Autistic recognition from EEG signals by extracted features from several time series models

Autistic recognition from EEG signals by extracted features from several time series models | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Autistic recognition from EEG signals by extracted features from several time series models Mehdi Rajabioun This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3931787/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Autism is a neurological and psychological disorder that typically manifests in childhood and persists into adulthood. It is characterized by atypical social, behavioral, and communication skills, as well as diminished attention to the surrounding environment. The detection and recognition of autism can contribute to the prevention of its development and the enhancement of social and communicational abilities. Various methods are employed for autism recognition, including questionnaire tests and neurological techniques. One such neuroimaging method is electroencephalography (EEG), which records the brain's electrical activities through sensors placed on the scalp. This paper proposes a method for identifying individuals with autism using EEG signals and features extracted from a multivariate autoregressive moving average (MVARMA) and multivariate integrated autoregressive(ARIMA) models. The approach begins by estimating active sources through source localization methods, followed by the application of a dual Kalman filter to estimate source activity. Subsequently, the MVARMA and ARIMA models are applied to the EEG sensor and active source data, enabling the calculation of model parameters. Principal component analysis is then utilized to select important parameters, and a K nearest neighbor classifier is employed to classify participants as either autistic or neurotypical. The results demonstrate superior classification performance, achieving higher accuracy compared to alternative methods. The proposed method yields superior classification outcomes when compared to other approaches, as it exhibits improved classification measures. Dual Kalman Filter Autoregressive moving average(ARMA) model Autoregressive integrated moving average(ARIMA) model Autism Electroencephalography(EEG) Figures Figure 1 Figure 2 Introduction Autism is a complex brain condition with many different parts and aspects. It can show up in various ways and affects people differently. People with autism might struggle with communicating emotions and socializing. They might also find it hard to adapt to new situations or change their behavior. Some noticeable signs in people with autism include difficulty speaking, not paying much attention to what's happening around them, showing fewer emotions, and finding it tough to express feelings on their faces. These things are especially noticeable in children with autism[ 1 – 3 ]. Autism mostly shows up when someone is very young or during their teenage years. It's important to mention that many adults with autism also go through epilepsy or seizures at some time in their lives. This happening together highlights how important it is to identify, provide complete care, and offer support to people who are on the autism spectrum[ 4 – 7 ]. There's strong proof showing that more and more people are being diagnosed with autism. A study from the Center for Disease Control and Prevention (CDC) in 2009 found that the number of autism cases has been going up consistently. In the United States, it went from being less than three cases for every 10,000 kids in 1970 to over 30 cases for every 10,000 kids in 1990. Then, in a report from 2012, the CDC said it had risen even more to one in 88 children, and especially high for boys at one in 54. These increasing numbers show how urgent it is to identify and support children with autism. By understanding more about how complex autism is, we can aim for better ways to spot it early, provide effective help, and improve the lives of those dealing with this condition[ 3 , 7 ]. Various methods have been created to identify autism, all with the goal of spotting autism spectrum disorder (ASD) early on. This helps in getting help and support when needed. Each method has its good points and bad points. One method, behavioral observation, involves carefully watching how a child behaves, interacts with others, talks, and plays. But because it relies on someone's judgment and experience, it might lead to different opinions about behaviors and can cause differences in diagnoses[ 8 – 10 ]. Different types of surveys and scales have been created to check for autism signs and measure how severe the symptoms are. Some examples are the Autism Diagnostic Interview-Revised (ADI-R) and the Autism Diagnostic Observation Schedule (ADOS)[ 11 , 12 ]. Relying on someone's personal reporting might bring in some unfairness and might not show all the different behaviors a person has. To look deeper, scientists use brain-scanning methods like functional magnetic resonance imaging (fMRI) and electroencephalography (EEG) to study how the brain works and connects in people with autism. These ways help without being invasive to see how the brain is structured and works. They give us clues about the brain reasons behind autism and might find special signs that could help diagnose it[ 12 – 15 ]. Electroencephalography (EEG) records the brain's electrical activity using electrodes on the scalp. This method has many benefits when identifying autism. It's non-invasive, meaning it doesn't involve surgery or going inside the body, and it's quite affordable. EEG helps study the brain's electrical patterns and connections. By looking at how the brain's rhythms and syncing work, we can learn a lot about the unusual functions linked to autism[ 15 , 16 ]. Because EEG records brain activity directly, it's really good at catching quick changes in how the brain works. These benefits show how valuable EEG signals can be in spotting and understanding autism. They help find it early, create specific ways to help, and make treatments personalized for each person. Detecting autism through EEG signals is a crucial aspect of neuroscience research, with various studies exploring different approaches in this area. Some research papers have used machine learning techniques to analyze EEG data, achieving high accuracy in distinguishing between individuals with autism and those without it [ 17 – 23 ]. Others have suggested deep learning methods that extract key features from EEG signals, showing promising results in autism detection [ 24 – 27 ]. Schwartz et al focused on investigating specific EEG frequency bands and their correlation with autism, revealing distinct patterns that could aid in identification [ 28 , 29 ]. Additionally, innovative approaches combining EEG analysis with graph theory, introduced by Jurriaan and Precenzano et al., offer fresh perspectives on recognizing autism[ 30 ]. Tawhid et al. explored time-frequency analysis techniques to extract dynamic information from EEG signals, allowing the detection of temporal patterns associated with autism[ 31 ]. Others, like Landowska, developed multi-modal approaches that integrate EEG data with other physiological signals, like heart rate and skin conductance, to improve the accuracy of identifying autism[ 32 ]. Qaysar investigated advanced signal processing techniques, such as wavelet transforms and independent component analysis, to reveal unique EEG signatures linked to autism[ 33 ]. These varied methods show global researchers' collaborative efforts, pushing the boundaries of autism detection using EEG signals and paving the way for more comprehensive diagnostic tools.Several studies have also pointed out abnormal connectivity patterns in specific brain regions of individuals with autism. Findings have indicated increased local connectivity but decreased long-distance connections in autism[ 34 – 39 ]. Wass et al. reported increased connectivity in frontal and short neural pathways, while Coben et al. found increased coherence in frontal regions and decreased coherence in bilateral posterior temporal regions when comparing autistic subjects with neurotypical children[ 36 ]. Studies utilizing Granger causality analysis found underconnectivity between distant brain regions, especially in the prefrontal cortex, anterior cingulate, and bilateral inferior parietal regions [ 37 ]. Another study by Coben et al. used Granger causality analysis to estimate effective connectivity from EEG signals and identified underconnectivity between regions that are distant from each other, specifically in the prefrontal cortex (PFC), anterior cingulate, and bilateral inferior parietal regions. Examining the relation between autism and effective connectivity during emotional processing tasks[ 40 ], Minshew and Williams observed increased frontal coherence but reduced anterior-to-posterior temporal coherence in autism[ 41 ]. Wataru Sato et al. applied dynamic causal modeling to fMRI data, revealing reduced activity in visual brain areas among autistic children[ 42 ]. This paper introduces novel approaches using multivariate autoregressive moving average (MVARMA) and multivariate autoregressive integrated moving average (MVARIMA) models. These models are applied to recorded signal and source activity time series. Features are derived from the parameters of these models, focusing on statistical values of the most influential ARMA and ARIMA model parameter time series. To compute source activity signals, an initial step involves applying a source localization method to EEG signals, isolating active sources. Then, a dual Kalman filter is employed on these active sources, estimating source activities alongside the source relationship matrix. Subsequently, the transformation occurs from sensor space (EEG signals) to source space (active brain regions). Finally, a multivariate ARMA and ARIMA model is fitted to each time sample of EEG signal based on past signal recordings and source activities. After the source localization process, the focus shifts to estimating source dynamics, which represents changes in source activity across time. This estimation is a complex and vital aspect, and several research papers propose solutions to tackle this challenge. One traditional method is the dynamic causal model (DCM), which employs linear or nonlinear models to estimate neural connections based on existing physiological knowledge. It assumes nonlinear relationships between sources or neural dynamics, optimizing model parameters accordingly[ 43 – 45 ]. Additionally, methods utilizing dual Kalman filters are utilized for estimating dynamic source activity[ 46 , 47 ]. For instance, A.H. Omidvarnia applies dual Kalman filter analysis to newborn EEG signals[ 48 ], while Eduardo Giraldo proposes a method using dual Kalman filters for source activity estimation. These approaches estimate source activity and their relationships concurrently across time, reducing estimation errors. In a study by Rajabioun et al., a dual Kalman filter-based approach is employed to estimate effective connectivity among sources, specifically applied to EEG signals from individuals with autism. This research revealed differences in effective connectivity between subjects with autism and those without it[ 47 ]. Materials and Methods This paper introduces a method aimed at distinguishing individuals with autism from control candidates. This classification is crucial for halting the advancement of disorders and enhancing the lives of those affected. The structure and flowchart detailing this proposed method are depicted in Fig. 1 . To begin, the EEG signal needs to be obtained or prepared. In this study, the signal was acquired by downloading it from [ 49 ].The dataset used in this research comprises EEG recordings gathered through the Biosemi ActiveTwo EEG system. It includes data from 28 individuals diagnosed with autism spectrum conditions and 28 neurotypical controls, spanning ages from 18 to 68 years. These recordings were conducted during a 2.5-minute (150 seconds) eyes-closed resting period. Permission for data collection and sharing was obtained from the Health Research Authority, specifically under the IRAS ID 212171[ 49 ]. Once the preprocessing stage is completed, the filtered signals are subjected to a source localization technique. This process aims to estimate the active brain sources or regions. Its primary goal is to simplify complexity by identifying a limited number of active sources. This leads to determining the active brain regions and their corresponding spatial coordinates as the final output. In the context of source localization or pinpointing active brain regions, the goal is to minimize the following function: The raw EEG signals underwent several preprocessing stages to eliminate unwanted noise and artifacts. Initially, a bandpass Butterworth filter was applied, setting the cutoff frequency between 0.5 and 100 Hz to minimize noise. Subsequently, the independent component analysis (ICA) method was utilized to separate independent components associated with brain activity. Any components identified as unrelated to brain function, such as those related to blinking, electromyography, 50 Hz powerline interference, auditory artifacts, etc., were removed from the component list, resulting in a refined signal. For more detailed insights into the techniques used for identifying artifacts and brain-related components, please refer to[ 50 – 52 ]. \(F=‖{V}_{K}-G{J}_{K}‖+\alpha ‖{J}_{K}‖\) (Eq. 1) where \({V}_{K}\left(m\times 1\right)\) is recorded EEG signal in K th sample, \({J}_{K}\left(3n\times 1\right)\) is the source activity of the brain in K th sample and G \(\left(m\times 3n\right)\) is leadfield matrix which is calculated by forward problem solution like finite element method(FEM) or boundary element method(BEM)[ 53 , 54 ]. This function consists of two distinct parts: the first part relates to estimating errors, while the second part focuses on controlling noise reduction and managing sharp variations in source activities. A parameter called α determines how much these components affect the final function. Calculating this parameter involves methods like Tikhonov regularization or using techniques such as the L-curve[ 55 ]. Various approaches exist for minimizing Eq. 1, one of which is sLORETA, known for its ability to achieve zero localization error[ 55 , 56 ]. In the case of sLORETA, the explicit solution can be obtained by utilizing the known values of G and \({V}_{K}\) : \(\widehat{{J}_{K}}=T{.V}_{K}\) (Eq. 2) where \(\widehat{{J}_{K}}\left(3n\times 1\right)\) is estimated source activity of the brain and T \(\left(3n\times m\right)\) is a matrix which can be calculated to source activity estimation from EEG signals( \({V}_{K}\) ) and in sLORETA it can calculated from the following equation: \(T={G}^{T}H{\left[HG{G}^{T}H+\alpha H\right]}^{+}\) (Eq. 3) where \({\left[\right]}^{+}\) is pseudoinverse of matrix and H is regularization matrix for smoothness control and is defined as follows: \(H=I-1{1}^{T}/{1}^{T}1\) (Eq. 4) In this study, we consider the use of the identity matrix, denoted as I, and the vector of ones, denoted as 1, with dimensions of (m×1). The purpose of employing these mathematical constructs is to facilitate the active region selection process. To initiate the active region selection, the source activity estimation(Eq. 2) technique is employed on time-varying EEG signals. For each sample, the estimation identifies certain sources as active. The final selection of active sources is based on the identification of regions or sources that exhibit a higher probability of being active in each sample. In essence, this entails selecting the brain source that exhibits a greater frequency of activity compared to other sources throughout the duration of the analysis. Subsequently, a linear dynamic model is fitted to the selected active sources. This process involves aligning the parameters of the model with the extracted active sources to establish a meaningful representation of their dynamics. \({J}_{K}={{F}_{K}J}_{K-1}+{\eta }_{K}\) (Eq. 5) where \({\eta }_{K}\) is state noise and \({F}_{K}\) is relation matrix at K th sample. The \({F}_{K}\) characterizes the interdependencies among different brain active regions, as well as the relationship between several active regions and its own activity at sample K in relation to sample K-1. On the contrary, the relationship between active sources and EEG signals is influenced by the leadfield matrix, which is derived through the implementation of the forward problem method. This matrix encapsulates the spatial sensitivity patterns that connect the active sources to the measured EEG signals. In a simplified manner, this relationship can be expressed as follows: \(\left\{\begin{array}{c}{J}_{K}={{F}_{K}J}_{K-1}+{\eta }_{K} \\ \\ {V}_{K}=G{J}_{K}+{\epsilon }_{K}\end{array}\right.\) (Eq. 6) In this problem, the source activity during the time( \({J}_{K}\) ) and their relation matrix in time and space( \({F}_{K}\) ) are the unknown parameters and they are estimated by dual Kalman filter. the estimation equations and formulas are described in [ 57 , 58 ]. After performing the calculation for dynamic source activity ( \({J}_{K}\) ) and by knowing \({V}_{K}\) as EEG recorded signal, the next step involves fitting a multivariate autoregressive moving average model on the EEG channels, with \({V}_{K}\) being modeled in relation to previous samples of V and J. This multivariate ARMA(p,q) model can be expressed as follows in its general form: \({V}_{K}=\sum _{i=1}^{p}{a}_{i}{V}_{K-i}+ \sum _{i=0}^{q}{b}_{i}{J}_{K-i}\) (Eq. 7) where \({a}_{i},{b}_{i}\) are the model parameter matrixes at i th sample. Given that V is a vector with a size of m and J is a vector with a size of n, the size of the coefficient matrix \({a}_{i}\) is m×p, and the size of the coefficient matrix \({b}_{i}\) is n×(q + 1). In addition to the aforementioned multivariate ARMA model, our method also incorporates a second time series model that accounts for nonstationary EEG signals. This model is known as the autoregressive integrated moving average (ARIMA) model. The ARIMA(p,d,q) model is defined as follows: \({V}_{K}=\sum _{i=1}^{p}{a}_{i}{V}_{K-i}+ \sum _{i=0}^{q}{b}_{i}{J}_{K-i}+\sum _{i=1}^{d}{c}_{i`}{(1-Z)}^{d}{Y}_{i}\) (Eq. 8) where Z is the delay factor which are defined as follows $$\left(1-Z\right){Y}_{i}={Y}_{i}-{Y}_{i-1}$$ \({\left(1-Z\right)}^{2}{Y}_{i}={Y}_{i}-2{Y}_{i-1}+{Y}_{i-2}\) (Eq. 9) $$\dots$$ In this section, the source activities are considered as the input component of the model, while EEG signals are considered as the output component. The aim is to model each sample of the EEG signal using its delayed samples and source activities. To achieve this, ARMA matrices (denoted as 'a' and 'b') and ARIMA matrices (denoted as 'a', 'b', and 'c') are calculated for each sample. The size of these matrices depends on the model orders. Then, various features are extracted from these model parameters for the purpose of classification. Firstly, to reduce complexity, these parameters are divided into two classes, and several features are extracted from each class: Class 1: Parameters with small variation and a standard deviation lower than 20% of the mean value of the array. The mean values of these parameters are selected to contribute to the feature vectors. Class 2: Parameters with values greater than those in Class 1. For this class, the following statistical features are selected for feature vector: Mean value of the array signal. Standard deviation of the array signal. Kurtosis of the array signal. Skewness of the array signal. Entropy of the array signal. Next, the horizontal[ 59 ] and natural visibility graphs[ 60 , 61 ] of each array time series are constructed, and specific features from these graphs are selected to be part of the feature vectors. For a detailed understanding of visibility graphs, additional information can be found in [ 60 , 62 , 63 ]. Readers are encouraged to refer to these sources for further exploration. The mean of the graph nodes The standard deviation of graph nodes The mean value of the shortest path from each node to other nodes Following feature extraction and the creation of the feature vector, it becomes important to reduce the dimensionality of this vector to simplify complexity and enhance classification accuracy. Principal Component Analysis (PCA) is a highly recognized and effective method for feature vector dimension reduction. PCA aims to transform a set of potentially correlated high-dimensional features into a new set of uncorrelated variables known as principal components. This transformation retains the most important information from the original features while decreasing their dimensionality. PCA begins by normalizing or centering each feature by subtracting its mean value. Then, a correlation matrix is formed from these normalized features, and the eigenvalues of this matrix are calculated. The eigenvectors corresponding to high-magnitude eigenvalues are selected and arranged to construct a transformation matrix. This matrix helps project the original feature vector onto a lower-dimensional space defined by these selected eigenvectors. By discarding eigenvectors with low eigenvalues, PCA effectively reduces dimensionality while maintaining critical information. In the final phase of the algorithm, a Support Vector Machine (SVM) is used as a classifier to differentiate and identify depressive subjects from normal individuals. SVM is selected for its strong capability in classifying high-dimensional features. It aims to find a hyperplane that maximizes the margin between different training classes, focusing on the closest points known as support vectors. While briefly described here, more comprehensive information about SVM's mechanisms and optimization techniques can be found in relevant literature. SVM exhibits robust classification performance and is widely applied across various fields due to its adeptness in handling complex feature spaces and efficiently managing classification tasks. Simulation and results In this section, we applied the proposed method to EEG signals obtained from individuals diagnosed with autism as well as control participants. The implementation involved a series of steps. Initially, the signals were acquired and retrieved from. Following this, the signals underwent preprocessing stages utilizing a Butterworth filter, specifically a bandpass filter with cutoff frequencies set between 0.5 and 30 Hz. Subsequently, independent component analysis (ICA) was performed on the signals. ICA facilitated the extraction of independent components from the signals, aiming to eliminate components not related to brain activity, such as blinking, EMG artifacts, ECG artifacts, 50Hz noise, auditory brain response, etc. Details regarding the specific methodologies used for this purpose are elaborated in [ 50 – 52 ]. Following the preprocessing stage, the EEG signals were subjected to sLORETA (standardized low-resolution electromagnetic tomography) with zero localization error[ 55 , 56 ], which enabled the extraction of the underlying sources. The regularization parameter for sLORETA was determined using the Tikhonov regularization method [ 54 ]. Following this, active sources during the ECG recording period were identified, and those exhibiting higher activity across all samples were chosen. The number of selected sources equaled the number of EEG channels. Subsequently, a multivariate autoregressive (MVAR) model was fitted to the active sources, incorporating the relationship between the sources and EEG channels to construct a state space model. To estimate the dynamic source activity signal and simultaneously calculate the source relationship matrix, a dual Kalman filter was employed. Moreover, an autoregressive moving average (ARMA) or autoregressive integrated moving average (ARIMA) model with various orders was fitted between the source activity (as input) and the EEG channel recordings (as output). From the estimated parameters of the ARMA or ARIMA model, several statistical and graph features were extracted. To reduce their dimensionality, principal component analysis (PCA) was applied, and the feature vector size was reduced to 15 components using PCA. Finally, a support vector machine (SVM) was trained using the reduced feature set, and the classification process was carried out using the SVM. To evaluate the classification performance, various simulations were conducted to investigate the impact of different parameter variations. Additionally, several measures were defined for the validation of the classification. \(Accurency=\frac{TP+TN}{TP+TN+FP+FN}\) (Eq. 10) \(sensitivity=\frac{TP}{TP+FN}\) (Eq. 11) \(specificity=\frac{TN}{TN+FP}\) (Eq. 12) For the initial simulation, the classification was performed by varying the order of the ARMA model. To achieve this, several model orders were assumed for the ARMA and ARIMA model (refer to Eq. 7), and the corresponding results were presented in Table 1 . Table 1 The accuracy, sensitivity, specificity of EEG classification to autistic and control classes by proposed method with different ARMA and ARIMA model degrees ARMA(2,2) ARMA(4,2) ARMA(4,3) ARMA(5,4) ARMA(6,5) Accuracy 0.9107 0.9286 0.9464 0.9821 0.9464 Sensitivity 0.9286 0.9643 0.9643 1 0.9643 Specificity 0.8929 0.8929 0.9286 0.9643 0.9286 ARIMA(2,1,2) ARIMA(4,2,2) ARIMA(4,2,3) ARIMA(4,3,4) ARIMA(6,4,5) Accuracy 0.9286 0.9821 0.9821 1 0.9464 Sensitivity 0.9643 0.9643 1 1 0.9643 Specificity 0.9286 0.9286 0.9643 1 0.9286 According to the findings presented in Table 1 , it can be concluded that the ARMA(5,4) model outperforms the other models. Various methods for model order estimation have been proposed in previous studies, among which Akaike model order estimation is one approach[ 64 , 65 ]. By employing the Akaike method, the ARMA model order is determined to be ARMA(5,5), which closely resembles the ARMA(5,4) model that yields superior results in this simulation. In terms of the ARIMA model, both the ARIMA(4,2,3) and ARIMA(4,3,4) exhibit better performance compared to other model orders. Consequently, it can be concluded that the ARIMA model yields more accurate results than the ARMA model when using the same model order. This observation highlights the advantage of ARIMA in handling nonstationary signals by incorporating differencing operations. In the second simulation, the effects of two types of features are analyzed. Initially, only statistical features are utilized for classification. Subsequently, classification is performed using visibility graph-based features. Finally, classification is conducted by considering both statistical and visibility graph features. The accuracies of these simulations for the following models: ARMA(4,3), ARMA(5,4), ARIMA(4,2,3), and ARIMA(4,3,4), are plotted in Fig. 2 . In the second simulation, the accuracy of classifiers trained using visibility graph features is found to be higher compared to classifiers trained solely on statistical features. This improvement can be attributed to the inherent characteristics of visibility graphs, which capture additional structural information from the data. Furthermore, by examining Fig. 2 , it is evident that the ARIMA(4,3,4) model exhibits superior performance in classification tasks. This finding suggests that the ARIMA(4,3,4) model is more effective in capturing the underlying patterns and dynamics of the data, leading to improved classification accuracy compared to other models such as ARMA(4,3), ARMA(5,4), and ARIMA(4,2,3). In third simulation, the number of reduced feature by PCA is discussed. In previous simulations the number of features are reduced to 15 by PCA. But in this simulation the number of reduced features are set 5, 10, 15, 20,30, 50 and the classification accuracy with simulation time is discussed. The results of this simulation are noted in Table 2 . In this simulation the selected models are ARMA(5,4) and ARIMA(4,3,4) Table 2 The accuracy and simulation time of proposed method with different number of features which are reduced by PCA with ARMA(5,4) and ARIMA(4,3,4) 5 10 15 20 30 50 Accuracy (ARMA(5,4)) 0.8929 0.9464 0.9821 0.9821 1 1 Simulation time (ARMA(5,4)) In sec 762 983 1463 2873 3182 8982 Accuracy (ARMA(5,4)) 0.9286 0.9821 1 1 1 1 Simulation time (ARIMA(4,3,4)) In sec 1282 1676 3593 4282 7083 10012 According to the results presented in Table 2 , increasing the number of features used in SVM training leads to improved accuracy. However, it is important to note that this increase in accuracy is accompanied by a longer simulation time. The extended simulation time indicates higher complexity and computational load during the simulations. Interestingly, beyond the selection of 15 features, the increase in the number of features does not result in any noticeable improvement in accuracy, and the simulation time continues to increase. Consequently, it is advisable to carefully select the number of reduced features using PCA. In this case, the optimal number of reduced features appears to be 15, as it strikes a balance between reasonable computation time and satisfactory accuracy. In the latest simulation, the proposed method is compared to other methods used for the recognition of autistic candidates. To achieve this, the proposed method and other methods mentioned in previous studies were applied to the same dataset, and their classification accuracies were recorded in Table 3 . Table 3 the classification accuracy of autistic data with methods which are proposed by several papers Method No.1(48) Method No.2 (20) Method No.3(24) Method No.4 (32) Proposed method ARMA(5,4) Proposed method ARIMA(4,3,4) Accuracy 0.8929 0.9464 0.9464 0.9643 0.9821 1 The results from Table 3 demonstrate that the proposed method achieves higher accuracy compared to other methods. Therefore, applying the proposed method with ARIMA(4,3,4) leads to improved classification performance. However, it should be noted that this method requires more time compared to the proposed method with ARMA(5,4). ARMA models are typically employed when shorter simulation times are desired. Discussion This study introduces a method for identifying individuals with autism by leveraging EEG signals and features derived from multivariate autoregressive moving average (MVARMA) and multivariate integrated autoregressive (ARIMA) models. The method encompasses several steps, starting with source localization, estimation of source activity via a dual Kalman filter, and employing MVARMA and ARIMA models for parameter calculation. Subsequently, principal component analysis (PCA) is used to select pertinent parameters, followed by participant classification using a K-nearest neighbor classifier. The results showcase superior classification performance compared to alternative methods, highlighting the efficacy of this approach. The primary focus lies in using EEG signals to distinguish autistic participants from neurotypical ones by estimating source activities and capturing the dynamics and connectivity between brain sources, known to be altered in autism. To evaluate the method's performance, various simulations explore different parameter variations. Results from Table 1 show that the ARMA(5,4) and ARIMA(4,3,4) models outperformed other orders, with the Akaike method suggesting an ARMA(5,5) model similar to the superior ARMA(5,4) model observed. Regarding ARIMA, both ARIMA(4,2,3) and ARIMA(4,3,4) showed enhanced performance, highlighting the advantage of ARIMA in handling nonstationary signals through differencing operations. Another simulation investigates the impact of different features on classification performance, revealing that features extracted from high visibility graph (HVG) and non-visible graph (NVG) play significant roles. Combining these features with statistical ones yielded better results. Considering the computational load associated with numerous features, PCA for feature dimensionality reduction was explored, indicating that increased reduced features improve accuracy but lead to longer computation times, necessitating a balance between accuracy and computational efficiency. Lastly, comparison with alternative methods demonstrates the superiority of ARIMA(4,3,4). In summary, this study presents a novel method for autism identification using EEG signals and MVARMA/ARIMA-derived features, demonstrating superior classification performance and potential applications in understanding autism dynamics and connectivity among brain sources. The exploration of parameter variations and feature selections provides valuable insights into the method's effectiveness in autism recognition. Conclusion The study focuses on autism, a complex condition impacting individuals throughout life, marked by unique social, behavioral, and communication traits alongside reduced environmental focus. Detecting it early is pivotal for prevention and enhancing social and communication skills. Various methods exist for this purpose, including EEG, which records brain electrical activities via scalp sensors. Utilizing EEG signals allows analysis of brain activity, offering insights into autism's neurological processes. Our method estimates source activities, scrutinizing brain region connectivity to reveal autism-specific patterns and dynamics. We introduce a method employing EEG signals and features from MVARMA and ARIMA models to classify autism. These models capture data dependencies, statistical traits, and nonstationarity common in autism-related brain activity. Our method outperforms alternatives, effectively identifying autism. It estimates source activities, analyzes brain region relationships, aiding accurate autism classification against neurotypical participants. Our approach includes signal preprocessing, source localization, modeling, feature extraction, and classification. Through simulations and parameter variations, optimal model orders and features yielding high accuracy are identified. The study emphasizes understanding brain source dynamics and connectivity in autism. EEG signals, MVARMA, and ARIMA models highlight altered brain activity in autism. Feature reduction using PCA enhances computation efficiency while maintaining accuracy. The choice between ARIMA and ARMA models balances accuracy and time; ARMA suits shorter simulations. This study's conclusion presents an effective method using EEG signals for precise autism classification, benefiting early intervention. Future research on larger and diverse datasets will fortify the method's robustness and applicability. Generalizability across populations and age groups warrants exploration. Advancements in EEG technology offer promising avenues for enhancing autism recognition, leading to personalized interventions and improved outcomes for affected individuals. Declarations Author Contribution all the paper are proposed, simulate and written by Mehdi Rajabioun and nobody helps him in it Ethical requirements **Conflict of Interest/Financial Disclosure:** The authors declare no conflict of interest or financial support from any company related to the research conducted in this study. **Informed Consent in Studies with Human Subjects:** The data utilized in this study were obtained from publicly available sources on the web. As such, no direct interaction with human subjects or their personal information occurred, and therefore, informed consent was not required. **Animal Studies:** This research does not involve any experimentation or data collection related to animals. No animals were used or harmed in the course of this study. The research adheres to the ethical standards of data acquisition and handling as per the guidelines outlined above. This segment provides a clear and concise statement addressing the ethical considerations of the research, including declarations of no conflict of interest, the ethical use of data obtained from web sources without the need for human consent, and the absence of animal studies in the research process. References A. Jack and J. P. Morris, "Neocerebellar contributions to social perception in adolescents with autism spectrum disorder," (in eng), Dev Cogn Neurosci, vol. 10, pp. 77–92, Oct 2014, doi: 10.1016/j.dcn.2014.08.001 . J. Grèzes, B. Wicker, S. Berthoz, and B. de Gelder, "A failure to grasp the affective meaning of actions in autism spectrum disorder subjects," Neuropsychologia , vol. 47, no. 8, pp. 1816–1825, 2009/07/01/ 2009, doi: https://doi.org/10.1016/j.neuropsychologia.2009.02.021 . W. Sato, M. Toichi, S. Uono, and T. 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Kuo, "Evaluation of parametric methods in EEG signal analysis," Medical Engineering & Physics, vol. 17, no. 1, pp. 71–78, 1995/01/01/ 1995, doi: https://doi.org/10.1016/1350-4533(95)90380-T . Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3931787","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":271248104,"identity":"aaa99782-35d1-4e73-9150-193bd249fe2a","order_by":0,"name":"Mehdi Rajabioun","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2ElEQVRIiWNgGAWjYJACA8YGCSDFfABISMiQooUtAaSFhzhrGBtAJI8BmCSoWnf24QcFP3dYyBnc7vn86kaNBQ8D++GjG/BpMTuXZmDYe0bC2ODO2W3WOceADuNJS7uBV8sZBgMD3jaJxA03crcZ57ABtUjwmBHQwv7B8C9YS84z45x/RGnhMTCG2JLD/Di3jTgtBcayQL9I3kgzY87tk+BhI+wX9m2Gb3fUyfHdSH78OedbnRw/++FjeLUAAZsBjCEBJgkoBwHmBzDGByJUj4JRMApGwQgEABa+Ry/T/72dAAAAAElFTkSuQmCC","orcid":"","institution":"Mamaghan Branch, Islamic Azad University","correspondingAuthor":true,"prefix":"","firstName":"Mehdi","middleName":"","lastName":"Rajabioun","suffix":""}],"badges":[],"createdAt":"2024-02-05 18:59:15","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3931787/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3931787/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":50816313,"identity":"564aaaa8-3fdb-44f9-82b9-6f0e5d3577e0","added_by":"auto","created_at":"2024-02-07 19:47:42","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":18950,"visible":true,"origin":"","legend":"\u003cp\u003eThe flowchart of the proposed method which are based on the extracted features from MVAR (Source activity as input and EEG signal as output time series) parameters.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-3931787/v1/4337fa664dd3c1e35aa57963.png"},{"id":50816312,"identity":"83a81884-b1c8-41df-886f-d0539385897b","added_by":"auto","created_at":"2024-02-07 19:47:42","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":20438,"visible":true,"origin":"","legend":"\u003cp\u003eThe Accuracy of classification with proposed method by different features(statistical, visibility graph and both of them). It is classified by different model (ARMA(4,3), ARMA(5,4), ARIMA(4,2,3) and ARIMA(4,3,4))\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-3931787/v1/26e758347c8f9fab3642f634.png"},{"id":50864875,"identity":"ad30f705-5beb-4956-9cd4-de0044c8dfd4","added_by":"auto","created_at":"2024-02-08 14:53:17","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":315687,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3931787/v1/73b5184c-de85-40c7-986f-f9eabc065c80.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Autistic recognition from EEG signals by extracted features from several time series models","fulltext":[{"header":"Introduction","content":"\u003cp\u003eAutism is a complex brain condition with many different parts and aspects. It can show up in various ways and affects people differently. People with autism might struggle with communicating emotions and socializing. They might also find it hard to adapt to new situations or change their behavior. Some noticeable signs in people with autism include difficulty speaking, not paying much attention to what's happening around them, showing fewer emotions, and finding it tough to express feelings on their faces. These things are especially noticeable in children with autism[\u003cspan additionalcitationids=\"CR2\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Autism mostly shows up when someone is very young or during their teenage years. It's important to mention that many adults with autism also go through epilepsy or seizures at some time in their lives. This happening together highlights how important it is to identify, provide complete care, and offer support to people who are on the autism spectrum[\u003cspan additionalcitationids=\"CR5 CR6\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. There's strong proof showing that more and more people are being diagnosed with autism. A study from the Center for Disease Control and Prevention (CDC) in 2009 found that the number of autism cases has been going up consistently. In the United States, it went from being less than three cases for every 10,000 kids in 1970 to over 30 cases for every 10,000 kids in 1990. Then, in a report from 2012, the CDC said it had risen even more to one in 88 children, and especially high for boys at one in 54. These increasing numbers show how urgent it is to identify and support children with autism. By understanding more about how complex autism is, we can aim for better ways to spot it early, provide effective help, and improve the lives of those dealing with this condition[\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eVarious methods have been created to identify autism, all with the goal of spotting autism spectrum disorder (ASD) early on. This helps in getting help and support when needed. Each method has its good points and bad points. One method, behavioral observation, involves carefully watching how a child behaves, interacts with others, talks, and plays. But because it relies on someone's judgment and experience, it might lead to different opinions about behaviors and can cause differences in diagnoses[\u003cspan additionalcitationids=\"CR9\" citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. Different types of surveys and scales have been created to check for autism signs and measure how severe the symptoms are. Some examples are the Autism Diagnostic Interview-Revised (ADI-R) and the Autism Diagnostic Observation Schedule (ADOS)[\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. Relying on someone's personal reporting might bring in some unfairness and might not show all the different behaviors a person has. To look deeper, scientists use brain-scanning methods like functional magnetic resonance imaging (fMRI) and electroencephalography (EEG) to study how the brain works and connects in people with autism. These ways help without being invasive to see how the brain is structured and works. They give us clues about the brain reasons behind autism and might find special signs that could help diagnose it[\u003cspan additionalcitationids=\"CR13 CR14\" citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. Electroencephalography (EEG) records the brain's electrical activity using electrodes on the scalp. This method has many benefits when identifying autism. It's non-invasive, meaning it doesn't involve surgery or going inside the body, and it's quite affordable. EEG helps study the brain's electrical patterns and connections. By looking at how the brain's rhythms and syncing work, we can learn a lot about the unusual functions linked to autism[\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. Because EEG records brain activity directly, it's really good at catching quick changes in how the brain works. These benefits show how valuable EEG signals can be in spotting and understanding autism. They help find it early, create specific ways to help, and make treatments personalized for each person.\u003c/p\u003e \u003cp\u003eDetecting autism through EEG signals is a crucial aspect of neuroscience research, with various studies exploring different approaches in this area. Some research papers have used machine learning techniques to analyze EEG data, achieving high accuracy in distinguishing between individuals with autism and those without it [\u003cspan additionalcitationids=\"CR18 CR19 CR20 CR21 CR22\" citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. Others have suggested deep learning methods that extract key features from EEG signals, showing promising results in autism detection [\u003cspan additionalcitationids=\"CR25 CR26\" citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. Schwartz et al focused on investigating specific EEG frequency bands and their correlation with autism, revealing distinct patterns that could aid in identification [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. Additionally, innovative approaches combining EEG analysis with graph theory, introduced by Jurriaan and Precenzano et al., offer fresh perspectives on recognizing autism[\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. Tawhid et al. explored time-frequency analysis techniques to extract dynamic information from EEG signals, allowing the detection of temporal patterns associated with autism[\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]. Others, like Landowska, developed multi-modal approaches that integrate EEG data with other physiological signals, like heart rate and skin conductance, to improve the accuracy of identifying autism[\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]. Qaysar investigated advanced signal processing techniques, such as wavelet transforms and independent component analysis, to reveal unique EEG signatures linked to autism[\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]. These varied methods show global researchers' collaborative efforts, pushing the boundaries of autism detection using EEG signals and paving the way for more comprehensive diagnostic tools.Several studies have also pointed out abnormal connectivity patterns in specific brain regions of individuals with autism. Findings have indicated increased local connectivity but decreased long-distance connections in autism[\u003cspan additionalcitationids=\"CR35 CR36 CR37 CR38\" citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e]. Wass et al. reported increased connectivity in frontal and short neural pathways, while Coben et al. found increased coherence in frontal regions and decreased coherence in bilateral posterior temporal regions when comparing autistic subjects with neurotypical children[\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]. Studies utilizing Granger causality analysis found underconnectivity between distant brain regions, especially in the prefrontal cortex, anterior cingulate, and bilateral inferior parietal regions [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]. Another study by Coben et al. used Granger causality analysis to estimate effective connectivity from EEG signals and identified underconnectivity between regions that are distant from each other, specifically in the prefrontal cortex (PFC), anterior cingulate, and bilateral inferior parietal regions. Examining the relation between autism and effective connectivity during emotional processing tasks[\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e], Minshew and Williams observed increased frontal coherence but reduced anterior-to-posterior temporal coherence in autism[\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e]. Wataru Sato et al. applied dynamic causal modeling to fMRI data, revealing reduced activity in visual brain areas among autistic children[\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThis paper introduces novel approaches using multivariate autoregressive moving average (MVARMA) and multivariate autoregressive integrated moving average (MVARIMA) models. These models are applied to recorded signal and source activity time series. Features are derived from the parameters of these models, focusing on statistical values of the most influential ARMA and ARIMA model parameter time series. To compute source activity signals, an initial step involves applying a source localization method to EEG signals, isolating active sources. Then, a dual Kalman filter is employed on these active sources, estimating source activities alongside the source relationship matrix. Subsequently, the transformation occurs from sensor space (EEG signals) to source space (active brain regions). Finally, a multivariate ARMA and ARIMA model is fitted to each time sample of EEG signal based on past signal recordings and source activities.\u003c/p\u003e \u003cp\u003eAfter the source localization process, the focus shifts to estimating source dynamics, which represents changes in source activity across time. This estimation is a complex and vital aspect, and several research papers propose solutions to tackle this challenge. One traditional method is the dynamic causal model (DCM), which employs linear or nonlinear models to estimate neural connections based on existing physiological knowledge. It assumes nonlinear relationships between sources or neural dynamics, optimizing model parameters accordingly[\u003cspan additionalcitationids=\"CR44\" citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e]. Additionally, methods utilizing dual Kalman filters are utilized for estimating dynamic source activity[\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e, \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e]. For instance, A.H. Omidvarnia applies dual Kalman filter analysis to newborn EEG signals[\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e], while Eduardo Giraldo proposes a method using dual Kalman filters for source activity estimation. These approaches estimate source activity and their relationships concurrently across time, reducing estimation errors. In a study by Rajabioun et al., a dual Kalman filter-based approach is employed to estimate effective connectivity among sources, specifically applied to EEG signals from individuals with autism. This research revealed differences in effective connectivity between subjects with autism and those without it[\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e].\u003c/p\u003e"},{"header":"Materials and Methods","content":"\u003cp\u003eThis paper introduces a method aimed at distinguishing individuals with autism from control candidates. This classification is crucial for halting the advancement of disorders and enhancing the lives of those affected. The structure and flowchart detailing this proposed method are depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo begin, the EEG signal needs to be obtained or prepared. In this study, the signal was acquired by downloading it from [\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e].The dataset used in this research comprises EEG recordings gathered through the Biosemi ActiveTwo EEG system. It includes data from 28 individuals diagnosed with autism spectrum conditions and 28 neurotypical controls, spanning ages from 18 to 68 years. These recordings were conducted during a 2.5-minute (150 seconds) eyes-closed resting period. Permission for data collection and sharing was obtained from the Health Research Authority, specifically under the IRAS ID 212171[\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eOnce the preprocessing stage is completed, the filtered signals are subjected to a source localization technique. This process aims to estimate the active brain sources or regions. Its primary goal is to simplify complexity by identifying a limited number of active sources. This leads to determining the active brain regions and their corresponding spatial coordinates as the final output. In the context of source localization or pinpointing active brain regions, the goal is to minimize the following function:\u003c/p\u003e \u003cp\u003eThe raw EEG signals underwent several preprocessing stages to eliminate unwanted noise and artifacts. Initially, a bandpass Butterworth filter was applied, setting the cutoff frequency between 0.5 and 100 Hz to minimize noise. Subsequently, the independent component analysis (ICA) method was utilized to separate independent components associated with brain activity. Any components identified as unrelated to brain function, such as those related to blinking, electromyography, 50 Hz powerline interference, auditory artifacts, etc., were removed from the component list, resulting in a refined signal. For more detailed insights into the techniques used for identifying artifacts and brain-related components, please refer to[\u003cspan additionalcitationids=\"CR51\" citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(F=‖{V}_{K}-G{J}_{K}‖+\\alpha ‖{J}_{K}‖\\)\u003c/span\u003e \u003c/span\u003e (Eq.\u0026nbsp;1)\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({V}_{K}\\left(m\\times 1\\right)\\)\u003c/span\u003e\u003c/span\u003e is recorded EEG signal in K\u003csup\u003eth\u003c/sup\u003e sample, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({J}_{K}\\left(3n\\times 1\\right)\\)\u003c/span\u003e\u003c/span\u003e is the source activity of the brain in K\u003csup\u003eth\u003c/sup\u003e sample and G\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left(m\\times 3n\\right)\\)\u003c/span\u003e\u003c/span\u003e is leadfield matrix which is calculated by forward problem solution like finite element method(FEM) or boundary element method(BEM)[\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e, \u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e]. This function consists of two distinct parts: the first part relates to estimating errors, while the second part focuses on controlling noise reduction and managing sharp variations in source activities. A parameter called α determines how much these components affect the final function. Calculating this parameter involves methods like Tikhonov regularization or using techniques such as the L-curve[\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e55\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eVarious approaches exist for minimizing Eq.\u0026nbsp;1, one of which is sLORETA, known for its ability to achieve zero localization error[\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e55\u003c/span\u003e, \u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e56\u003c/span\u003e]. In the case of sLORETA, the explicit solution can be obtained by utilizing the known values of G and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({V}_{K}\\)\u003c/span\u003e\u003c/span\u003e:\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\widehat{{J}_{K}}=T{.V}_{K}\\)\u003c/span\u003e \u003c/span\u003e (Eq.\u0026nbsp;2)\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\widehat{{J}_{K}}\\left(3n\\times 1\\right)\\)\u003c/span\u003e\u003c/span\u003e is estimated source activity of the brain and T\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left(3n\\times m\\right)\\)\u003c/span\u003e\u003c/span\u003e is a matrix which can be calculated to source activity estimation from EEG signals(\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({V}_{K}\\)\u003c/span\u003e\u003c/span\u003e) and in sLORETA it can calculated from the following equation:\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(T={G}^{T}H{\\left[HG{G}^{T}H+\\alpha H\\right]}^{+}\\)\u003c/span\u003e \u003c/span\u003e (Eq.\u0026nbsp;3)\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\left[\\right]}^{+}\\)\u003c/span\u003e\u003c/span\u003eis pseudoinverse of matrix and H is regularization matrix for smoothness control and is defined as follows:\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(H=I-1{1}^{T}/{1}^{T}1\\)\u003c/span\u003e \u003c/span\u003e (Eq.\u0026nbsp;4)\u003c/p\u003e \u003cp\u003eIn this study, we consider the use of the identity matrix, denoted as I, and the vector of ones, denoted as 1, with dimensions of (m\u0026times;1). The purpose of employing these mathematical constructs is to facilitate the active region selection process.\u003c/p\u003e \u003cp\u003eTo initiate the active region selection, the source activity estimation(Eq.\u0026nbsp;2) technique is employed on time-varying EEG signals. For each sample, the estimation identifies certain sources as active. The final selection of active sources is based on the identification of regions or sources that exhibit a higher probability of being active in each sample. In essence, this entails selecting the brain source that exhibits a greater frequency of activity compared to other sources throughout the duration of the analysis.\u003c/p\u003e \u003cp\u003eSubsequently, a linear dynamic model is fitted to the selected active sources. This process involves aligning the parameters of the model with the extracted active sources to establish a meaningful representation of their dynamics.\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({J}_{K}={{F}_{K}J}_{K-1}+{\\eta }_{K}\\)\u003c/span\u003e \u003c/span\u003e (Eq.\u0026nbsp;5)\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\eta }_{K}\\)\u003c/span\u003e\u003c/span\u003e is state noise and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({F}_{K}\\)\u003c/span\u003e\u003c/span\u003e is relation matrix at K\u003csup\u003eth\u003c/sup\u003e sample. The \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({F}_{K}\\)\u003c/span\u003e\u003c/span\u003e characterizes the interdependencies among different brain active regions, as well as the relationship between several active regions and its own activity at sample K in relation to sample K-1. On the contrary, the relationship between active sources and EEG signals is influenced by the leadfield matrix, which is derived through the implementation of the forward problem method. This matrix encapsulates the spatial sensitivity patterns that connect the active sources to the measured EEG signals. In a simplified manner, this relationship can be expressed as follows:\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\left\\{\\begin{array}{c}{J}_{K}={{F}_{K}J}_{K-1}+{\\eta }_{K} \\\\ \\\\ {V}_{K}=G{J}_{K}+{\\epsilon }_{K}\\end{array}\\right.\\)\u003c/span\u003e \u003c/span\u003e (Eq.\u0026nbsp;6)\u003c/p\u003e \u003cp\u003eIn this problem, the source activity during the time(\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({J}_{K}\\)\u003c/span\u003e\u003c/span\u003e) and their relation matrix in time and space(\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({F}_{K}\\)\u003c/span\u003e\u003c/span\u003e) are the unknown parameters and they are estimated by dual Kalman filter. the estimation equations and formulas are described in [\u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e57\u003c/span\u003e, \u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e58\u003c/span\u003e]. After performing the calculation for dynamic source activity (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({J}_{K}\\)\u003c/span\u003e\u003c/span\u003e) and by knowing \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({V}_{K}\\)\u003c/span\u003e\u003c/span\u003e as EEG recorded signal, the next step involves fitting a multivariate autoregressive moving average model on the EEG channels, with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({V}_{K}\\)\u003c/span\u003e\u003c/span\u003e being modeled in relation to previous samples of V and J. This multivariate ARMA(p,q) model can be expressed as follows in its general form:\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({V}_{K}=\\sum _{i=1}^{p}{a}_{i}{V}_{K-i}+ \\sum _{i=0}^{q}{b}_{i}{J}_{K-i}\\)\u003c/span\u003e \u003c/span\u003e (Eq.\u0026nbsp;7)\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({a}_{i},{b}_{i}\\)\u003c/span\u003e\u003c/span\u003e are the model parameter matrixes at i\u003csup\u003eth\u003c/sup\u003e sample. Given that V is a vector with a size of m and J is a vector with a size of n, the size of the coefficient matrix \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({a}_{i}\\)\u003c/span\u003e\u003c/span\u003e is m\u0026times;p, and the size of the coefficient matrix \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({b}_{i}\\)\u003c/span\u003e\u003c/span\u003e is n\u0026times;(q\u0026thinsp;+\u0026thinsp;1).\u003c/p\u003e \u003cp\u003eIn addition to the aforementioned multivariate ARMA model, our method also incorporates a second time series model that accounts for nonstationary EEG signals. This model is known as the autoregressive integrated moving average (ARIMA) model. The ARIMA(p,d,q) model is defined as follows:\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({V}_{K}=\\sum _{i=1}^{p}{a}_{i}{V}_{K-i}+ \\sum _{i=0}^{q}{b}_{i}{J}_{K-i}+\\sum _{i=1}^{d}{c}_{i`}{(1-Z)}^{d}{Y}_{i}\\)\u003c/span\u003e \u003c/span\u003e (Eq.\u0026nbsp;8)\u003c/p\u003e \u003cp\u003ewhere Z is the delay factor which are defined as follows\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\left(1-Z\\right){Y}_{i}={Y}_{i}-{Y}_{i-1}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\({\\left(1-Z\\right)}^{2}{Y}_{i}={Y}_{i}-2{Y}_{i-1}+{Y}_{i-2}\\)\u003c/span\u003e \u003c/span\u003e(Eq.\u0026nbsp;9)\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$$\\dots$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn this section, the source activities are considered as the input component of the model, while EEG signals are considered as the output component. The aim is to model each sample of the EEG signal using its delayed samples and source activities. To achieve this, ARMA matrices (denoted as 'a' and 'b') and ARIMA matrices (denoted as 'a', 'b', and 'c') are calculated for each sample. The size of these matrices depends on the model orders.\u003c/p\u003e \u003cp\u003eThen, various features are extracted from these model parameters for the purpose of classification. Firstly, to reduce complexity, these parameters are divided into two classes, and several features are extracted from each class:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eClass 1: Parameters with small variation and a standard deviation lower than 20% of the mean value of the array. The mean values of these parameters are selected to contribute to the feature vectors.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eClass 2: Parameters with values greater than those in Class 1. For this class, the following statistical features are selected for feature vector:\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eMean value of the array signal.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eStandard deviation of the array signal.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eKurtosis of the array signal.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eSkewness of the array signal.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eEntropy of the array signal.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eNext, the horizontal[\u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e59\u003c/span\u003e] and natural visibility graphs[\u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e60\u003c/span\u003e, \u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e61\u003c/span\u003e] of each array time series are constructed, and specific features from these graphs are selected to be part of the feature vectors. For a detailed understanding of visibility graphs, additional information can be found in [\u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e60\u003c/span\u003e, \u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e62\u003c/span\u003e, \u003cspan citationid=\"CR63\" class=\"CitationRef\"\u003e63\u003c/span\u003e]. Readers are encouraged to refer to these sources for further exploration.\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eThe mean of the graph nodes\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eThe standard deviation of graph nodes\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eThe mean value of the shortest path from each node to other nodes\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eFollowing feature extraction and the creation of the feature vector, it becomes important to reduce the dimensionality of this vector to simplify complexity and enhance classification accuracy. Principal Component Analysis (PCA) is a highly recognized and effective method for feature vector dimension reduction. PCA aims to transform a set of potentially correlated high-dimensional features into a new set of uncorrelated variables known as principal components. This transformation retains the most important information from the original features while decreasing their dimensionality. PCA begins by normalizing or centering each feature by subtracting its mean value. Then, a correlation matrix is formed from these normalized features, and the eigenvalues of this matrix are calculated. The eigenvectors corresponding to high-magnitude eigenvalues are selected and arranged to construct a transformation matrix. This matrix helps project the original feature vector onto a lower-dimensional space defined by these selected eigenvectors. By discarding eigenvectors with low eigenvalues, PCA effectively reduces dimensionality while maintaining critical information.\u003c/p\u003e \u003cp\u003eIn the final phase of the algorithm, a Support Vector Machine (SVM) is used as a classifier to differentiate and identify depressive subjects from normal individuals. SVM is selected for its strong capability in classifying high-dimensional features. It aims to find a hyperplane that maximizes the margin between different training classes, focusing on the closest points known as support vectors. While briefly described here, more comprehensive information about SVM's mechanisms and optimization techniques can be found in relevant literature. SVM exhibits robust classification performance and is widely applied across various fields due to its adeptness in handling complex feature spaces and efficiently managing classification tasks.\u003c/p\u003e"},{"header":"Simulation and results","content":"\u003cp\u003eIn this section, we applied the proposed method to EEG signals obtained from individuals diagnosed with autism as well as control participants. The implementation involved a series of steps. Initially, the signals were acquired and retrieved from. Following this, the signals underwent preprocessing stages utilizing a Butterworth filter, specifically a bandpass filter with cutoff frequencies set between 0.5 and 30 Hz. Subsequently, independent component analysis (ICA) was performed on the signals. ICA facilitated the extraction of independent components from the signals, aiming to eliminate components not related to brain activity, such as blinking, EMG artifacts, ECG artifacts, 50Hz noise, auditory brain response, etc. Details regarding the specific methodologies used for this purpose are elaborated in [\u003cspan additionalcitationids=\"CR51\" citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e]. Following the preprocessing stage, the EEG signals were subjected to sLORETA (standardized low-resolution electromagnetic tomography) with zero localization error[\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e55\u003c/span\u003e, \u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e56\u003c/span\u003e], which enabled the extraction of the underlying sources. The regularization parameter for sLORETA was determined using the Tikhonov regularization method [\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e]. Following this, active sources during the ECG recording period were identified, and those exhibiting higher activity across all samples were chosen. The number of selected sources equaled the number of EEG channels. Subsequently, a multivariate autoregressive (MVAR) model was fitted to the active sources, incorporating the relationship between the sources and EEG channels to construct a state space model. To estimate the dynamic source activity signal and simultaneously calculate the source relationship matrix, a dual Kalman filter was employed. Moreover, an autoregressive moving average (ARMA) or autoregressive integrated moving average (ARIMA) model with various orders was fitted between the source activity (as input) and the EEG channel recordings (as output). From the estimated parameters of the ARMA or ARIMA model, several statistical and graph features were extracted. To reduce their dimensionality, principal component analysis (PCA) was applied, and the feature vector size was reduced to 15 components using PCA. Finally, a support vector machine (SVM) was trained using the reduced feature set, and the classification process was carried out using the SVM. To evaluate the classification performance, various simulations were conducted to investigate the impact of different parameter variations. Additionally, several measures were defined for the validation of the classification.\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(Accurency=\\frac{TP+TN}{TP+TN+FP+FN}\\)\u003c/span\u003e \u003c/span\u003e (Eq.\u0026nbsp;10)\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(sensitivity=\\frac{TP}{TP+FN}\\)\u003c/span\u003e \u003c/span\u003e (Eq.\u0026nbsp;11)\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(specificity=\\frac{TN}{TN+FP}\\)\u003c/span\u003e \u003c/span\u003e (Eq.\u0026nbsp;12)\u003c/p\u003e \u003cp\u003eFor the initial simulation, the classification was performed by varying the order of the ARMA model. To achieve this, several model orders were assumed for the ARMA and ARIMA model (refer to Eq.\u0026nbsp;7), and the corresponding results were presented in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe accuracy, sensitivity, specificity of EEG classification to autistic and control classes by proposed method with different ARMA and ARIMA model degrees\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eARMA(2,2)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eARMA(4,2)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eARMA(4,3)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eARMA(5,4)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eARMA(6,5)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAccuracy\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.9107\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9286\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.9464\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9821\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.9464\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSensitivity\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.9286\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9643\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.9643\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.9643\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSpecificity\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.8929\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.8929\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.9286\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9643\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.9286\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eARIMA(2,1,2)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eARIMA(4,2,2)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eARIMA(4,2,3)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eARIMA(4,3,4)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eARIMA(6,4,5)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAccuracy\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.9286\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9821\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.9821\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.9464\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSensitivity\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.9643\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9643\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.9643\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSpecificity\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.9286\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9286\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.9643\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.9286\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eAccording to the findings presented in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, it can be concluded that the ARMA(5,4) model outperforms the other models. Various methods for model order estimation have been proposed in previous studies, among which Akaike model order estimation is one approach[\u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e64\u003c/span\u003e, \u003cspan citationid=\"CR65\" class=\"CitationRef\"\u003e65\u003c/span\u003e]. By employing the Akaike method, the ARMA model order is determined to be ARMA(5,5), which closely resembles the ARMA(5,4) model that yields superior results in this simulation. In terms of the ARIMA model, both the ARIMA(4,2,3) and ARIMA(4,3,4) exhibit better performance compared to other model orders. Consequently, it can be concluded that the ARIMA model yields more accurate results than the ARMA model when using the same model order. This observation highlights the advantage of ARIMA in handling nonstationary signals by incorporating differencing operations.\u003c/p\u003e \u003cp\u003eIn the second simulation, the effects of two types of features are analyzed. Initially, only statistical features are utilized for classification. Subsequently, classification is performed using visibility graph-based features. Finally, classification is conducted by considering both statistical and visibility graph features. The accuracies of these simulations for the following models: ARMA(4,3), ARMA(5,4), ARIMA(4,2,3), and ARIMA(4,3,4), are plotted in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn the second simulation, the accuracy of classifiers trained using visibility graph features is found to be higher compared to classifiers trained solely on statistical features. This improvement can be attributed to the inherent characteristics of visibility graphs, which capture additional structural information from the data. Furthermore, by examining Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, it is evident that the ARIMA(4,3,4) model exhibits superior performance in classification tasks. This finding suggests that the ARIMA(4,3,4) model is more effective in capturing the underlying patterns and dynamics of the data, leading to improved classification accuracy compared to other models such as ARMA(4,3), ARMA(5,4), and ARIMA(4,2,3).\u003c/p\u003e \u003cp\u003eIn third simulation, the number of reduced feature by PCA is discussed. In previous simulations the number of features are reduced to 15 by PCA. But in this simulation the number of reduced features are set 5, 10, 15, 20,30, 50 and the classification accuracy with simulation time is discussed. The results of this simulation are noted in Table \u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. In this simulation the selected models are ARMA(5,4) and ARIMA(4,3,4)\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe accuracy and simulation time of proposed method with different number of features which are reduced by PCA with ARMA(5,4) and ARIMA(4,3,4)\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAccuracy (ARMA(5,4))\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.8929\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9464\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.9821\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9821\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSimulation time (ARMA(5,4))\u003c/p\u003e \u003cp\u003eIn sec\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e762\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e983\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1463\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2873\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e3182\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e8982\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAccuracy (ARMA(5,4))\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.9286\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9821\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSimulation time (ARIMA(4,3,4))\u003c/p\u003e \u003cp\u003eIn sec\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1282\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1676\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3593\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e4282\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e7083\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e10012\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eAccording to the results presented in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, increasing the number of features used in SVM training leads to improved accuracy. However, it is important to note that this increase in accuracy is accompanied by a longer simulation time. The extended simulation time indicates higher complexity and computational load during the simulations. Interestingly, beyond the selection of 15 features, the increase in the number of features does not result in any noticeable improvement in accuracy, and the simulation time continues to increase. Consequently, it is advisable to carefully select the number of reduced features using PCA. In this case, the optimal number of reduced features appears to be 15, as it strikes a balance between reasonable computation time and satisfactory accuracy.\u003c/p\u003e \u003cp\u003eIn the latest simulation, the proposed method is compared to other methods used for the recognition of autistic candidates. To achieve this, the proposed method and other methods mentioned in previous studies were applied to the same dataset, and their classification accuracies were recorded in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ethe classification accuracy of autistic data with methods which are proposed by several papers\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMethod No.1(48)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMethod No.2 (20)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMethod No.3(24)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eMethod No.4 (32)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eProposed method ARMA(5,4)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eProposed method ARIMA(4,3,4)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAccuracy\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.8929\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9464\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.9464\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9643\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.9821\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe results from Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e demonstrate that the proposed method achieves higher accuracy compared to other methods. Therefore, applying the proposed method with ARIMA(4,3,4) leads to improved classification performance. However, it should be noted that this method requires more time compared to the proposed method with ARMA(5,4). ARMA models are typically employed when shorter simulation times are desired.\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eThis study introduces a method for identifying individuals with autism by leveraging EEG signals and features derived from multivariate autoregressive moving average (MVARMA) and multivariate integrated autoregressive (ARIMA) models. The method encompasses several steps, starting with source localization, estimation of source activity via a dual Kalman filter, and employing MVARMA and ARIMA models for parameter calculation. Subsequently, principal component analysis (PCA) is used to select pertinent parameters, followed by participant classification using a K-nearest neighbor classifier. The results showcase superior classification performance compared to alternative methods, highlighting the efficacy of this approach. The primary focus lies in using EEG signals to distinguish autistic participants from neurotypical ones by estimating source activities and capturing the dynamics and connectivity between brain sources, known to be altered in autism.\u003c/p\u003e \u003cp\u003eTo evaluate the method's performance, various simulations explore different parameter variations. Results from Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e show that the ARMA(5,4) and ARIMA(4,3,4) models outperformed other orders, with the Akaike method suggesting an ARMA(5,5) model similar to the superior ARMA(5,4) model observed. Regarding ARIMA, both ARIMA(4,2,3) and ARIMA(4,3,4) showed enhanced performance, highlighting the advantage of ARIMA in handling nonstationary signals through differencing operations.\u003c/p\u003e \u003cp\u003eAnother simulation investigates the impact of different features on classification performance, revealing that features extracted from high visibility graph (HVG) and non-visible graph (NVG) play significant roles. Combining these features with statistical ones yielded better results. Considering the computational load associated with numerous features, PCA for feature dimensionality reduction was explored, indicating that increased reduced features improve accuracy but lead to longer computation times, necessitating a balance between accuracy and computational efficiency.\u003c/p\u003e \u003cp\u003eLastly, comparison with alternative methods demonstrates the superiority of ARIMA(4,3,4). In summary, this study presents a novel method for autism identification using EEG signals and MVARMA/ARIMA-derived features, demonstrating superior classification performance and potential applications in understanding autism dynamics and connectivity among brain sources. The exploration of parameter variations and feature selections provides valuable insights into the method's effectiveness in autism recognition.\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eThe study focuses on autism, a complex condition impacting individuals throughout life, marked by unique social, behavioral, and communication traits alongside reduced environmental focus. Detecting it early is pivotal for prevention and enhancing social and communication skills. Various methods exist for this purpose, including EEG, which records brain electrical activities via scalp sensors. Utilizing EEG signals allows analysis of brain activity, offering insights into autism's neurological processes. Our method estimates source activities, scrutinizing brain region connectivity to reveal autism-specific patterns and dynamics.\u003c/p\u003e \u003cp\u003eWe introduce a method employing EEG signals and features from MVARMA and ARIMA models to classify autism. These models capture data dependencies, statistical traits, and nonstationarity common in autism-related brain activity. Our method outperforms alternatives, effectively identifying autism. It estimates source activities, analyzes brain region relationships, aiding accurate autism classification against neurotypical participants. Our approach includes signal preprocessing, source localization, modeling, feature extraction, and classification. Through simulations and parameter variations, optimal model orders and features yielding high accuracy are identified.\u003c/p\u003e \u003cp\u003eThe study emphasizes understanding brain source dynamics and connectivity in autism. EEG signals, MVARMA, and ARIMA models highlight altered brain activity in autism. Feature reduction using PCA enhances computation efficiency while maintaining accuracy. The choice between ARIMA and ARMA models balances accuracy and time; ARMA suits shorter simulations. This study's conclusion presents an effective method using EEG signals for precise autism classification, benefiting early intervention. Future research on larger and diverse datasets will fortify the method's robustness and applicability. Generalizability across populations and age groups warrants exploration. Advancements in EEG technology offer promising avenues for enhancing autism recognition, leading to personalized interventions and improved outcomes for affected individuals.\u003c/p\u003e "},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eall the paper are proposed, simulate and written by Mehdi Rajabioun and nobody helps him in it\u003c/p\u003e\u003cp\u003eEthical requirements \u0026nbsp;\u003c/p\u003e\n\u003cp\u003e**Conflict of Interest/Financial Disclosure:** The authors declare no conflict of interest or financial support from any company related to the research conducted in this study.\u003c/p\u003e\n\u003cp\u003e**Informed Consent in Studies with Human Subjects:** The data utilized in this study were obtained from publicly available sources on the web. As such, no direct interaction with human subjects or their personal information occurred, and therefore, informed consent was not required.\u003c/p\u003e\n\u003cp\u003e**Animal Studies:** This research does not involve any experimentation or data collection related to animals. No animals were used or harmed in the course of this study.\u003c/p\u003e\n\u003cp\u003eThe research adheres to the ethical standards of data acquisition and handling as per the guidelines outlined above.\u003c/p\u003e\n\u003cp\u003eThis segment provides a clear and concise statement addressing the ethical considerations of the research, including declarations of no conflict of interest, the ethical use of data obtained from web sources without the need for human consent, and the absence of animal studies in the research process.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eA. Jack and J. P. 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It is characterized by atypical social, behavioral, and communication skills, as well as diminished attention to the surrounding environment. The detection and recognition of autism can contribute to the prevention of its development and the enhancement of social and communicational abilities. Various methods are employed for autism recognition, including questionnaire tests and neurological techniques. One such neuroimaging method is electroencephalography (EEG), which records the brain's electrical activities through sensors placed on the scalp. This paper proposes a method for identifying individuals with autism using EEG signals and features extracted from a multivariate autoregressive moving average (MVARMA) and multivariate integrated autoregressive(ARIMA) models. The approach begins by estimating active sources through source localization methods, followed by the application of a dual Kalman filter to estimate source activity. Subsequently, the MVARMA and ARIMA models are applied to the EEG sensor and active source data, enabling the calculation of model parameters. Principal component analysis is then utilized to select important parameters, and a K nearest neighbor classifier is employed to classify participants as either autistic or neurotypical. The results demonstrate superior classification performance, achieving higher accuracy compared to alternative methods. The proposed method yields superior classification outcomes when compared to other approaches, as it exhibits improved classification measures.\u003c/p\u003e","manuscriptTitle":"Autistic recognition from EEG signals by extracted features from several time series models","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-02-07 19:47:37","doi":"10.21203/rs.3.rs-3931787/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"2482a021-1e4e-414b-977a-1ed65b81f604","owner":[],"postedDate":"February 7th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-02-08T14:45:09+00:00","versionOfRecord":[],"versionCreatedAt":"2024-02-07 19:47:37","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-3931787","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3931787","identity":"rs-3931787","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}