, we proposed an ensemble framework involving hierarchical GCN and transfer learning for sparse brain networks, which allows GCN to capture the intrinsic correlation among the subjects and domains, to improve the network embedding learning for disease diagnosis. Extensive experiments on two real medical clinical applications: diagnosis of Autism spectrum disorder (ASD) and diagnosis of Alzheimer's disease (AD) on both the ADNI and ABIDE databases, showing the effectiveness of the proposed framework. We achieved state-of-the-art accuracy and AUC for AD/MCI and ASD/NC (Normal control) classification in comparison with studies that used functional connectivity as features or GCN models. The proposed TE-HI-GCN model achieves the best classification performance, leading to about 27.93% (31.38%) improvement for ASD and 16.86% (44.50%) for AD in terms of accuracy and AUC compared with the traditional GCN model. Moreover, the obtained clustering results show high correspondence with the previous neuroimaging derived evidence of within and between-networks biomarkers for ASD. The discovered subnetworks are used as evidence for the proposed TE-HI-GCN model. Furthermore, this work is the first attempt of transfer learning on the two related disorder domains to uncover the correlation among the two diseases with a transfer learning scheme.

Predicting cognitive scores with graph neural networks through sample selection learning

Analyzing the relation between intelligence and neural activity is of the utmost importance in understanding the working principles of the human brain in health and disease. In existing literature, functional brain connectomes have been used successfully to predict cognitive measures such as intelligence quotient (IQ) scores in both healthy and disordered cohorts using machine learning models. However, existing methods resort to flattening the brain connectome (i.e., graph) through vectorization which overlooks its topological properties. To address this limitation and inspired from the emerging graph neural networks (GNNs), we design a novel regression GNN model (namely RegGNN) for predicting IQ scores from brain connectivity. On top of that, we introduce a novel, fully modular sample selection method to select the best samples to learn from for our target prediction task. However, since such deep learning architectures are computationally expensive to train, we further propose a learning-based sample selection method that learns how to choose the training samples with the highest expected predictive power on unseen samples. For this, we capitalize on the fact that connectomes (i.e., their adjacency matrices) lie in the symmetric positive definite (SPD) matrix cone. Our results on full-scale and verbal IQ prediction outperforms comparison methods in autism spectrum disorder cohorts and achieves a competitive performance for neurotypical subjects using 3-fold cross-validation. Furthermore, we show that our sample selection approach generalizes to other learning-based methods, which shows its usefulness beyond our GNN architecture.

Diagnosis of Autism Spectrum Disorder Based on Functional Brain Networks with Deep Learning

Autism spectrum disorder (ASD) is a neurological and developmental disorder. Traditional diagnosis of ASD is typically performed through the observation of behaviors and interview of a patient. However, these diagnosis methods are time-consuming and can be misleading sometimes. Integrating machine learning algorithms with neuroimages, a diagnosis method, can possibly be established to detect ASD subjects from typical control subjects. In this study, we develop deep learning methods for diagnosis of ASD from functional brain networks constructed with brain functional magnetic resonance imaging (fMRI) data. The entire Autism Brain Imaging Data Exchange 1 (ABIDE 1) data set is utilized to investigate the performance of our proposed methods. First, we construct the brain networks from brain fMRI images and define the raw features based on such brain networks. Second, we employ an autoencoder (AE) to learn the advanced features from the raw features. Third, we train a deep neural network (DNN) with the advanced features, which achieves the classification accuracy of 76.2% and the receiving operating characteristic curve (AUC) of 79.7%. As a comparison, we also apply the same advanced features to train several traditional machine learning algorithms to benchmark the classification performance. Finally, we combine the DNN with the pretrained AE and train it with the raw features, which achieves the classification accuracy of 79.2% and the AUC of 82.4%. These results show that our proposed deep learning methods outperform the state-of-the-art methods.

Towards a brain-based predictome of mental illness

Neuroimaging-based approaches have been extensively applied to study mental illness in recent years and have deepened our understanding of both cognitively healthy and disordered brain structure and function. Recent advancements in machine learning techniques have shown promising outcomes for individualized prediction and characterization of patients with psychiatric disorders. Studies have utilized features from a variety of neuroimaging modalities, including structural, functional, and diffusion magnetic resonance imaging data, as well as jointly estimated features from multiple modalities, to assess patients with heterogeneous mental disorders, such as schizophrenia and autism. We use the term "predictome" to describe the use of multivariate brain network features from one or more neuroimaging modalities to predict mental illness. In the predictome, multiple brain network-based features (either from the same modality or multiple modalities) are incorporated into a predictive model to jointly estimate features that are unique to a disorder and predict subjects accordingly. To date, more than 650 studies have been published on subject-level prediction focusing on psychiatric disorders. We have surveyed about 250 studies including schizophrenia, major depression, bipolar disorder, autism spectrum disorder, attention-deficit hyperactivity disorder, obsessive-compulsive disorder, social anxiety disorder, posttraumatic stress disorder, and substance dependence. In this review, we present a comprehensive review of recent neuroimaging-based predictomic approaches, current trends, and common shortcomings and share our vision for future directions.