EEG-Based Brain Functional Network Analysis for Differential Identification of Dementia-Related Disorders and Their Onset

Diagnosing and treating dementia, including mild cognitive impairment (MCI), is challenging due to diverse disease types and overlapping symptoms. Early MCI detection is vital as it can precede dementia, yet distinguishing it from later stage dementia is intricate due to subtle symptoms. The primary objective of this study is to adopt a complex network perspective to unravel the underlying pathophysiological mechanisms of dementia-related disorders. Leveraging the extensive availability of electroencephalogram (EEG) data, our study focuses on the meticulous identification and analysis of EEG-based brain functional network (BFNs) associated with dementia-related disorders. To achieve this, we employ the Phase Lag Index (PLI) as a connectivity measure, offering a comprehensive view of neural interactions. To enhance the analytical rigor, we introduce a data-driven threshold selection technique. This innovative approach allows us to compare the topological structures of the formulated BFNs using complex network measures quantitatively and statistically. Furthermore, we harness the power of these BFNs by utilizing them as pre-defined graph inputs for a Graph Convolution Network (GCN-net) based approach. The results demonstrate that graph theory metrics, such as the rich-club coefficient, transitivity, and assortativity coefficients, effectively distinguish between MCI, Alzheimer’s disease (AD) and vascular dementia (VD). Furthermore, GCN-net achieves high accuracy (95.07% delta, 80.62% theta) and F1-scores (0.92 delta, 0.67 theta), highlighting the effectiveness of EEG-based BFNs in the analysis of dementia-related disorders.


I. INTRODUCTION
D EMENTIA, characterized by a decline in cognitive function impacting daily activities, comprises various neurodegenerative disorders, with Alzheimer's disease (AD) being the most common [1].Despite extensive research, the precise etiology remains elusive [2].While the amyloid hypothesis, attributing dementia to amyloid-beta protein accumulation, has been prominent, recent studies challenge this notion, implicating tau protein and inflammation [3].
Neuroimaging, pivotal in neurological disease diagnosis, includes magnetic resonance imaging (MRI) and positron emission tomography (PET).While these modalities are valuable, they have limitations in temporal resolution and cost.Electroencephalography (EEG), offering affordability and portability [4], [5], [6], emerges as a promising alternative, particularly in light of the evolving understanding of dementia's etiology.Its potential in the differential diagnosis of Mild Cognitive Impairment (MCI) and late-onset dementias remains underexplored.
Complex network analysis, a prominent tool in cognitive and computational neuroscience [7], [8], offers a comprehensive view of the brain as a complex network with nodes (regions or neurons) and edges (functional interactions).Exploring topological properties such as degree distribution and clustering coefficient provides valuable insights into network characteristics.Brain network analysis encompasses two primary approaches: weighted and unweighted [9], [10].In weighted networks, connection strength is quantified using techniques like coherence or phase synchronization, while unweighted networks represent connections as binary values through thresholding [9].Challenges in both approaches, such as threshold selection and noise filtering, have prompted various techniques, including arbitrary/random threshold selection [11], [12], sparsity thresholding [13], statistical methods [14], global cost efficiency maximization [15], giant component analysis [16], and threshold selection based on maximum and minimum spanning trees [17].Despite these advancements, the underutilization of traditional network properties in formulating brain functional networks for dementia-related disorders underscores the need for continued exploration and refinement in network analysis methodologies.
Additionally, conventional EEG classification employing machine learning techniques relies on approaches like common spatial patterns [18], wavelet transform [19], Hilbert-Huang transform, and empirical mode decomposition [20], [21] for feature extraction.While these methods are crucial in various applications, particularly in binary EEG classification, they often encounter challenges related to subjectivity, biases, and cumbersome engineering and selection processes [1].Similarly, the integration of EEG-based functional connectivity features with traditional machine learning for dementia disorder recognition is not immune to these issues [6], [22].Therefore, there is a pressing need for automated feature extraction methods to manage the highlighted limitations.
To tackle the highlighted challenges, the field is transitioning towards deep learning, specifically embracing Graph Neural Networks (GNNs) designed for graph-structured data like EEG networks [1].GNNs excel in capturing spatial dependencies and managing temporal dynamics in EEG signals, outperforming alternatives such as convolutional neural networks (CNN) and long short-term memory (LSTM) [23].They exhibit promise in various applications, spanning braincomputer interfaces, affective computing, and neurological disorder diagnosis.However, despite their potential, the exploration of data-driven techniques for GNN design in the EEG context is relatively limited compared to model-driven GNN approaches.
To address these limitations, we propose a framework for functional connectivity analysis of EEG datasets from healthy and dementia subjects.Utilizing the phase lag index, we introduce a novel threshold selection framework based on eigenvector centrality for enhanced interpretability.Brain Functional Networks (BFNs) are formulated, and graph theory metrics are employed for a comprehensive analysis.Differential diagnosis is performed using a Graph Convolutional Network (GCN-net), providing a holistic approach.
To this end, the main contributions of this study are: • Introduction of a novel framework for threshold selection based on the eigenvector centrality of connectivity matrices for the formulation of brain functional networks (BFNs).This approach identifies significant network connections in dementia-related subjects, enhancing interpretability in network analysis.
• Quantification of the formulated BFNs with various graph theory metrics for a comprehensive understanding of network alterations in various dementia-related disorders.
• Development of a data-driven Graph Convolutional Network (GCN) for the differential diagnosis of dementia-related disorders to highlight the potential of combining EEG-based functional connectivity analysis with deep learning for clinical purposes.The proposed framework's workflow is illustrated in Fig. 1.The rest of this article is organized as follows: methodology details are presented in Section II, followed by validation results in Section III and their discussion in Section IV.The paper concludes with final remarks in Section V.
The electroencephalogram signals (EEG) were recorded using an EEG cap containing 23 to 30 active electrode locations.EEG signals from 23 common electrode locations, comprising Fp1, Fp2, F3, F4, F7, F8, Fz, FT9, FT10, T1, T2, T7, T8, C3, C4, Cz, P3, P4, P7, P8, Pz, O1, and O2 in the 10-20 configuration, were extracted and used in this paper.Specifically, only the eyes-open data from the last 10 minutes of the original 20-minute EEG recording were utilized, while the first 10 minutes represented the resting data in eyesclosed condition.Subjects were carefully monitored during the experimental course to minimize movement and prevent signal contamination with artifacts.The recorded signals were bandpassed between 1 Hz to 45 Hz, covering the delta, theta, alpha, beta, and lower gamma bands, respectively.The band-passed signals were down-sampled to 256 Hz, and eye blinks and head movement artifacts were removed using the EEGLAB toolbox.Artifact-free EEG signals were segmented into epochs of 10 seconds each by sliding a moving window with a 50% overlap across the signal's length.The 10-second epoch is referred to as a single trial for analysis in this study.

A. Phase Lag Index, PLI
Phase synchronization metrics, such as Phase Locking Value (PLV) and Phase Lag Index (PLI), are used in neuroscience to quantify interactions between brain areas.PLI is more robust to common sources and addresses issues with phase differences around 0 and π [26], [27], [28].It quantifies asymmetry in phase distribution.The PLI between EEG channel pairs over N trials is defined as: where n (t, f ) is the phase difference between pairs of nodes in the nth trial, defined as: Here, ch1 (t, f) and ch2 (t, f) represent the instantaneous phases of EEG channel 1 and channel 2 signals.The average  PLI computed over all trials is indicative of phase locking strength, ranging from 0 (no coupling or coupling around 0 mod π) to 1 (perfect phase locking at a value of other than 0 mod π ).

B. Identification of Band-Specific Most Significant Connections
Brain Functional Networks (BFNs) are composed of nodes and connections, with varying centrality values indicating node contributions to network properties.Among these connections, certain ones, referred to as Most Significant Connections (MSCs), play a pivotal role in identifying network characteristics.In this study, MSCs are defined as those revealing substantial variation in functional connectivity measures between a neurological state and a reference state (see Fig. 2).Identifying MSCs involves considering node importance based on eigenvector centrality measures, a method widely used to pinpoint the most crucial nodes in a network.Eigenvector centrality accounts for both the number of connections a node possesses and the centrality of its connected nodes [29].
In this study, we introduce the algorithm for identifying 'n' significant electrodes, outlined in Algorithm 1.The algorithm incorporates the concept of PLI sub (band), representing subject-specific PLI matrices from dementia-related groups, and PLI ref (band), indicating the reference PLI matrix derived from the average PLI matrix of the normal control (NC) group.Utilizing the average PLI matrix of the NC group as a reference serves multiple purposes within our framework: • Establishing a Reasonable Baseline for Comparison: This choice provides a robust baseline, representing expected connectivity patterns in a healthy population.It enables quantifying differences between the connectivity of dementia-related subjects and that of the average NC group.
• Quantifying Differences in Connectivity: The reference PLI matrix facilitates quantifying differences in connectivity, essential for identifying and characterizing abnormalities in the brain networks of dementia patients.This step is crucial for diagnosis and understanding disease mechanisms in conditions like MCI, AD, and VD.
• Insight into Disease Mechanisms: Contrasting connectivity patterns between dementia-related subjects and the NC group yields insights into specific alterations in brain network connectivity associated with each disorder.This knowledge aids understanding disease progression and guiding the development of targeted interventions.Upon identifying 'n' significant electrodes, MSCs are determined by considering all edges connecting these electrodes and those connecting them with non-significant ones, as illustrated in Fig. 2.This process ensures a focused exploration of connectivity alterations in dementia-related disorders, contributing to a deeper understanding of the intricate dynamics within brain networks associated with these conditions.

C. Threshold Selection and Brain Functional Network Formulation
For the analysis of the neurological state related to the network's dynamical mechanism, it is imperative to establish a proper and unbiased threshold that preserves important connections while removing spurious ones.In this approach, Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
a pair of nodes is considered connected if the strength of the connection between them is greater than or equal to a certain threshold value.Averaging the Phase Lag Index (PLI) over a given frequency band, the proposed threshold value is obtained by the relation: where, ⟨PLI MSCs sub ⟩ is the mean PLI of the subject equivalent to the identified Most Significant Connections (MSCs), and ⟨PLI MSCs ref ⟩ is the mean PLI of the reference equivalent to the identified MSCs for the subject.The inclusion of ⟨PLI MSCs ref ⟩ ensures that the network formed after thresholding is relative to the given reference network.The brain functional network (BFN), whether weighted or unweighted, can then be formulated by applying the selected threshold while keeping the MSCs to preserve the connectedness of the network.

D. Threshold Validation
To affirm the non-random nature of the formulated Brain Functional Networks (BFNs) using our proposed threshold selection, a comparison is made with equivalent random and lattice networks generated from a null model, employing the small-worldness concept.For a network with clustering coefficient C and path length L, if the clustering coefficients of the corresponding random network and lattice network are C r and C l , with path lengths L r and L l respectively, the small-worldness metric Q is given by: While Q suggests a small-world network [30], its application has limitations, such as dependency on network size and mean degree, and inappropriate comparisons to the same reference (random graph).To overcome these, two normalized small-worldness metrics were proposed: • Normalized Small Worldness Coefficient (Metric 1): Addressing limitations in traditional small-worldness calculations [31], this metric (SW 1 ) considers the deviation of a network's clustering coefficient and path length from a reference (random network) and their adherence to identify the 'n' number of electrodes with 95% confidence interval of their EC sub (band) 8: end for another reference (lattice network).It is defined as The small-world coefficient (SW 1 ), obtained through this metric, captures the network's adherence to both the random network and lattice network references.
• Normalized Small Worldness Coefficient (Metric 2): Another metric [32], denoted as SW 2 , combines path length and clustering coefficient comparisons, providing a more comprehensive assessment of small-worldness: These metrics offer a robust evaluation of the small-worldness of BFNs, addressing limitations and ensuring a more accurate comparison to random and lattice networks.

E. Brain Functional Network Quantification
To discern the distinctions among networks associated with different neurological states, we employ appropriate metrics for quantifying brain functional networks.While various graph theory metrics exist for complex network quantification, the choice of a metric for specific brain functional network quantification requires consideration of the network's nature and intended application.In this paper, we focus on the rich-club organization measure, transitivity, and assortativity coefficients as our chosen metrics for quantifying the formulated brain functional networks.The selection of these three metrics is based on their significance in quantifying network topology [33].
1) Rich-Club Coefficient: The rich-club organization measure is a crucial metric for evaluating the interconnectedness among highly connected nodes, often referred to as the "richclub," within a network [34].In the context of brain functional networks, this metric sheds light on the significance of highly connected regions in understanding brain function and connectivity [35].
The rich-club coefficient ( r ) of a network quantifies the interaction among rich nodes in the network and is mathematically defined as: where E >k denotes the number of edges among N >k nodes with a degree higher than a specified value k and N >k (N >k −1) is the maximum number of edges among the N >k nodes.
2) Measure of Functional Segregation Using Transitivity: The transitivity coefficient serves as a metric for quantifying the degree to which nodes in a network exhibit clustering, providing insights into the local connectivity of brain functional networks [36].Mathematically, the transitivity of a network is defined as: where the numerator represents the number of triangles in the network, and the denominator denotes the total number of connected triplets in the network.
3) Network Resilience Measure Using Assortativity Coefficient: The assortativity coefficient is a metric that gauges the degree to which nodes with similar connectivity patterns tend to be connected, providing insights into the overall organization of brain functional networks [35].Mathematically, the assortativity coefficient is defined as: where M represents the total number of edges in the network, j i and k i are the degrees of the vertices at the ends of the i-th edge, with i = 1, 2, . . ., M.

F. Graph Convolution Network
1) Graph Learning: In recent years, the concept of graph learning has gained prominence, finding applications in domains such as emotion recognition and brain-computer interfaces using EEG.The detailed conceptualization of the graph convolution network (GCN), along with general information about graphs and graph filtering, is presented below.
2) General Representation of Graph: Consider an undirected graph G = {V, E, A}, where V is the set of nodes (|V| = N), E represents edges connecting the nodes, and A ∈ R N×N is the adjacency matrix indicating connectivity strengths between nodes.The degree of a node j, denoted as d j is the sum of weights of all edges connecting node j to other.The degree matrix D is a diagonal matrix, with diagonal entries d j .The Laplacian matrix L of the graph is defined as: Normalized forms of the adjacency and Laplacian matrices, denoted Ã and L respectively, are often used.They are obtained by pre-multiplying with the inverse square root of the degree matrix.
3) Spectral Graph Filtering: The laplacian matrix, L has eigenvectors known as graph Fourier modes, {U N −1 l } ∈ R N which are orthonormal complete.The associated eigenvalues are the graph Fourier frequencies.The convolution operation on a graph G is expressed as: A non-parametric filter g θ with Chebyshev polynomial approximation is commonly used.Thus, the convolution operation becomes:  reduces dimensionality by selecting maximum values, enhancing computational efficiency.The Fully Connected layer introduces non-linearity for discerning complex patterns, and the Softmax layer produces predictions for dementia-related disorders.
Hyperparameters such as learning rate, dropout rate, and L2 regularization coefficient were empirically chosen.The model employed SGD for weight updates with the Adam optimizer.A dropout rate of 30%, ReLU activation function, and batch normalization were applied to prevent overfitting.The loss function used was cross-entropy with L2 regularization.Evaluation metrics included classification accuracy and F1-score and are respectively defined in eqn.16 and eqn.17.

Accuracy
where T P, T N , F P, F N are the true positives, true negatives, false positives and false negatives respectively.Therefore, the study leverages the inherent graph structure of EEG signal to enhance the performance of a classification model for dementia-related disorders.The GCN model processes EEG data, capturing intricate patterns critical for accurate predictions.

III. RESULTS
The 10-minute eyes-open EEG rest data is segmented into 10-second epoch trials after preprocessing, followed by the computation of Phase Lag Index (PLI) between all pairs of electrodes in forward order.The resulting connectivity matrix is then segmented into five frequency bands for all subjects.Subsequently, the most significant electrode(s) and connections are identified for each subject.With the identification of these significant connections, subject-specific threshold values are computed and applied to form Brain Functional Networks (BFNs) for the EEG trials of all dementia-related subjects.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.The formulated BFNs are subjected to comparison and testing for randomness by computing the normalized smallworldness metrics.Additionally, the topologies of the BFNs are quantified and statistically analyzed for significant differences across dementia-related disorder groups using Kruskal-Wallis test adjusted for Bonferroni correction, as detailed in the following sections.

A. Phase Lag Index
The pre-processed EEG data undergo initial decomposition into time-frequency components using a continuous wavelet transform with morlet wavelet.Subsequently, the Phase Lag Index (PLI) is computed using eqn. 1.The resulting PLI values are then segmented into delta, theta, alpha, beta, and gamma bands for each subject.For visual representation, Fig. 3 illustrates the PLI distributions in time-frequency for an electrode pair across subjects in all groups.
To explore the variation of PLI across different groups, the PLI values are grouped based on their frequency band and electrode locations.Specifically, PLI values for each frequency band are categorized into frontal, temporal, central, parietal, and occipital regions based on electrode locations.A Kruskal-Wallis statistical test is performed on the average PLI values across the five scalp regions in all frequency bands.The analysis identifies a significant difference (at p < 0.05) in the delta and theta bands.Fig. 4 displays the distribution of average PLI values for the NC, MCI, AD, and VD groups in the delta and theta bands across the five scalp regions.
To delve deeper into group differences, a Kruskal-Wallis post-hoc analysis, adjusted by Bonferroni correction, is performed using IBM SPSS Statistics 26.The results reveal that in the occipital region of the delta band, the PLI values of the NC and MCI groups are significantly lower than those of the AD group (at p < 0.05 and p < 0.01, respectively).Similarly, in the theta band, the PLI values of the MCI group are lower than those of the AD and VD groups in the temporal region (at p < 0.05 and p < 0.01, respectively).
Furthermore, to facilitate additional analysis, the study computes the average time-frequency PLI values of all subjects in the NC group, using them as a reference for subjects in all dementia-related disorder groups.This approach enables the comparison of PLI values between different groups and provides insights into changes in brain connectivity patterns in subjects with dementia-related disorders compared to normal controls.

B. Most Significant Electrode(s) and Most Significant Connections Identification
The band-specific most significant electrodes for subjects with dementia-related disorders are identified following the procedure outlined in Section II-B and employing Algorithm 1.The identified Most Significant Electrodes for dementia-related disorders are subsequently utilized to construct the Most Significant Connections (MSCs) between these electrodes.The MSCs encompass both the edges connecting the significant electrodes together and the edges linking significant electrodes with non-significant ones, ensuring the preservation of connectedness in the brain functional networks, as depicted in Fig. 5, where Fig. 5(a)-(d) clearly shows the results of various stages involved in the formation of the most significant electrode(s) and the MSCs, with the most significant electrodes highlighted in Fig. 5(d).
The most significant electrode(s) and MSCs of a subject from MCI, AD, and VD groups are presented in Fig. 5(e).Notably, the identified most significant electrode(s) from the MCI group belong to the frontal scalp region, while those identified from AD and VD groups belong to the temporal scalp region.These results suggest a predominant loss of connections at the temporal region for the AD and VD subjects and a predominant loss of connections at the frontal region for the MCI subjects.

C. Threshold Selection
The Brain Functional Network (BFN) corresponding to a neurological state is identified through proper threshold selection, crucial for distinguishing true connections from spurious ones.The selected threshold, determined by the strength of Most Significant Connections (MSCs) as detailed in section II-C, influences the formation of BFNs, whether weighted or unweighted.Therefore, by applying the proposed threshold selection procedures, the BFNs of all the subjects are formulated.It is noteworthy that the density of the formulated  BFNs varies among subjects.To assess the consistency of dementia-related subjects' BFNs over time, we present the variation of BFNs for a sample subject from MCI, AD, and VD groups over time, as well as the threshold value at each instance in Fig. 6.The formulated BFNs for all subjects are consistent with the passage of time, showing the robustness of the proposed threshold selection approach.
Further, to validate the genuineness and non-randomness of the formulated Brain Functional Networks (BFNs), the normalized small-worldness coefficients are computed based on eqn.6 and eqn.7 respectively.The computed small-worldness coefficients from the formulated BFNs of all the subjects with dementia-related disorders are presented in Fig. 7.As evident from the results in Fig. 7(a)-(b), the values of the small-world coefficient computed for all the BFNs are significantly greater than 0 in both cases, indicating the reality of the formulated BFNs.This observation validates the proposed threshold selection technique, highlighting the small-world properties inherent in the connectivity patterns of dementia-related subjects' brain networks.Further demonstration of the robustness of the proposed threshold selection approach in discriminating neurodegenerative diseases can be found in the supplementary materials.

D. Network Topology Quantification
The study conducted an analysis of brain functional networks (BFNs) for subjects in three different groups: MCI, AD, and VD.The networks were quantified using three measures-rich-club coefficient, network transitivity, and network assortativity.The values of these measures in different frequency bands were compared using one-way ANOVA with Bonferroni correction.As presented in Table I, the rich-club coefficient measure was found to be highest for subjects in the MCI group across all frequency bands, except for the beta band.A significant p-value of 0.00 was observed only in the alpha band, where the rich-club coefficients of the MCI group were significantly greater than those of the AD and VD groups at a significance level of p < 0.05.
The analysis of the network transitivity coefficient measure revealed an increasing trend with the severity of impairments.Subjects in the MCI group had the least values, and the Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.transitivity coefficients were significantly less than those of the AD and VD groups at a significance level of p < 0.05 in all frequency bands except for the alpha band.Additionally, the transitivity coefficients of the AD group were significantly less than those of the VD group in all frequency bands except for the alpha band.This suggests that as the severity of impairments increases, the network transitivity coefficient tends to rise, with the VD group having the highest transitivity coefficients, followed by the AD group, and then the MCI group.The finding that the transitivity coefficients of the MCI group were significantly less than those of the other groups in all frequency bands except for the alpha band suggests that this measure may be a useful biomarker for detecting and monitoring the progression of cognitive impairments in MCI and AD.
The study also explored the coefficient of assortativity measure for the three groups-MCI, AD, and VD.The observed trend of this measure was non-uniform across different frequency bands, as highlighted in Table I.Sta-tistically significant differences were identified between the coefficients of assortativity of the MCI group and the other groups at a significance level of p < 0.05 in all frequency bands, except for the beta band.This finding suggests that the coefficient of assortativity measure might serve as a valuable biomarker for identifying the prodromal stage of dementia.The MCI group exhibited significant differences in this measure compared to the other groups in most of the analyzed frequency bands.Nevertheless, further research is essential to confirm these findings and ascertain the utility of this measure as a biomarker for identifying the prodromal stage of dementia.

E. Graph Convolution Network Classification
In order to highlight the significance of the proposed framework, we utilize the formulated Brain Functional Networks (BFNs) as input graphs in GCN-nets for the differential identification of the various included dementia-related disorders 1) Implementation Details: As described in section II-F, the GCN-net proposed consists of convolution layers and fully connected layers.We carried out several experimentation considering different combinations and depths of the convolution layers, depths of fully connected (FC) layers, numbers of filters at the convolution layers, order of Chebyshev's filter and other hyper-parameters before settling for the architecture that gave the best performance.The GCN-net architecture employed finally comprises of two graph convolution layers with 256 filters in each layer, followed by a GlobalMaxPool layer and then five fully connected layers with a softmax layers for the final classification.Batch normalization and a dropout rate of 30% were implemented at each FC layer to prevent varnishing gradient and overfitting respectively.5-th order Chebyshev filter was found to be appropriate for the feature extraction task in this study.
For single trial analysis, 2.5 sec epochs of EEG signals were employed for the formulation of BFNs that were employed as predefined graphs for the GCN-net classification (considering the whole 10mins section of eyes-open resting condition for all the subjects with the exception of data segments removed due to eye-blinks and other related artifacts).In all, a total of 15664 trials comprising of 3160 trials of NC group, 4672 trials of MCI group, 4932 trials of AD group and 2900 trials of VD group respectively were employed for the GCN-net classification.The entire trials were divided into 80% (representing the data from 40 subjects) for the model training and 10% each (representing the data from 5 subjects) for the model validation and testing respectively for all the considered frequency bands [39], [40].
2) Model Performance: The model is implemented across five frequency bands (delta, theta, alpha, beta, and gamma), as well as a broad band covering 1H z −40H z.Both statistical and differential entropy features extracted from EEG data, along with graph Laplacians computed from the formulated Brain Functional Networks (BFNs) using the proposed technique, serve as inputs for the GCN-net.The training process involves 2000 iterations, with early stopping applied after 200 consecutive iterations of increasing loss function values.Table II reveals that the highest accuracy and F1-score are achieved in the delta band, underscoring its significance in identifying the onset of dementia-related disorders.Both accuracy and F1-score exhibit a decreasing trend from delta to gamma bands.Additionally, the broadband model exhibits slightly higher accuracy and F1-score than the higher frequency bands but lower than the lower frequency bands.
Comparing the proposed threshold selection technique with existing methods, such as the minimum connected component technique [16], sparsity thresholding with 20% of the total connections employed in [37], sparsity thresholding with 30% of the total connections employed in [38], and no threshold technique employed in [39], the GCN-net implemented on the proposed framework excels in identifying dementia-related disorders based on Brain Functional Networks (BFNs).The results in Table II highlight its superior performance, achieving a maximum accuracy of 95.07% and an F1-score of 0.92 in the delta band.
Moreover, we conducted a performance comparison between the GCN-net developed based on the proposed Brain Functional Networks (BFNs) formulation technique and dementia recognition methods presented in [6] and [22].The techniques in these works use network features (seed Region of Interest (ROI) features and Node degree features) for support vector machine (SVM)-based classification.Initially designed for binary classification, we adapted both methods for the multiclassification case under consideration.Table III presents the accuracy and F1-scores of the proposed approach and the techniques from [6] and [22] in broad band.The results indicate that the proposed approach outperforms the respective techniques.late onsets of dementia.The Kruskal-Wallis significance test with Bonferroni correction unveils a substantial increase in PLI in the occipital and temporal regions within the delta and theta frequency bands.Emphasizing the importance of functional connectivity in both the temporal and occipital regions for identifying dementia-related disorders aligns with findings from [41].

IV. DISCUSSION
Additionally, the proposed framework introduces a novel Brain Functional Network (BFN) formulation technique, considering both dementia onset and normal control states.As demonstrated in Figs. 6 and 7, respectively, this approach consistently generates connected BFNs over time with smallworld properties, potentially enhancing accuracy in detecting changes associated with dementia-related disorders.Further exploration is needed for validation and clinical applicability.The study underscores the significance of considering both dementia onset and normal control states in complex network analysis.
Topological quantification of formulated BFNs provides insights into the organization and functional segregation properties of brain networks linked to dementia-related disorders.The presence of a rich-club organization in EEG-based BFNs suggests a distinctive network organization, with high-degree nodes more strongly interconnected.However, the decreasing trend of rich-club organization in older adults' BFNs as impairment severity increases indicates its loss with neurological damage like dementia.Additionally, there is an observed increase in functional segregation properties with rising impairment severity, showcasing the potential of these metrics in gauging the progression of dementia-related disorders.
As indicated in Table I, functional segregation, measured by transitivity, proves effective in identifying MCI from late onset dementia and differentiating between AD and VD in the theta frequency band.This accentuates the utility of transitivity in detecting changes in functional segregation within brain networks associated with dementia-related disorders.However, it is noteworthy to state that the observed increase in functional segregation in this study is strongly associated with the use of differential networks.
Expanding the analysis to brain network resilience linked to dementia-related disorders, the study utilizes the assortativity coefficient.As evident in Table I, the presence of negative assortative coefficients among nodes for all dementia-related subjects indicates a functional dissociation between the nodes and damage or degradation in network efficiency.However, in Mild Cognitive Impairment (MCI), more positive assortative coefficients are observed in lower frequency bands compared to Alzheimer's Disease (AD) and Vascular Dementia (VD), suggesting increased vulnerability in the latter.Similarly, the assortative coefficients of the subjects in the VD group are lower than those of the subjects in the AD group.This finding further suggests more extensive network damage in AD compared to VD.
The field of neurodegenerative disorder recognition is dynamically evolving, undergoing a significant transition towards discriminating various forms of dementia in recent research [42], [43], [44].While multiclass classification of dementia-related disorders is gradually advancing, this study stands as the first, to the best of the authors' knowledge, showcasing the application of Graph Convolutional Networks (GCNs) for discriminating between Alzheimer's Disease (AD) and Vascular Dementia (VD) alongside Mild Cognitive Impairment (MCI) stages.The realm of GCNs in EEG, particularly within the context of dementia-related disorders, is experiencing rapid growth [1], [37], [38], [45], [46].
By leading the use of GCN-net for EEG-based differential identification of dementia-related disorders, this study not only pioneers a novel approach but also surpasses existing thresholding frameworks, demonstrating superior performance with an accuracy and F1-score of 76.35% and 0.73, respectively, in the broad band (see Table II).This outperformance is notable compared to those employed in [16], [37], [38], [39] with GCN-nets.Therefore, by implication, the proposed input graph formulation technique is not only groundbreaking but also excels in capturing the underlying patterns of functional connectivity in EEG signals associated with dementia-related disorders, holding implications for accurate diagnostic tools.
Furthermore, the GCN-net classification, based on the proposed Brain Functional Networks (BFNs) formulation approach, demonstrates superior performance compared to dementia-related disorders recognition frameworks presented in [6], [22], as detailed in Table III.
Despite offering promising insights, it is essential to acknowledge the inherent limitations in our study.The proposed data-driven threshold selection technique may exhibit sensitivity to variations in datasets, influenced by factors such as differences in protocols and subject characteristics.Future research will prioritize evaluating the progression from mild cognitive impairment to the Dementia stage and will include various types of dementia disorders to allow for a comprehensive sensitivity analysis, ensuring complete generalization.

V. CONCLUSION
This study introduces a comprehensive framework for analyzing EEG-based brain functional networks (BFNs) in individuals with dementia-related disorders.Our method involves a subject-specific data-driven threshold selection, leveraging eigencentrality, to create BFNs that capture distinctive neurological characteristics compared to healthy older adults.Our research highlights the potential of precise quantification of BFN topologies for differentiating complex neurological states.We successfully distinguish BFNs of the prodromal dementia stage (MCI) from late-onset dementia disorders (AD and VD).Notably, our approach demonstrates discriminative capabilities across various frequency bands, even within the late-onset disorders category.
Our results, showcasing high accuracy (95.07%delta, 80.62% theta) and F1-scores (0.92 delta, 0.67 theta), effectively differentiate dementia levels, outperforming existing methods for Graph Convolution Network (GCN-net) graph input.This underscores the robustness and efficacy of our holistic methodology, spanning threshold selection, network formulation, graph theory analysis, and GCN-based diagnosis.This comprehensive approach is the cornerstone of our study, giving it unique significance.While it suggests the potential utility in early dementia detection, rigorous testing and validation are essential before clinical implementation.Nevertheless, our research paves the way for the GCN-net framework's application, promising improved accuracy and efficiency in dementia-related disorders identification-a significant advancement in dementia research.

ETHIC STATEMENT
The study involving human participants was reviewed and approved by Institutional Review Board of Kyungpook National University Chilgok Hospital.The patients/ participants provided their written informed consent to participate in this study.All experimental procedures involving human subjects were carried out in accordance with the relevant guidelines and regulations.

4 )
Model Architecture and Initialization: The proposed model architecture integrates the GCN layer, GlobalMaxPool layer, Fully Connected layer, and Softmax layer.The GCN layer extracts graph-based features, capturing local and global dependencies in brain networks.The GlobalMaxPool layer

Fig. 3 .
Fig. 3. PLI in Time-Frequency of a pair for for all the groups.

Fig. 4 .
Fig.4.Mean PLI averaged over all electrode pairs within the various scalp regions for dementia related subjects and the normal control subjects across delta and theta frequency bands.

Fig. 5 .
Fig. 5. Identification of the most significant electrode(s) and MSCs (The significant nodes of the representative subjects are highlighted in (d) and (e)).

Fig. 6 .Fig. 7 .
Fig. 6.Variation of Brain Functional Networks of selected subjects from MCI, AD and VD groups in time.
This study investigates EEG signals related to dementiarelated disorders, revealing significant trends in the phase lag index (PLI) across Mild Cognitive Impairment (MCI) and Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

TABLE II COMPARISON
OF GCN-NET ACCURACIES BASED ON BRAIN FUNCTIONAL NETWORKS OBTAINED FROM VARIOUS THRESHOLDING TECHNIQUES, WHERE METH 1 DENOTES THE PROPOSED THRESHOLDING TECHNIQUE, METH 2 DENOTES THE MINIMUM CONNECTED COMPONENT TECHNIQUE [16], METH 3 REPRESENTS THE STATISTICAL THRESHOLD WITH 95% CONFIDENCE INTERVAL, METH 4 REPRESENTS THE THRESHOLDING BY INCLUDING 20% OF THE TOTAL CONNECTIONS [37], METH 5 REPRESENTS THRESHOLDING BY INCLUDING 30% OF THE TOTAL CONNECTIONS [38] AND METH 6 REPRESENTS NO THRESHOLD [39]