Graph Autoencoders for Embedding Learning in Brain Networks and Major Depressive Disorder Identification.

Brain functional connectivity (FC) networks inferred from functional magnetic resonance imaging (fMRI) have shown altered or aberrant brain functional connectome in various neuropsychiatric disorders. Recent application of deep neural networks to connectome-based classification mostly relies on traditional convolutional neural networks (CNNs) using input FCs on a regular Euclidean grid to learn spatial maps of brain networks neglecting the topological information of the brain networks, leading to potentially sub-optimal performance in brain disorder identification. We propose a novel graph deep learning framework that leverages non-Euclidean information inherent in the graph structure for classifying brain networks in major depressive disorder (MDD). We introduce a novel graph autoencoder (GAE) architecture, built upon graph convolutional networks (GCNs), to embed the topological structure and node content of large fMRI networks into low-dimensional representations. For constructing the brain networks, we employ the Ledoit-Wolf (LDW) shrinkage method to efficiently estimate high-dimensional FC metrics from fMRI data. We explore both supervised and unsupervised techniques for graph embedding learning. The resulting embeddings serve as feature inputs for a deep fully-connected neural network (FCNN) to distinguish MDD from healthy controls (HCs). Evaluating our model on resting-state fMRI MDD dataset, we observe that the GAE-FCNN outperforms several state-of-the-art methods for brain connectome classification, achieving the highest accuracy when using LDW-FC edges as node features. The graph embeddings of fMRI FC networks also reveal significant group differences between MDD and HCs. Our framework demonstrates the feasibility of learning graph embeddings from brain networks, providing valuable discriminative information for diagnosing brain disorders.

Brain waves spectral analysis of human responses to odorous and non-odorous substances: a preliminary study.

OBJECTIVE: The aim of this study was to identify the potential electrophysiological biomarkers of human responses by comparing the electroencephalogram brain wave changes towards lavender versus normal saline in a healthy human population. METHOD: This study included a total of 44 participants without subjective olfactory disturbances. Lavender and normal saline were used as the olfactory stimulant and control. Electroencephalogram was recorded and power spectra were analysed by the spectral analysis for each alpha, beta, delta, theta and gamma bandwidth frequency upon exposure to lavender and normal saline independently. RESULTS: The oscillatory brain activities in response to the olfactory stimulant indicated that the lavender smell decreased the beta activity in the left frontal (F7 electrode) and central region (C3 electrode) with a reduction in the gamma activity in the right parietal region (P4 electrode) (p < 0.05). CONCLUSION: Olfactory stimulants result in changes of electrical brain activities in different brain regions, as evidenced by the topographical brain map and spectra analysis of each brain wave.

Separating Stimulus-Induced and Background Components of Dynamic Functional Connectivity in Naturalistic fMRI.

We consider the challenges in extracting stimulus-related neural dynamics from other intrinsic processes and noise in naturalistic functional magnetic resonance imaging (fMRI). Most studies rely on inter-subject correlations (ISC) of low-level regional activity and neglect varying responses in individuals. We propose a novel, data-driven approach based on low-rank plus sparse ( [Formula: see text]) decomposition to isolate stimulus-driven dynamic changes in brain functional connectivity (FC) from the background noise, by exploiting shared network structure among subjects receiving the same naturalistic stimuli. The time-resolved multi-subject FC matrices are modeled as a sum of a low-rank component of correlated FC patterns across subjects, and a sparse component of subject-specific, idiosyncratic background activities. To recover the shared low-rank subspace, we introduce a fused version of principal component pursuit (PCP) by adding a fusion-type penalty on the differences between the columns of the low-rank matrix. The method improves the detection of stimulus-induced group-level homogeneity in the FC profile while capturing inter-subject variability. We develop an efficient algorithm via a linearized alternating direction method of multipliers to solve the fused-PCP. Simulations show accurate recovery by the fused-PCP even when a large fraction of FC edges are severely corrupted. When applied to natural fMRI data, our method reveals FC changes that were time-locked to auditory processing during movie watching, with dynamic engagement of sensorimotor systems for speech-in-noise. It also provides a better mapping to auditory content in the movie than ISC.

Detecting Dynamic Community Structure in Functional Brain Networks Across Individuals: A Multilayer Approach.

OBJECTIVE: We present a unified statistical framework for characterizing community structure of brain functional networks that captures variation across individuals and evolution over time. Existing methods for community detection focus only on single-subject analysis of dynamic networks; while recent extensions to multiple-subjects analysis are limited to static networks. METHOD: To overcome these limitations, we propose a multi-subject, Markov-switching stochastic block model (MSS-SBM) to identify state-related changes in brain community organization over a group of individuals. We first formulate a multilayer extension of SBM to describe the time-dependent, multi-subject brain networks. We develop a novel procedure for fitting the multilayer SBM that builds on multislice modularity maximization which can uncover a common community partition of all layers (subjects) simultaneously. By augmenting with a dynamic Markov switching process, our proposed method is able to capture a set of distinct, recurring temporal states with respect to inter-community interactions over subjects and the change points between them. RESULTS: Simulation shows accurate community recovery and tracking of dynamic community regimes over multilayer networks by the MSS-SBM. Application to task fMRI reveals meaningful non-assortative brain community motifs, e.g., core-periphery structure at the group level, that are associated with language comprehension and motor functions suggesting their putative role in complex information integration. Our approach detected dynamic reconfiguration of modular connectivity elicited by varying task demands and identified unique profiles of intra and inter-community connectivity across different task conditions. CONCLUSION: The proposed multilayer network representation provides a principled way of detecting synchronous, dynamic modularity in brain networks across subjects.

Clinical interpretations of the effectiveness of changes in body position during aerobic fitness after neurologic injury.

The purpose is to estimate the effectiveness of electrocardiograms during resting and active participation by the differentiation between the electrical activity of the heart while standing and sitting in a resting state. The concern is to identify the electrocardiogram parameters that did not show significant changes within these positions. The electrocardiogram parameters can be considered to be a standard marker for medically compromised patients. The electrocardiogram is recorded in the standing and sitting positions focusing on healthy participants using standard electrode placement of lead-I. Combined lead-I patterns (camel-hump or ST-segment prolongation) are usually seen in neurologic injury or hypothermia patients. The pairwise comparisons of a year data are about 454,400 cycles of sitting and 493,470 cycles of standing data. Thus, it is essential to quantify the nature and magnitude of changes seen in the electrocardiogram with a change of posture from sitting to standing in a healthy individual. This makes the findings of electrocardiogram analysis in this paper interesting in which some parameters (i.e., camel-hump patterns in lead-I) are helpful for clinical interpretations and could be suggestive of neurologic injury.

A Multi-Domain Connectome Convolutional Neural Network for Identifying Schizophrenia From EEG Connectivity Patterns.

OBJECTIVE: We exploit altered patterns in brain functional connectivity as features for automatic discriminative analysis of neuropsychiatric patients. Deep learning methods have been introduced to functional network classification only very recently for fMRI, and the proposed architectures essentially focused on a single type of connectivity measure. METHODS: We propose a deep convolutional neural network (CNN) framework for classification of electroencephalogram (EEG)-derived brain connectome in schizophrenia (SZ). To capture complementary aspects of disrupted connectivity in SZ, we explore combination of various connectivity features consisting of time and frequency-domain metrics of effective connectivity based on vector autoregressive model and partial directed coherence, and complex network measures of network topology. We design a novel multi-domain connectome CNN (MDC-CNN) based on a parallel ensemble of 1D and 2D CNNs to integrate the features from various domains and dimensions using different fusion strategies. We also consider an extension to dynamic brain connectivity using the recurrent neural networks. RESULTS: Hierarchical latent representations learned by the multiple convolutional layers from EEG connectivity reveals apparent group differences between SZ and healthy controls (HC). Results on a large resting-state EEG dataset show that the proposed CNNs significantly outperform traditional support vector machine classifier. The MDC-CNN with combined connectivity features further improves performance over single-domain CNNs using individual features, achieving remarkable accuracy of 91.69% with a decision-level fusion. CONCLUSION: The proposed MDC-CNN by integrating information from diverse brain connectivity descriptors is able to accurately discriminate SZ from HC. SIGNIFICANCE: The new framework is potentially useful for developing diagnostic tools for SZ and other disorders.

A Markov-Switching Model Approach to Heart Sound Segmentation and Classification.

OBJECTIVE: We consider challenges in accurate segmentation of heart sound signals recorded under noisy clinical environments for subsequent classification of pathological events. Existing state-of-the-art solutions to heart sound segmentation use probabilistic models such as hidden Markov models (HMMs), which, however, are limited by its observation independence assumption and rely on pre-extraction of noise-robust features. METHODS: We propose a Markov-switching autoregressive (MSAR) process to model the raw heart sound signals directly, which allows efficient segmentation of the cyclical heart sound states according to the distinct dependence structure in each state. To enhance robustness, we extend the MSAR model to a switching linear dynamic system (SLDS) that jointly model both the switching AR dynamics of underlying heart sound signals and the noise effects. We introduce a novel algorithm via fusion of switching Kalman filter and the duration-dependent Viterbi algorithm, which incorporates the duration of heart sound states to improve state decoding. RESULTS: Evaluated on Physionet/CinC Challenge 2016 dataset, the proposed MSAR-SLDS approach significantly outperforms the hidden semi-Markov model (HSMM) in heart sound segmentation based on raw signals and comparable to a feature-based HSMM. The segmented labels were then used to train Gaussian-mixture HMM classifier for identification of abnormal beats, achieving high average precision of 86.1% on the same dataset including very noisy recordings. CONCLUSION: The proposed approach shows noticeable performance in heart sound segmentation and classification on a large noisy dataset. SIGNIFICANCE: It is potentially useful in developing automated heart monitoring systems for pre-screening of heart pathologies.

Statistical model for dynamically-changing correlation matrices with application to brain connectivity.

BACKGROUND: Recent studies have indicated that functional connectivity is dynamic even during rest. A common approach to modeling the dynamic functional connectivity in whole-brain resting-state fMRI is to compute the correlation between anatomical regions via sliding time windows. However, the direct use of the sample correlation matrices is not reliable due to the image acquisition and processing noises in resting-sate fMRI. NEW METHOD: To overcome these limitations, we propose a new statistical model that smooths out the noise by exploiting the geometric structure of correlation matrices. The dynamic correlation matrix is modeled as a linear combination of symmetric positive-definite matrices combined with cosine series representation. The resulting smoothed dynamic correlation matrices are clustered into disjoint brain connectivity states using the k-means clustering algorithm. RESULTS: The proposed model preserves the geometric structure of underlying physiological dynamic correlation, eliminates unwanted noise in connectivity and obtains more accurate state spaces. The difference in the estimated dynamic connectivity states between males and females is identified. COMPARISON WITH EXISTING METHODS: We demonstrate that the proposed statistical model has less rapid state changes caused by noise and improves the accuracy in identifying and discriminating different states. CONCLUSIONS: We propose a new regression model on dynamically changing correlation matrices that provides better performance over existing windowed correlation and is more reliable for the modeling of dynamic connectivity.

Estimating Dynamic Connectivity States in fMRI Using Regime-Switching Factor Models.

We consider the challenges in estimating the state-related changes in brain connectivity networks with a large number of nodes. Existing studies use the sliding-window analysis or time-varying coefficient models, which are unable to capture both smooth and abrupt changes simultaneously, and rely on ad-hoc approaches to the high-dimensional estimation. To overcome these limitations, we propose a Markov-switching dynamic factor model, which allows the dynamic connectivity states in functional magnetic resonance imaging (fMRI) data to be driven by lower-dimensional latent factors. We specify a regime-switching vector autoregressive (SVAR) factor process to quantity the time-varying directed connectivity. The model enables a reliable, data-adaptive estimation of change-points of connectivity regimes and the massive dependencies associated with each regime. We develop a three-step estimation procedure: 1) extracting the factors using principal component analysis, 2) identifying connectivity regimes in a low-dimensional subspace based on the factor-based SVAR model, and 3) constructing high-dimensional state connectivity metrics based on the subspace estimates. Simulation results show that our estimator outperforms -means clustering of time-windowed coefficients, providing more accurate estimate of time-evolving connectivity. It achieves percentage of reduction in mean squared error by 60% when the network dimension is comparable to the sample size. When applied to the resting-state fMRI data, our method successfully identifies modular organization in the resting-statenetworksin consistencywith other studies. It further reveals changes in brain states with variations across subjects and distinct large-scale directed connectivity patterns across states.

Statistical models for brain signals with properties that evolve across trials.

Most neuroscience cognitive experiments involve repeated presentations of various stimuli across several minutes or a few hours. It has been observed that brain responses, even to the same stimulus, evolve over the course of the experiment. These changes in brain activation and connectivity are believed to be associated with learning and/or habituation. In this paper, we present two general approaches to modeling dynamic brain connectivity using electroencephalograms (EEGs) recorded across replicated trials in an experiment. The first approach is the Markovian regime-switching vector autoregressive model (MS-VAR) which treats EEGs as realizations of an underlying brain process that switches between different states both within a trial and across trials in the entire experiment. The second is the slowly evolutionary locally stationary process (SEv-LSP) which characterizes the observed EEGs as a mixture of oscillatory activities at various frequency bands. The SEv-LSP model captures the dynamic nature of the amplitudes of the band-oscillations and cross-correlations between them. The MS-VAR model is able to capture abrupt changes in the dynamics while the SEv-LSP directly gives interpretable results. Moreover, it is nonparametric and hence does not suffer from model misspecification. For both of these models, time-evolving connectivity metrics in the frequency domain are derived from the model parameters for both functional and effective connectivity. We illustrate these two models for estimating cross-trial connectivity in selective attention using EEG data from an oddball paradigm auditory experiment where the goal is to characterize the evolution of brain responses to target stimuli and to standard tones presented randomly throughout the entire experiment. The results suggest dynamic changes in connectivity patterns over trials with inter-subject variability.

A Unified Estimation Framework for State-Related Changes in Effective Brain Connectivity.

OBJECTIVE: This paper addresses the critical problem of estimating time-evolving effective brain connectivity. Current approaches based on sliding window analysis or time-varying coefficient models do not simultaneously capture both slow and abrupt changes in causal interactions between different brain regions. METHODS: To overcome these limitations, we develop a unified framework based on a switching vector autoregressive (SVAR) model. Here, the dynamic connectivity regimes are uniquely characterized by distinct vector autoregressive (VAR) processes and allowed to switch between quasi-stationary brain states. The state evolution and the associated directed dependencies are defined by a Markov process and the SVAR parameters. We develop a three-stage estimation algorithm for the SVAR model: 1) feature extraction using time-varying VAR (TV-VAR) coefficients, 2) preliminary regime identification via clustering of the TV-VAR coefficients, 3) refined regime segmentation by Kalman smoothing and parameter estimation via expectation-maximization algorithm under a state-space formulation, using initial estimates from the previous two stages. RESULTS: The proposed framework is adaptive to state-related changes and gives reliable estimates of effective connectivity. Simulation results show that our method provides accurate regime change-point detection and connectivity estimates. In real applications to brain signals, the approach was able to capture directed connectivity state changes in functional magnetic resonance imaging data linked with changes in stimulus conditions, and in epileptic electroencephalograms, differentiating ictal from nonictal periods. CONCLUSION: The proposed framework accurately identifies state-dependent changes in brain network and provides estimates of connectivity strength and directionality. SIGNIFICANCE: The proposed approach is useful in neuroscience studies that investigate the dynamics of underlying brain states.

Is First-Order Vector Autoregressive Model Optimal for fMRI Data?

We consider the problem of selecting the optimal orders of vector autoregressive (VAR) models for fMRI data. Many previous studies used model order of one and ignored that it may vary considerably across data sets depending on different data dimensions, subjects, tasks, and experimental designs. In addition, the classical information criteria (IC) used (e.g., the Akaike IC (AIC)) are biased and inappropriate for the high-dimensional fMRI data typically with a small sample size. We examine the mixed results on the optimal VAR orders for fMRI, especially the validity of the order-one hypothesis, by a comprehensive evaluation using different model selection criteria over three typical data types--a resting state, an event-related design, and a block design data set--with varying time series dimensions obtained from distinct functional brain networks. We use a more balanced criterion, Kullback's IC (KIC) based on Kullback's symmetric divergence combining two directed divergences. We also consider the bias-corrected versions (AICc and KICc) to improve VAR model selection in small samples. Simulation results show better small-sample selection performance of the proposed criteria over the classical ones. Both bias-corrected ICs provide more accurate and consistent model order choices than their biased counterparts, which suffer from overfitting, with KICc performing the best. Results on real data show that orders greater than one were selected by all criteria across all data sets for the small to moderate dimensions, particularly from small, specific networks such as the resting-state default mode network and the task-related motor networks, whereas low orders close to one but not necessarily one were chosen for the large dimensions of full-brain networks.

Discriminative tandem features for HMM-based EEG classification.

We investigate the use of discriminative feature extractors in tandem configuration with generative EEG classification system. Existing studies on dynamic EEG classification typically use hidden Markov models (HMMs) which lack discriminative capability. In this paper, a linear and a non-linear classifier are discriminatively trained to produce complementary input features to the conventional HMM system. Two sets of tandem features are derived from linear discriminant analysis (LDA) projection output and multilayer perceptron (MLP) class-posterior probability, before appended to the standard autoregressive (AR) features. Evaluation on a two-class motor-imagery classification task shows that both the proposed tandem features yield consistent gains over the AR baseline, resulting in significant relative improvement of 6.2% and 11.2% for the LDA and MLP features respectively. We also explore portability of these features across different subjects.

Linear dynamic models for classification of single-trial EEG.

This paper investigates the use of linear dynamic models (LDMs) to improve classification of single-trial EEG signals. Existing dynamic classification of EEG uses discrete-state hidden Markov models (HMMs) based on piecewise-stationary assumption, which is inadequate for modeling the highly non-stationary dynamics underlying EEG. The continuous hidden states of LDMs could better describe this continuously changing characteristic of EEG, and thus improve the classification performance. We consider two examples of LDM: a simple local level model (LLM) and a time-varying autoregressive (TVAR) state-space model. AR parameters and band power are used as features. Parameter estimation of the LDMs is performed by using expectation-maximization (EM) algorithm. We also investigate different covariance modeling of Gaussian noises in LDMs for EEG classification. The experimental results on two-class motor-imagery classification show that both types of LDMs outperform the HMM baseline, with the best relative accuracy improvement of 14.8% by LLM with full covariance for Gaussian noises. It may due to that LDMs offer more flexibility in fitting the underlying dynamics of EEG.

Acoustic cardiac signals analysis: a Kalman filter-based approach.

Auscultation of the heart is accompanied by both electrical activity and sound. Heart auscultation provides clues to diagnose many cardiac abnormalities. Unfortunately, detection of relevant symptoms and diagnosis based on heart sound through a stethoscope is difficult. The reason GPs find this difficult is that the heart sounds are of short duration and separated from one another by less than 30 ms. In addition, the cost of false positives constitutes wasted time and emotional anxiety for both patient and GP. Many heart diseases cause changes in heart sound, waveform, and additional murmurs before other signs and symptoms appear. Heart-sound auscultation is the primary test conducted by GPs. These sounds are generated primarily by turbulent flow of blood in the heart. Analysis of heart sounds requires a quiet environment with minimum ambient noise. In order to address such issues, the technique of denoising and estimating the biomedical heart signal is proposed in this investigation. Normally, the performance of the filter naturally depends on prior information related to the statistical properties of the signal and the background noise. This paper proposes Kalman filtering for denoising statistical heart sound. The cycles of heart sounds are certain to follow first-order Gauss-Markov process. These cycles are observed with additional noise for the given measurement. The model is formulated into state-space form to enable use of a Kalman filter to estimate the clean cycles of heart sounds. The estimates obtained by Kalman filtering are optimal in mean squared sense.

An expectation-maximization algorithm based Kalman smoother approach for single-trial estimation of event-related potentials.

This paper applies an expectation-maximization (EM) based Kalman smoother (KS) approach for single-trial event-related potential (ERP) estimation. Existing studies assume a Markov diffusion process for the dynamics of ERP parameters which is recursively estimated by optimal filtering approaches such as Kalman filter (KF). However, these studies only consider estimation of ERP state parameters while the model parameters are pre-specified using manual tuning, which is time-consuming for practical usage besides giving suboptimal estimates. We extend the KF approach by adding EM based maximum likelihood estimation of the model parameters to obtain more accurate ERP estimates automatically. We also introduce different model variants by allowing flexibility in the covariance structure of model noises. Optimal model selection is performed based on Akaike Information Criterion (AIC). The method is applied to estimation of chirp-evoked auditory brainstem responses (ABRs) for detection of wave V critical for assessment of hearing loss. Results shows that use of more complex covariances are better estimating inter-trial variability.

Spectral estimation of nonstationary EEG using particle filtering with application to event-related desynchronization (ERD).

This paper proposes non-Gaussian models for parametric spectral estimation with application to event-related desynchronization (ERD) estimation of nonstationary EEG. Existing approaches for time-varying spectral estimation use time-varying autoregressive (TVAR) state-space models with Gaussian state noise. The parameter estimation is solved by a conventional Kalman filtering. This study uses non-Gaussian state noise to model autoregressive (AR) parameter variation with estimation by a Monte Carlo particle filter (PF). Use of non-Gaussian noise such as heavy-tailed distribution is motivated by its ability to track abrupt and smooth AR parameter changes, which are inadequately modeled by Gaussian models. Thus, more accurate spectral estimates and better ERD tracking can be obtained. This study further proposes a non-Gaussian state space formulation of time-varying autoregressive moving average (TVARMA) models to improve the spectral estimation. Simulation on TVAR process with abrupt parameter variation shows superior tracking performance of non-Gaussian models. Evaluation on motor-imagery EEG data shows that the non-Gaussian models provide more accurate detection of abrupt changes in alpha rhythm ERD. Among the proposed non-Gaussian models, TVARMA shows better spectral representations while maintaining reasonable good ERD tracking performance.