Visibility graphs for fMRI data: Multiplex temporal graphs and their modulations across resting-state networks

Network Representation of fMRI Data Using Visibility Graphs: The Impact of Motion and Test-Retest Reliability

Visibility graphs provide a novel approach for analysing time-series data. Graph theoretical analysis of visibility graphs can provide new features for data mining applications in fMRI. However, visibility graphs features have not been used widely in the field of neuroscience. This is likely due to a lack of understanding of their robustness in the presence of noise (e.g., motion) and their test-retest reliability. In this study, we investigated visibility graph properties of fMRI data in the human connectome project (N = 1010) and tested their sensitivity to motion and test-retest reliability. We also characterised the strength of connectivity obtained using degree synchrony of visibility graphs. We found that strong correlation (r > 0.5) between visibility graph properties, such as the number of communities and average degrees, and motion in the fMRI data. The test-retest reliability (Intraclass correlation coefficient (ICC)) of graph theoretical features was high for the average degrees (0.74, 95% CI = [0.73, 0.75]), and moderate for clustering coefficient (0.43, 95% CI = [0.41, 0.44]) and average path length (0.41, 95% CI = [0.38, 0.44]). Functional connectivity between brain regions was measured by correlating the visibility graph degrees. However, the strength of correlation was found to be moderate to low (r < 0.35). These findings suggest that even small movement in fMRI data can strongly influence robustness and reliability of visibility graph features, thus, requiring robust motion correction strategies prior to data analysis. Further studies are necessary for better understanding of the potential application of visibility graph features in fMRI.

Daylight Saving Time transitions and Cardiovascular Disease in Andalusia: Time Series Modeling and Analysis Using Visibility Graphs

The present study aimed to determine whether transitions both to and from daylight saving time (DST) led to an increase in the incidence of hospital admissions for major acute cardiovascular events (MACE). To support the analysis, natural visibility graphs (NVGs) were used with data from Andalusian public hospitals between 2009 and 2019. We calculated the incidence rates of hospital admissions for MACE, and specifically acute myocardial infarction and ischemic stroke during the 2 weeks leading up to, and 2 weeks after, the DST transition. NVG were applied to identify dynamic patterns. The study included 157 221 patients diagnosed with MACE, 71 992 with AMI (42 975 ST-elevation myocardial infarction (STEMI) and 26 752 non-ST-elevation myocardial infarction (NSTEMI)), and 51 420 with ischemic stroke. Observed/expected ratios shown an increased risk of AMI (1.06; 95% CI (1.00-1.11); P = .044), NSTEMI (1.12; 95% CI (1.02-1.22); P = .013), and acute coronary syndrome (1.05; 95% CI (1.00-1.10); P = .04) around the autumn DST. The NVG showed slight variations in the daily pattern of pre-DST and post-DST hospitalization admissions for all pathologies, but indicated that the increase in the incidence of hospital admissions after the DST is not sufficient to change the normal pattern significantly.

Visibility graph analysis for brain: scoping review

In the past two decades, network-based analysis has garnered considerable attention for analyzing time series data across various fields. Time series data can be transformed into graphs or networks using different methods, with the visibility graph (VG) being a widely utilized approach. The VG holds extensive applications in comprehending, identifying, and predicting specific characteristics of time series data. Its practicality extends to domains such as medicine, economics, meteorology, tourism, and others. This research presents a scoping review of scholarly articles published in reputable English-language journals and conferences, focusing on VG-based analysis methods related to brain disorders. The aim is to provide a foundation for further and future research endeavors, beginning with an introduction to the VG and its various types. To achieve this, a systematic search and refinement of relevant articles were conducted in two prominent scientific databases: Google Scholar and Scopus. A total of 51 eligible articles were selected for a comprehensive analysis of the topic. These articles categorized based on publication year, type of VG used, rationale for utilization, machine learning algorithms employed, frequently occurring keywords, top authors and universities, evaluation metrics, applied network properties, and brain disorders examined, such as Epilepsy, Alzheimer's disease, Autism, Alcoholism, Sleep disorders, Fatigue, Depression, and other related conditions. Moreover, there are recommendations for future advancements in research, which involve utilizing cutting-edge techniques like graph machine learning and deep learning. Additionally, the exploration of understudied medical conditions such as attention deficit hyperactivity disorder and Parkinson's disease is also suggested.

Environmental pollution in North-Eastern Italy and its influence on chronic obstructive pulmonary disease: time series modelling and analysis using visibility graphs

The impact on human health from environmental pollution is receiving increasing attention. In the case of respiratory diseases such as chronic obstructive pulmonary disease (COPD), the relationship is now well documented. However, few studies have been carried out in areas with low population density and low industrial production, such as the province of Belluno (North-Eastern Italy). The aim of the study was to analyze the effect of exposure to certain pollutants on the temporal dynamics of hospital admissions for COPD in the province of Belluno. Daily air pollution concentration, humidity, precipitations, and temperature were collected from the air monitoring stations in Belluno. Generalized additive mixed models (GAMM) and visibility graphs were used to determine the effects of the short-term exposure to environmental agents on hospital admissions associated to COPD. In the case of the city of Belluno, the GAMM showed that hospital admissions were associated with NO₂, PM₁₀, date, and temperature, while for the city of Feltre, GAMM produced no associated variables. Several visibility graph indices (average edge overlap and interlayer mutual information) showed a significant overlap between environmental agents and hospital admission for both cities. Our study has shown that visibility graphs can be useful in establishing associations between environmental agents and COPD hospitalization in sparsely populated areas.

Network Analysis of Time Series: Novel Approaches to Network Neuroscience

In the last two decades, there has been an explosion of interest in modeling the brain as a network, where nodes correspond variously to brain regions or neurons, and edges correspond to structural or statistical dependencies between them. This kind of network construction, which preserves spatial, or structural, information while collapsing across time, has become broadly known as "network neuroscience." In this work, we provide an alternative application of network science to neural data: network-based analysis of non-linear time series and review applications of these methods to neural data. Instead of preserving spatial information and collapsing across time, network analysis of time series does the reverse: it collapses spatial information, instead preserving temporally extended dynamics, typically corresponding to evolution through some kind of phase/state-space. This allows researchers to infer a, possibly low-dimensional, "intrinsic manifold" from empirical brain data. We will discuss three methods of constructing networks from nonlinear time series, and how to interpret them in the context of neural data: recurrence networks, visibility networks, and ordinal partition networks. By capturing typically continuous, non-linear dynamics in the form of discrete networks, we show how techniques from network science, non-linear dynamics, and information theory can extract meaningful information distinct from what is normally accessible in standard network neuroscience approaches.

Automated sleep state classification of wide-field calcium imaging data via multiplex visibility graphs and deep learning

BACKGROUND

Wide-field calcium imaging (WFCI) allows for monitoring of cortex-wide neural dynamics in mice. When applied to the study of sleep, WFCI data are manually scored into the sleep states of wakefulness, non-REM (NREM) and REM by use of adjunct EEG and EMG recordings. However, this process is time-consuming and often suffers from low inter- and intra-rater reliability and invasiveness. Therefore, an automated sleep state classification method that operates on WFCI data alone is needed.

NEW METHOD

A hybrid, two-step method is proposed. In the first step, spatial-temporal WFCI data is mapped to multiplex visibility graphs (MVGs). Subsequently, a two-dimensional convolutional neural network (2D CNN) is employed on the MVGs to be classified as wakefulness, NREM and REM.

RESULTS

Sleep states were classified with an accuracy of 84% and Cohen's κ of 0.67. The method was also effectively applied on a binary classification of wakefulness/sleep (accuracy=0.82, κ = 0.62) and a four-class wakefulness/sleep/anesthesia/movement classification (accuracy=0.74, κ = 0.66). Gradient-weighted class activation maps revealed that the CNN focused on short- and long-term temporal connections of MVGs in a sleep state-specific manner. Sleep state classification performance when using individual brain regions was highest for the posterior area of the cortex and when cortex-wide activity was considered.

COMPARISON WITH EXISTING METHOD

On a 3-hour WFCI recording, the MVG-CNN achieved a κ of 0.65, comparable to a κ of 0.60 corresponding to the human EEG/EMG-based scoring.

CONCLUSIONS

The hybrid MVG-CNN method accurately classifies sleep states from WFCI data and will enable future sleep-focused studies with WFCI.

Cuff-less Blood Pressure Estimation from Photoplethysmography via Visibility Graph and Transfer Learning

This paper presents a new solution that enables the use of transfer learning for cuff-less blood pressure (BP) monitoring via short duration of photoplethysmogram (PPG). The proposed method estimates BP with low computational budget by 1) creating images from segments of PPG via visibility graph (VG) that preserves the temporal information of the PPG waveform, 2) using pre-trained deep convolutional neural network (CNN) to extract feature vectors from VG images, and 3) solving for the weights and bias between the feature vectors and the reference BPs with ridge regression. Using the University of California Irvine (UCI) database consisting of 348 records, the proposed method achieves a best error performance of 0.008.46 mmHg for systolic blood pressure (SBP), and -0.045.36 mmHg for diastolic blood pressure (DBP), respectively, in terms of the mean error (ME) and the standard deviation (SD) of error, ranking grade B for SBP and grade A for DBP under the British Hypertension Society (BHS) protocol. Our novel data-driven method offers a computationally-efficient end-to-end solution for rapid and user-friendly cuff-less PPG-based BP estimation.

Cuff-Less Blood Pressure Estimation via Small Convolutional Neural Networks

Deep learning-based cuff-less blood pressure (BP) estimation methods have recently gained increased attention as they can provide accurate BP estimation with only one physiological signal as input. In this paper, we present a simple and effective method for cuff-less BP estimation by training a small-scale convolutional neural network (CNN), modified from LeNet-5, with images created from short segments of the photoplethysmogram (PPG) signal via visibility graph (VG). Results show that the trained modified LeNet-5 model achieves an error performance of 0.184±7.457 mmHg for the systolic BP (SBP), and 0.343±4.065 mmHg for the diastolic BP (DBP) in terms of the mean error (ME) and the standard deviation (SD) of error between the estimated and reference BP. Both the SBP and the DBP accuracy rank grade A under the British Hypertension Society (BHS) protocol, demonstrating that our proposed method is an accurate way for cuff-less BP estimation.

Visibility graph based temporal community detection with applications in biological time series

Temporal behavior is an essential aspect of all biological systems. Time series have been previously represented as networks. Such representations must address two fundamental problems on how to: (1) Create appropriate networks to reflect the characteristics of biological time series. (2) Detect characteristic dynamic patterns or events as network temporal communities. General community detection methods use metrics comparing the connectivity within a community to random models, or are based on the betweenness centrality of edges or nodes. However, such methods were not designed for network representations of time series. We introduce a visibility-graph-based method to build networks from time series and detect temporal communities within these networks. To characterize unevenly sampled time series (typical of biological experiments), and simultaneously capture events associated to peaks and troughs, we introduce the Weighted Dual-Perspective Visibility Graph (WDPVG). To detect temporal communities in individual signals, we first find the shortest path of the network between start and end nodes, identifying high intensity nodes as the main stem of our community detection algorithm that act as hubs for each community. Then, we aggregate nodes outside the shortest path to the closest nodes found on the main stem based on the closest path length, thereby assigning every node to a temporal community based on proximity to the stem nodes/hubs. We demonstrate the validity and effectiveness of our method through simulation and biological applications.

Horizontal visibility graph of a random restricted growth sequence

We study the distributional properties of horizontal visibility graphs associated with random restrictive growth sequences and random set partitions of size n. Our main results are formulas expressing the expected degree of graph nodes in terms of simple explicit functions of a finite collection of Stirling and Bernoulli numbers.

A multiplex visibility graph motif‐based convolutional neural network for characterizing sleep stages using EEG signals

Sleep is an essential integrant in everyone’s daily life; therefore, it is an important but challenging problem to characterize sleep stages from electroencephalogram (EEG) signals. The network motif has been developed as a useful tool to investigate complex networks. In this study, we developed a multiplex visibility graph motif‐based convolutional neural network (CNN) for characterizing sleep stages using EEG signals and then introduced the multiplex motif entropy as the quantitative index to distinguish the six sleep stages. The independent samples t‐test shows that the multiplex motif entropy values have significant differences among the six sleep stages. Furthermore, we developed a CNN model and employed the multiplex motif sequence as the input of the model to classify the six sleep stages. Notably, the classification accuracy of the six‐state stage detection was 85.27%. Results demonstrated the effectiveness of the multiplex motif in characterizing the dynamic features underlying different sleep stages, whereby they further provide an essential strategy for future sleep‐stage detection research.

Texture classification based on image (natural and horizontal) visibility graph constructing methods

Texture classification is widely used in image analysis and some other related fields. In this paper, we designed a texture classification algorithm, named by TCIVG (Texture Classification based on Image Visibility Graph), based on a newly proposed image visibility graph network constructing method by Lacasa et al. By using TCIVG on a Brodatz texture image database, the whole procedure is illustrated. First, each texture image in the image database was transformed to an associated image natural visibility graph network and an image horizontal visibility graph network. Then, the degree distribution measure [P(k)] was extracted as a key characteristic parameter to different classifiers. Numerical experiments show that for artificial texture images, a 100% classification accuracy can be obtained by means of a quadratic discriminant based on natural TCIVG. For natural texture images, 94.80% classification accuracy can be obtained by a linear SVM (Support Vector Machine) based on horizontal TCIVG. Our results are better than that reported in some existing literature studies based on the same image database.

Shopper intent prediction from clickstream e-commerce data with minimal browsing information

We address the problem of user intent prediction from clickstream data of an e-commerce website via two conceptually different approaches: a hand-crafted feature-based classification and a deep learning-based classification. In both approaches, we deliberately coarse-grain a new clickstream proprietary dataset to produce symbolic trajectories with minimal information. Then, we tackle the problem of trajectory classification of arbitrary length and ultimately, early prediction of limited-length trajectories, both for balanced and unbalanced datasets. Our analysis shows that k-gram statistics with visibility graph motifs produce fast and accurate classifications, highlighting that purchase prediction is reliable even for extremely short observation windows. In the deep learning case, we benchmarked previous state-of-the-art (SOTA) models on the new dataset, and improved classification accuracy over SOTA performances with our proposed LSTM architecture. We conclude with an in-depth error analysis and a careful evaluation of the pros and cons of the two approaches when applied to realistic industry use cases.

Timescales of spontaneous fMRI fluctuations relate to structural connectivity in the brain

Intrinsic timescales of activity fluctuations vary hierarchically across the brain. This variation reflects a broad gradient of functional specialization in information storage and processing, with integrative association areas displaying slower timescales that are thought to reflect longer temporal processing windows. The organization of timescales is associated with cognitive function, distinctive between individuals, and disrupted in disease, but we do not yet understand how the temporal properties of activity dynamics are shaped by the brain's underlying structural connectivity network. Using resting-state fMRI and diffusion MRI data from 100 healthy individuals from the Human Connectome Project, here we show that the timescale of resting-state fMRI dynamics increases with structural connectivity strength, matching recent results in the mouse brain. Our results hold at the level of individuals, are robust to parcellation schemes, and are conserved across a range of different timescale- related statistics. We establish a comprehensive BOLD dynamical signature of structural connectivity strength by comparing over 6,000 time series features, highlighting a range of new temporal features for characterizing BOLD dynamics, including measures of stationarity and symbolic motif frequencies. Our findings indicate a conserved property of mouse and human brain organization in which a brain region's spontaneous activity fluctuations are closely related to their surrounding structural scaffold.

Improving graph-based detection of singular events for photochemical smog agents

Recently, a set of graph-based tools have been introduced for the identification of singular events of O₃, NO₂ and temperature time series, as well as description of their dynamics. These are based on the use of the Visibility Graphs (VG). In this work, an improvement of the original approach is proposed, being called Upside-Down Visibility Graph (UDVG). It adds the possibility of investigating the singular lowest episodes, instead of the highest. Results confirm the applicability of the new method for describing the multifractal nature of the underlying O₃, NO₂, and temperature. Asymmetries in the NO₂ degree distribution are observed, possibly due to the interaction with different chemicals. Furthermore, a comparison of VG and UDVG has been performed and the outcomes show that they describe opposite subsets of the time series (low and high values) as expected. The combination of the results from the two networks is proposed and evaluated, with the aim of obtaining all the information at once. It turns out to be a more complete tool for singularity detection in photochemical time series, which could be a valuable asset for future research.

Altered inter-frequency dynamics of brain networks in disorder of consciousness

OBJECTIVE

Growing evidence have linked disorders of consciousness (DOC) with the changes in frequency-specific functional networks. However, the alteration of inter-frequency dynamics in brain networks remain largely unknown. In this study, we investigated the network integration and segregation across frequency bands in a multiplex network framework.

APPROACH

Resting-state EEG data were recorded and analysed from 19 patients in minimally conscious state, 35 patients in unresponsive wakefulness syndrome (UWS) and 23 healthy controls. Frequency-based multiplex (cross-frequency) networks were reconstructed by integrating the five frequency-specific networks. Multiplex graph metrics, named multiplex participation coefficient and multiplex clustering coefficient, were employed to assess the network topology of subjects with different levels of consciousness.

MAIN RESULTS

Results revealed DOC networks, compared to those of healthy controls, may work at a less optimal point (closer to complete disorder) with increased integration and decreased segregation considering inter-frequency dynamics. Both metrics show increased spatial and temporal variability with the consciousness levels. Moreover, significant correlation can be found between the alteration of cross-frequency networks in DOC patients and their behavioural performance at both local and global scales.

SIGNIFICANCE

These findings may contribute to the development of EEG network study and benefit our understanding of the processes of consciousness and their pathophysiology for DOC.

Estimation of Dynamic Bivariate Correlation Using a Weighted Graph Algorithm

Dynamic correlation is the correlation between two time series across time. Two approaches that currently exist in neuroscience literature for dynamic correlation estimation are the sliding window method and dynamic conditional correlation. In this paper, we first show the limitations of these two methods especially in the presence of extreme values. We present an alternate approach for dynamic correlation estimation based on a weighted graph and show using simulations and real data analyses the advantages of the new approach over the existing ones. We also provide some theoretical justifications and present a framework for quantifying uncertainty and testing hypotheses.

Visibility Graphs for Image Processing

The family of image visibility graphs (IVG/IHVGs) have been recently introduced as simple algorithms by which scalar fields can be mapped into graphs. Here we explore the usefulness of such\an operator in the scenario of image processing and image classification. We demonstrate that the link architecture of the image visibility graphs encapsulates relevant information on the structure of the images and we explore their potential as image filters. We introduce several graph features, including the novel concept of Visibility Patches, and show through several examples that these features are highly informative, computationally efficient and universally applicable for general pattern recognition and image classification tasks.

Novel Automatic Epilepsy Detection Method Multi-weight Transition Network

The automatic diagnosis of epilepsy using Electroencephalogram (EEG) signals had always been an important research direction. A novel automatic epilepsy detection method based on multi-weight transition network was proposed in this paper. The epileptic EEG signal was first transformed into complex network according to our proposed multi-weight transition network algorithm. Then, based on the statistical characteristics of the multi-weight transition network, the degree of network and the local entropy of network were extracted as features. Finally, the extracted features and support vector machines (SVM) were combined to classify epileptic seizure and non-seizure signals, and the classification performance was evaluated by k-fold cross validation. Seven different experimental cases were tested. The experimental results indicate that the algorithm had high classification accuracy for all cases.

Can complex networks describe the urban and rural tropospheric O3 dynamics?

Tropospheric ozone (O₃) time series have been converted into complex networks through the recent so-called Visibility Graph (VG), using the data from air quality stations located in the western part of Andalusia (Spain). The aim is to apply this novel method to differentiate the behavior between rural and urban regions when it comes to the ozone dynamics. To do so, some centrality parameters of the resulting complex networks have been investigated: the degree, betweenness and shortest path. Some of them are expected to corroborate previous works in order to support the use of this technique; while others to supply new information. Results coincide when describing the difference that tropospheric ozone exhibits seasonally and geographically. It is seen that ozone behavior is fractal, in accordance to previous works. Also, it has been demonstrated that this methodology is able to characterize the divergence encountered between measurements in urban environments and countryside. In addition to that, the promising outcomes of this technique support the use of complex networks for the study of air pollutants dynamics. Particularly, new nuances are offered such as the identification and description of singularities in the signal.

Analysis of Spontaneous EEG Activity in Alzheimer's Disease Using Weighted Visibility Graph

This study was aimed at characterizing spontaneous electroencephalography (EEG) activity in Alzheimer's disease (AD) using a novel approach named weighted visibility graph (WVG). More than 10 minutes of spontaneous EEG were recorded from 15 AD patients and 15 age-matched normal controls. Two graph metrics, clustering coefficient and average weighted degree, are extracted in different frequency bands for each EEG channel based on the WVG methodology. Furthermore, statistical analysis was performed in different bands and channels for both groups. It is demonstrated that AD patients are characterized with a significant increase of clustering coefficient and degree in theta band, which can be observed in most brain regions. Our results suggest that the WVG method can be are effective to distinguish different brain states (AD and normal) and may provide further insights into the underlying brain dynamics in AD.

Decoding cortical brain states from widefield calcium imaging data using visibility graph

Widefield optical imaging of neuronal populations over large portions of the cerebral cortex in awake behaving animals provides a unique opportunity for investigating the relationship between brain function and behavior. In this paper, we demonstrate that the temporal characteristics of calcium dynamics obtained through widefield imaging can be utilized to infer the corresponding behavior. Cortical activity in transgenic calcium reporter mice (n=6) expressing GCaMP6f in neocortical pyramidal neurons is recorded during active whisking (AW) and no whisking (NW). To extract features related to the temporal characteristics of calcium recordings, a method based on visibility graph (VG) is introduced. An extensive study considering different choices of features and classifiers is conducted to find the best model capable of predicting AW and NW from calcium recordings. Our experimental results show that temporal characteristics of calcium recordings identified by the proposed method carry discriminatory information that are powerful enough for decoding behavior.

A multiplex network approach for the analysis of intracranial pressure and heart rate data in traumatic brain injured patients

BACKGROUND

We present a multiplex network model for the analysis of Intracranial Pressure (ICP) and Heart Rate (HR) behaviour after severe brain traumatic injuries in pediatric patients. The ICP monitoring is of vital importance for checking life threathening conditions, and understanding the behaviour of these parameters is crucial for a successful intervention of the clinician. Our own observations, exhibit cross-talks interaction events happening between HR and ICP, i.e. transients in which both the ICP and the HR showed an increase of 20% with respect to their baseline value in the window considered. We used a complex event processing methodology, to investigate the relationship between HR and ICP, after traumatic brain injuries (TBI). In particular our goal has been to analyse events of simultaneous increase by HR and ICP (i.e. cross-talks), modelling the two time series as a unique multiplex network system (Lacasa et al., Sci Rep 5:15508-15508, 2014).

METHODS AND DATA

We used a complex network approach based on visibility graphs (Lacasa et al., Sci Rep 5:15508-15508, 2014) to model and study the behaviour of our system and to investigate how and if network topological measures can give information on the possible detection of crosstalks events taking place in the system. Each time series was converted as a layer in a multiplex network. We therefore studied the network structure, focusing on the behaviour of the two time series in the cross-talks events windows detected. We used a dataset of 27 TBI pediatric patients, admitted to Addenbrooke's Hospital, Cambridge, Pediatric Intensive Care Unit (PICU) between August 2012 and December 2014.

RESULTS

Following a preliminary statistical exploration of the two time series of ICP and HR, we analysed the multiplex network proposed, focusing on two standard topological network metrics: the mutual interaction, and the average edge overlap (Lacasa et al., Sci Rep 5:15508-15508, 2014). We compared results obtained for these two indicators, considering windows in which a cross talks event between HR and ICP was detected with windows in which cross talks events were not present. The analysis of such metrics gave us interesting insights on the time series behaviour. More specifically we observed an increase in the value of the mutual interaction in the case of cross talk as compared to non cross talk. This seems to suggest that mutual interaction could be a potentially interesting "marker" for cross talks events.

Sample entropy reveals an age-related reduction in the complexity of dynamic brain

Dynamic reconfiguration of the human brain is characterized by the nature of complexity. The purpose of this study was to measure such complexity and also analyze its association with age. We modeled the dynamic reconfiguration process by dynamic functional connectivity, which was established by resting-state functional magnetic resonance imaging (fMRI) data, and we measured complexity within the dynamic functional connectivity by sample entropy (SampEn). A brainwide map of SampEn in healthy subjects shows larger values in the caudate, the olfactory gyrus, the amygdala, and the hippocampus, and lower values in primary sensorimotor and visual areas. Association analysis in healthy subjects indicated that SampEn of the amygdala-cortical connectivity decreases with advancing age. Such age-related loss of SampEn, however, disappears in patients with schizophrenia. These findings suggest that SampEn of the dynamic functional connectivity is a promising indicator of normal aging.