Analysis of alcoholic EEG signals based on horizontal visibility graph entropy

Efficient novel network and index for alcoholism detection from EEGs

Background

Alcoholism is a catastrophic condition that causes brain damage as well as neurological, social, and behavioral difficulties.

Limitations

This illness is often assessed using the Cut down, Annoyed, Guilty, and Eye-opener examination technique, which assesses the intensity of an alcohol problem. This technique is protracted, arduous, error-prone, and errant.

Method

As a result, the intention of this paper is to design a cutting-edge system for automatically identifying alcoholism utilizing electroencephalography (EEG) signals, that can alleviate these problems and aid practitioners and investigators. First, we investigate the feasibility of using the Fast Walsh-Hadamard transform of EEG signals to explore the unpredictable essence and variability of EEG indicators in the suggested framework. Second, thirty-six linear and nonlinear features for deciphering the dynamic pattern of healthy and alcoholic EEG signals are discovered. Subsequently, we suggested a strategy for selecting powerful features. Finally, nineteen machine learning algorithms and five neural network classifiers are used to assess the overall performance of selected attributes.

Results

The extensive experiments show that the suggested method provides the best classification efficiency, with 97.5% accuracy, 96.7% sensitivity, and 98.3% specificity for the features chosen using the correlation-based FS approach with Recurrent Neural Networks. With recently introduced matrix determinant features, a classification accuracy of 93.3% is also attained. Moreover, we developed a novel index that uses clinically meaningful features to differentiate between healthy and alcoholic categories with a unique integer. This index can assist health care workers, commercial companies, and design engineers in developing a real-time system with 100% classification results for the computerized framework.

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.

Relation between the degree and betweenness centrality distribution in complex networks

The centrality measures, like betweenness b and degree k in complex networks remain fundamental quantities helping to classify them. It is realized from Barthelemy's paper [Eur. Phys. J. B 38, 163 (2004)10.1140/epjb/e2004-00111-4] that the maximal b-k exponent for the scale-free (SF) networks is η_{max}=2, belonging to SF trees, based on which one concludes δ≥γ+1/2, where γ and δ are the scaling exponents for the distribution functions of the degree and the betweenness centralities, respectively. This conjecture was violated for some special models and systems. Here we present a systematic study on this problem for visibility graphs of correlated time series, and show evidence that this conjecture fails in some correlation strengths. We consider the visibility graph of three models: two-dimensional Bak-Tang-Weisenfeld (BTW) sandpile model, one-dimensional (1D) fractional Brownian motion (FBM), and 1D Levy walks, the two latter cases are controlled by the Hurst exponent H and the step index α, respectively. In particular, for the BTW model and FBM with H≲0.5, η is greater than 2, and also δ<γ+1/2 for the BTW model, while the Barthelemy's conjecture remains valid for the Levy process. We assert that the failure of the Barthelemy's conjecture is due to large fluctuations in the scaling b-k relation resulting in the violation of hyperscaling relation η=γ-1/δ-1 and emergent anomalous behavior for the BTW model and FBM. Universal distribution function of generalized degree is found for these models which have the same scaling behavior as the Barabasi-Albert network.

Visibility graph for time series prediction and image classification: a review

The analysis of time series and images is significant across different fields due to their widespread applications. In the past few decades, many approaches have been developed, including data-driven artificial intelligence methods, mechanism-driven physical methods, and hybrid mechanism and data-driven models. Complex networks have been used to model numerous complex systems due to its characteristics, including time series prediction and image classification. In order to map time series and images into complex networks, many visibility graph algorithms have been developed, such as horizontal visibility graph, limited penetrable visibility graph, multiplex visibility graph, and image visibility graph. The family of visibility graph algorithms will construct different types of complex networks, including (un-) weighted, (un-) directed, and (single-) multi-layered networks, thereby focusing on different kinds of properties. Different types of visibility graph algorithms will be reviewed in this paper. Through exploring the topological structure and information in the network based on statistical physics, the property of time series and images can be discovered. In order to forecast (multivariate) time series, several variations of local random walk algorithms and different information fusion approaches are applied to measure the similarity between nodes in the network. Different forecasting frameworks are also proposed to consider the information in the time series based on the similarity. In order to classify the image, several machine learning models (such as support vector machine and linear discriminant) are used to classify images based on global features, local features, and multiplex features. Through various simulations on a variety of datasets, researchers have found that the visibility graph algorithm outperformed existing algorithms, both in time series prediction and image classification. Clearly, complex networks are closely connected with time series and images by visibility graph algorithms, rendering complex networks to be an important tool for understanding the characteristics of time series and images. Finally, we conclude in the last section with future outlooks for the visibility graph.

Jumping Knowledge Based Spatial-temporal Graph Convolutional Networks for Automatic Sleep Stage Classification

A novel jumping knowledge spatial-temporal graph convolutional network (JK-STGCN) is proposed in this paper to classify sleep stages. Based on this method, different types of multi-channel bio-signals, including electroencephalography (EEG), electromyogram (EMG), electrooculogram (EOG), and electrocardiogram (ECG) are utilized to classify sleep stages, after extracting features by a standard convolutional neural network (CNN) named FeatureNet. Intrinsic connections among different bio-signal channels from the identical epoch and neighboring epochs can be obtained through two adaptive adjacency matrices learning methods. A jumping knowledge spatial-temporal graph convolution module helps the JK-STGCN model to extract spatial features from the graph convolutions efficiently and temporal features are extracted from its common standard convolutions to learn the transition rules among sleep stages. Experimental results on the ISRUC-S3 dataset showed that the overall accuracy achieved 0.831 and the F1-score and Cohen kappa reached 0.814 and 0.782, respectively, which are the competitive classification performance with the state-of-the-art baselines. Further experiments on the ISRUC-S3 dataset are also conducted to evaluate the execution efficiency of the JK-STGCN model. The training time on 10 subjects is 2621s and the testing time on 50 subjects is 6.8s, which indicates its highest calculation speed compared with the existing high-performance graph convolutional networks and U-Net architecture algorithms. Experimental results on the ISRUC-S1 dataset also demonstrate its generality, whose accuracy, F1-score, and Cohen kappa achieve 0.820, 0.798, and 0.767 respectively.

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.

Extracting Epileptic Features in EEGs Using a Dual-Tree Complex Wavelet Transform Coupled with a Classification Algorithm

The detection of epileptic seizures from electroencephalogram (EEG) signals is traditionally performed by clinical experts through visual inspection. It is a long process, is error prone, and requires a highly trained expert. In this research, a new method is presented for seizure classification for EEG signals using a dual-tree complex wavelet transform (DT-CWT) and fast Fourier transform (FFT) coupled with a least square support vector machine (LS-SVM) classifier. In this method, each EEG signal is divided into four segments. Each segment is further split into smaller sub-segments. The DT-CWT is applied to decompose each sub-segment into detailed and approximation coefficients (real and imaginary parts). The obtained coefficients by the DT-CWT at each decomposition level are passed through an FFT to identify the relevant frequency bands. Finally, a set of effective features are extracted from the sub-segments, and are then forwarded to the LS-SVM classifier to classify epileptic EEGs. In this paper, two epileptic EEG databases from Bonn and Bern Universities are used to evaluate the extracted features using the proposed method. The experimental results demonstrate that the method obtained an average accuracy of 97.7% and 96.8% for the Bonn and Bern databases, respectively. The results prove that the proposed DT-CWT and FFT based features extraction is an effective way to extract discriminative information from brain signals. The obtained results are also compared to those by k-means and Naïve Bayes classifiers as well as with the results from the previous methods reported for classifying epileptic seizures and identifying the focal and non-focal EEG signals. The obtained results show that the proposed method outperforms the others and it is effective in detecting epileptic seziures in EEG signals. The technique can be adopted to aid neurologists to better diagnose neurological disorders and for an early seizure warning system.

Detection of alcoholism using EEG signals and a CNN-LSTM-ATTN network

Alcoholism is a serious disorder that poses a problem for modern society, but the detection of alcoholism has no widely accepted standard tests or procedures. If alcoholism goes undetected at its early stages, it can create havoc in the patient's life. An electroencephalography (EEG) is a method used to measure the brain's electrical activity and can detect alcoholism. EEG signals are complex and multi-channel and thus can be difficult to interpret manually. Several previous works have tried to classify a subject as alcoholic or control (non-alcoholic) based on EEG signals. Such works have mainly used machine learning or statistical techniques along with handcrafted features such as entropy, correlation dimension, Hurst exponent. With the growth in computational power and data volume worldwide, deep learning models have recently been gaining momentum in various fields. However, only a few studies are available on the application of deep learning models for the classification of alcoholism using EEG signals. This paper proposes a deep learning architecture that uses a combination of fast Fourier transform (FFT), a convolution neural network (CNN), long short-term memory (LSTM), and a recently proposed attention mechanism for extracting Spatio-temporal features from multi-channel EEG signals. The proposed architecture can classify a subject as an alcoholic or control with a high degree of accuracy by analyzing EEG signals of that subject and can be used for automating alcoholism detection. The analytical results using the proposed architecture show a 98.83% accuracy, making it better than most state-of-the-art algorithms.

Assessing time series irreversibility through micro-scale trends

Time irreversibility, defined as the lack of invariance of the statistical properties of a system or time series under the operation of time reversal, has received increasing attention during the last few decades, thanks to the information it provides about the mechanisms underlying the observed dynamics. Following the need of analyzing real-world time series, many irreversibility metrics and tests have been proposed, each one associated with different requirements in terms of, e.g., minimum time series length or computational cost. We here build upon previously proposed tests based on the concept of permutation patterns but deviating from them through the inclusion of information about the amplitude of the signal and how this evolves over time. We show, by means of synthetic time series, that the results yielded by this method are complementary to the ones obtained by using permutation patterns alone, thus suggesting that "one irreversibility metric does not fit all." We further apply the proposed metric to the analysis of two real-world data sets.

Deep Convolutional Neural Network Regularization for Alcoholism Detection Using EEG Signals

Alcoholism is attributed to regular or excessive drinking of alcohol and leads to the disturbance of the neuronal system in the human brain. This results in certain malfunctioning of neurons that can be detected by an electroencephalogram (EEG) using several electrodes on a human skull at appropriate positions. It is of great interest to be able to classify an EEG activity as that of a normal person or an alcoholic person using data from the minimum possible electrodes (or channels). Due to the complex nature of EEG signals, accurate classification of alcoholism using only a small dataset is a challenging task. Artificial neural networks, specifically convolutional neural networks (CNNs), provide efficient and accurate results in various pattern-based classification problems. In this work, we apply CNN on raw EEG data and demonstrate how we achieved 98% average accuracy by optimizing a baseline CNN model and outperforming its results in a range of performance evaluation metrics on the University of California at Irvine Machine Learning (UCI-ML) EEG dataset. This article explains the stepwise improvement of the baseline model using the dropout, batch normalization, and kernel regularization techniques and provides a comparison of the two models that can be beneficial for aspiring practitioners who aim to develop similar classification models in CNN. A performance comparison is also provided with other approaches using the same dataset.

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.

The Entropy Universe

About 160 years ago, the concept of entropy was introduced in thermodynamics by Rudolf Clausius. Since then, it has been continually extended, interpreted, and applied by researchers in many scientific fields, such as general physics, information theory, chaos theory, data mining, and mathematical linguistics. This paper presents The Entropy Universe, which aims to review the many variants of entropies applied to time-series. The purpose is to answer research questions such as: How did each entropy emerge? What is the mathematical definition of each variant of entropy? How are entropies related to each other? What are the most applied scientific fields for each entropy? We describe in-depth the relationship between the most applied entropies in time-series for different scientific fields, establishing bases for researchers to properly choose the variant of entropy most suitable for their data. The number of citations over the past sixteen years of each paper proposing a new entropy was also accessed. The Shannon/differential, the Tsallis, the sample, the permutation, and the approximate entropies were the most cited ones. Based on the ten research areas with the most significant number of records obtained in the Web of Science and Scopus, the areas in which the entropies are more applied are computer science, physics, mathematics, and engineering. The universe of entropies is growing each day, either due to the introducing new variants either due to novel applications. Knowing each entropy's strengths and of limitations is essential to ensure the proper improvement of this research field.

On fractality of functional near-infrared spectroscopy signals: analysis and applications

Significance: The human brain is a highly complex system with nonlinear, dynamic behavior. A majority of brain imaging studies employing functional near-infrared spectroscopy (fNIRS), however, have considered only the spatial domain and have ignored the temporal properties of fNIRS recordings. Methods capable of revealing nonlinearities in fNIRS recordings can provide new insights about how the brain functions. Aim: The temporal characteristics of fNIRS signals are explored by comprehensively investigating their fractal properties. Approach: Fractality of fNIRS signals is analyzed using scaled windowed variance (SWV), as well as using visibility graph (VG), a method which converts a given time series into a graph. Additionally, the fractality of fNIRS signals obtained under resting-state and task-based conditions is compared, and the application of fractality in differentiating brain states is demonstrated for the first time via various classification approaches. Results: Results from SWV analysis show the existence of high fractality in fNIRS recordings. It is shown that differences in the temporal characteristics of fNIRS signals related to task-based and resting-state conditions can be revealed via the VGs constructed for each case. Conclusions: fNIRS recordings, regardless of the experimental conditions, exhibit high fractality. Furthermore, VG-based metrics can be employed to differentiate rest and task-execution brain states.

K-complexes Detection in EEG Signals using Fractal and Frequency Features Coupled with an Ensemble Classification Model

K-complexes are important transient bio-signal waveforms in sleep stage 2. Detecting k-complexes visually requires a highly qualified expert. In this study, an efficient method for detecting k-complexes from electroencephalogram (EEG) signals based on fractal and frequency features coupled with an ensemble model of three classifiers is presented. EEG signals are first partitioned into segments, using a sliding window technique. Then, each EEG segment is decomposed using a dual-tree complex wavelet transform (DT-CWT) to a set of real and imaginary parts. A total of 10 sub-bands are used based on four levels of decomposition, and the high sub-bands are considered in this research for feature extraction. Fractal and frequency features based on DT-CWT and Higuchi's algorithm are pulled out from each sub-band and then forwarded to an ensemble classifier to detect k-complexes. A twelve-feature set is finally used to detect the sleep EEG characteristics using the ensemble model. The ensemble model is designed using a combination of three classification techniques including a least square support vector machine (LS-SVM), k-means and Naïve Bayes. The proposed method for the detection of the k-complexes achieves an average accuracy rate of 97.3 %. The results from the ensemble classifier were compared with those by individual classifiers. Comparisons were also made with existing k-complexes detection approaches for which the same datasets were used. The results demonstrate that the proposed approach is efficient in identifying the k-complexes in EEG signals; it yields optimal results with a window size 0.5 s. It can be an effective tool for sleep stages classification and can be useful for doctors and neurologists for diagnosing sleep disorders.

Machine Learning Approach to Dysphonia Detection

This paper addresses the processing of speech data and their utilization in a decision support system. The main aim of this work is to utilize machine learning methods to recognize pathological speech, particularly dysphonia. We extracted 1560 speech features and used these to train the classification model. As classifiers, three state-of-the-art methods were used: K-nearest neighbors, random forests, and support vector machine. We analyzed the performance of classifiers with and without gender taken into account. The experimental results showed that it is possible to recognize pathological speech with as high as a 91.3% classification accuracy.

Wave2Vec: Vectorizing Electroencephalography Bio-Signal for Prediction of Brain Disease

Interest in research involving health-medical information analysis based on artificial intelligence, especially for deep learning techniques, has recently been increasing. Most of the research in this field has been focused on searching for new knowledge for predicting and diagnosing disease by revealing the relation between disease and various information features of data. These features are extracted by analyzing various clinical pathology data, such as EHR (electronic health records), and academic literature using the techniques of data analysis, natural language processing, etc. However, still needed are more research and interest in applying the latest advanced artificial intelligence-based data analysis technique to bio-signal data, which are continuous physiological records, such as EEG (electroencephalography) and ECG (electrocardiogram). Unlike the other types of data, applying deep learning to bio-signal data, which is in the form of time series of real numbers, has many issues that need to be resolved in preprocessing, learning, and analysis. Such issues include leaving feature selection, learning parts that are black boxes, difficulties in recognizing and identifying effective features, high computational complexities, etc. In this paper, to solve these issues, we provide an encoding-based Wave2vec time series classifier model, which combines signal-processing and deep learning-based natural language processing techniques. To demonstrate its advantages, we provide the results of three experiments conducted with EEG data of the University of California Irvine, which are a real-world benchmark bio-signal dataset. After converting the bio-signals (in the form of waves), which are a real number time series, into a sequence of symbols or a sequence of wavelet patterns that are converted into symbols, through encoding, the proposed model vectorizes the symbols by learning the sequence using deep learning-based natural language processing. The models of each class can be constructed through learning from the vectorized wavelet patterns and training data. The implemented models can be used for prediction and diagnosis of diseases by classifying the new data. The proposed method enhanced data readability and intuition of feature selection and learning processes by converting the time series of real number data into sequences of symbols. In addition, it facilitates intuitive and easy recognition, and identification of influential patterns. Furthermore, real-time large-capacity data analysis is facilitated, which is essential in the development of real-time analysis diagnosis systems, by drastically reducing the complexity of calculation without deterioration of analysis performance by data simplification through the encoding process.

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 review on EEG-based methods for screening and diagnosing alcohol use disorder

The screening test for alcohol use disorder (AUD) patients has been of subjective nature and could be misleading in particular cases such as a misreporting the actual quantity of alcohol intake. Although the neuroimaging modality such as electroencephalography (EEG) has shown promising research results in achieving objectivity during the screening and diagnosis of AUD patients. However, the translation of these findings for clinical applications has been largely understudied and hence less clear. This study advocates the use of EEG as a diagnostic and screening tool for AUD patients that may help the clinicians during clinical decision making. In this context, a comprehensive review on EEG-based methods is provided including related electrophysiological techniques reported in the literature. More specifically, the EEG abnormalities associated with the conditions of AUD patients are summarized. The aim is to explore the potentials of objective techniques involving quantities/features derived from resting EEG, event-related potentials or event-related oscillations data.

An EEG-based machine learning method to screen alcohol use disorder

Screening alcohol use disorder (AUD) patients has been challenging due to the subjectivity involved in the process. Hence, robust and objective methods are needed to automate the screening of AUD patients. In this paper, a machine learning method is proposed that utilized resting-state electroencephalography (EEG)-derived features as input data to classify the AUD patients and healthy controls and to perform automatic screening of AUD patients. In this context, the EEG data were recorded during 5 min of eyes closed and 5 min of eyes open conditions. For this purpose, 30 AUD patients and 15 aged-matched healthy controls were recruited. After preprocessing the EEG data, EEG features such as inter-hemispheric coherences and spectral power for EEG delta, theta, alpha, beta and gamma bands were computed involving 19 scalp locations. The selection of most discriminant features was performed with a rank-based feature selection method assigning a weight value to each feature according to a criterion, i.e., receiver operating characteristics curve. For example, a feature with large weight was considered more relevant to the target labels than a feature with less weight. Therefore, a reduced set of most discriminant features was identified and further be utilized during classification of AUD patients and healthy controls. As results, the inter-hemispheric coherences between the brain regions were found significantly different between the study groups and provided high classification efficiency (Accuracy = 80.8, sensitivity = 82.5, and specificity = 80, F-Measure = 0.78). In addition, the power computed in different EEG bands were found significant and provided an overall classification efficiency as (Accuracy = 86.6, sensitivity = 95, specificity = 82.5, and F-Measure = 0.88). Further, the integration of these EEG feature resulted into even higher results (Accuracy = 89.3 %, sensitivity = 88.5 %, specificity = 91 %, and F-Measure = 0.90). Based on the results, it is concluded that the EEG data (integration of the theta, beta, and gamma power and inter-hemispheric coherence) could be utilized as objective markers to screen the AUD patients and healthy controls.

Multiscale limited penetrable horizontal visibility graph for analyzing nonlinear time series

Visibility graph has established itself as a powerful tool for analyzing time series. We in this paper develop a novel multiscale limited penetrable horizontal visibility graph (MLPHVG). We use nonlinear time series from two typical complex systems, i.e., EEG signals and two-phase flow signals, to demonstrate the effectiveness of our method. Combining MLPHVG and support vector machine, we detect epileptic seizures from the EEG signals recorded from healthy subjects and epilepsy patients and the classification accuracy is 100%. In addition, we derive MLPHVGs from oil-water two-phase flow signals and find that the average clustering coefficient at different scales allows faithfully identifying and characterizing three typical oil-water flow patterns. These findings render our MLPHVG method particularly useful for analyzing nonlinear time series from the perspective of multiscale network analysis.