SGAAE-AC: A Semi-Supervised Graph Attention Autoencoder for Electroencephalography (EEG) Age Clustering

Abstract

The structural and cognitive functions of the brain undergo significant changes throughout an individual’s lifetime. The analysis of EEG background waves based on age groups will help reveal the correlation between human cognitive development ability and their age, and provide a new perspective for a deeper understanding of neurodegenerative diseases. Unfortunately, the available literature shows that, in recent years, the analysis of EEG signal background waves at different age groups has been extremely rare. To address the vacuum of this research, this paper introduces an innovative semi-supervised graph attention autoencoder method, SGAAE-AC, an age-based clustering method based on EEG background wave analysis. This method utilizes feedback from the labels generated by age-based clustering to guide the encoder in generating more accurate EEG graph embeddings. Furthermore, by adopting multi-objective optimization techniques, the accuracy and interpretability of EEG signal clustering are significantly improved. Our experimental outcomes elucidate the relationship and impact between human age and EEG background waves from perspectives such as comprehensive EEG spectral activity and frequency band attention, thereby uncovering the patterns of EEG background wave activity as they evolve with age.

1. Introduction

The development of the human brain is a continuous process that evolves with age. As individuals mature, significant transformations occur in both the structure and function of the brain, particularly in the development of cognitive functions. Moreover, with advancing age, the brain may also be at risk of various neurodegenerative diseases, such as Alzheimer’s disease.

As a non-invasive neurophysiological monitoring technique, electroencephalography (EEG) [1] provides researchers with a unique and effective means to deeply explore the patterns of brain evolution with age.

Our research is dedicated to the analysis of the background wave activity of EEG across different stages of human age, aiming to reveal the unique characteristics and patterns of the EEG background waves hidden in different age groups [2]. This knowledge is pivotal for scientists to reveal the fundamental patterns underlying the development of human cognitive functions, and plays a valuable role in establishing benchmark references for the correlation between EEG background wave activities and brain diseases. Such a benchmark can then be used to incorporate the EEG background wave patterns of a specific age group as diagnostic knowledge into treatment. A case in point is the detection and treatment of neurodegenerative brain diseases. The discovered knowledge about the EEG background wave in relation to a certain age group enables doctors to more accurately identify age-related normal variations, thereby avoiding the misdiagnosis of these variations as abnormal signals of neurological diseases.

Unfortunately, to the best of our knowledge, there has been almost no research or academic achievement in recent years on the analysis of EEG background waves in the available literature. The few existing studies primarily originate from the late last century and the beginning of this century, employing methods that are relatively outdated. We will elaborate on this issue in the Related Work Section 2.

Based on this analysis, we conduct research within the niche of EEG background wave analysis. Specifically, we employ deep neural network models and semi-supervised learning techniques for the age-based clustering study of EEG background waves. The outcomes of our research are expected to facilitate a deeper understanding among researchers about the relationship between brainwave activity and the aging process, provide a benchmark that can be referenced in the study of brain science and clinical practice, and also open new avenues for intelligent brain disease detection and diagnostic tasks.

2. Related Work

In the fields of neuroscience and medicine, scholars have long been dedicated to studying the complex relationship between brain function and age. Historically, a variety of research methodologies, including time frequency domain analysis and nonlinear dynamics analysis, have been employed to uncover the impacts of aging or neurodegenerative diseases on EEG background activity.

In this domain, the work of Lindsey et al., starting from 1939, marked an important early attempt in time frequency domain analysis [2]. Their findings indicated that, with increasing age, there is an increase in the activity of high-frequency waves in various regions of the brain, while the activity of low-frequency waves decreases. This discovery was further refined in subsequent studies [3,4,5,6], with research from the 1970s and 1980s indicating that before the age of four, δ waves and θ waves dominate brain activity, whereas α and β wave activities gradually increase throughout childhood.

In the field of nonlinear dynamics analysis, in 2006, the work of Abásolo et al. was dedicated to using nonlinear dynamical methods of EEG to diagnose the impact of neurodegenerative diseases on EEG background activity [7]. In 2021, Ma M K H and colleagues [8] introduced advanced nonlinear dynamics analysis methods to measure the complexity of EEG in a resting state, aiming to elucidate the patterns of aging.

Despite some progress in both the time frequency domain and nonlinear dynamics analysis in previous studies, due to technological limitations and the precision of the methods, these early research efforts often lacked detailed quantitative analysis, making it insufficient to provide effective data support for a deeper understanding of human cognitive function development or for enhancing the accuracy of disease diagnosis and treatment.

In recent years, multiple achievements have been made in the field of brain age prediction and classification using EEG, thanks to the technological advances in machine learning and the continuous development of deep learning. Particularly since 2010, the application of traditional machine learning methods has gradually increased [9,10,11]. For instance, Kaur and colleagues applied the random forest algorithm to predict age and gender [11], achieving an age classification accuracy of 88.33% and a gender classification accuracy of 96.66%. Around the 2020s, deep learning technology made breakthrough progress in this area [12,13,14]. Among these, Jusseaume et al. utilized Long Short-Term Memory (LSTM) networks to analyze EEG records of epilepsy patients [13], successfully predicting the patients’ brain age with an accuracy of up to 90%. However, despite these advances in EEG-based age prediction and classification, none of the studies addressed the patterns of how aging affects EEG background wave activity, nor the characteristics of EEG background waves at different ages.

Further reviewing the literature of the past decade or so, we have come to a disappointing conclusion that research exploring the patterns of age-related changes in EEG background wave activity is very rare. Therefore, there is an urgent need to undertake pioneering research in this area using modern artificial intelligence technologies.

Among the various attempts to study age-related EEG, the unique advantages and potential value of clustering methods have not been fully recognized and utilized. Unlike methods that rely on predefined labels for classification and prediction, the strength of cluster analysis lies in its ability to identify latent patterns within the data without supervision. This advantage makes cluster analysis an ideal fit for the task of revealing the patterns of brain background waves across different age groups.

While we consider a direct clustering of EEG background waves by age groups to be an intuitive approach, it must be acknowledged that direct clustering without considering the multi-channeled property of EEG signals overlooks the inherently spatial connections among EEG channels, thereby preventing the best performance that clustering can achieve. Graph AutoEncoders (GAEs) and their variants, such as Variational Graph AutoEncoders (VGAEs) [15], have demonstrated effectiveness in enhancing the performance of EEG-related tasks [16,17,18] and sleep staging [19,20] by modeling the interrelationships between EEG channels as graph structures and analyzing them through graph embeddings. Although there are some works related to graph clustering, such as Adaptive Graph Clustering (AGC) [21,22,23,24], their application in clustering EEG signals by age groups has not been explored or applied, partly due to the challenges posed by the high dimensionality and complexity of EEG data. Nevertheless, leveraging GAE to understand the interconnectivity between channels and apply it to age-based clustering analysis remains a promising approach.

We currently face three main challenges in the task of clustering EEG signals using GAE. Firstly, as an unsupervised learning model, GAE cannot learn from true labels, which increases the complexity of results validating and optimizing, making it more difficult to ensure the model’s accuracy and generalizability compared to supervised learning tasks. The next challenge relates to the issue of the separateness of the encoder’s training process. Traditionally, the training of the encoder often occurs separately from downstream tasks (such as prediction, clustering, or classification). This separated training strategy prevents the encoder from fully utilizing task-specific information, thus reducing the model’s accuracy in accomplishing specific tasks. Lastly, existing methods have not effectively leveraged the inherent spectral properties of graph structures. In EEG signal analysis, the spectral characteristics of graph structures are crucial for identifying similar wave patterns and functional regions, yet conventional graph encoder approaches often overlook this aspect.

To address these challenges, this study proposes the following three innovative solutions.

First, by integrating graph encoder methods with semi-supervised learning [25], we are able to identify representative cluster centers from the clustering outcomes and feed these centers’ label information back to the graph attention encoder. This allows for the guidance of the encoder in generating graph embeddings with distinct separability, without the need for explicit labels.

Secondly, we employ a multi-objective optimization strategy that jointly optimizes the graph reconstruction loss of the decoder and the clustering loss, guided by pseudo-labels. This joint optimization approach facilitates the encoder in learning feature representations more relevant to the downstream tasks and provides a self-supervised validation mechanism.

Lastly, by integrating Laplacian filters into the graph attention encoder, we optimize the graph embedding process, enhancing the local consistency and maintenance of global information among nodes. This helps improve the precision and interpretability of clustering, especially in the domain of spectral clustering and EEG data processing.

3. Materials and Methods

The construction of SGAAE-AC begins by converting EEG signals into a graphical representation to capture the complex interactions between the electrodes of electroencephalography machines (see Figure 1). Upon completing the graph structure construction, we apply a Laplacian-enhanced graph attention autoencoder to generate graph embeddings, where a Laplacian filter is integrated into this autoencoder to enhance the model’s feature extraction capabilities. The Laplacian filter plays a triple role here: smoothing data features, reducing signal noise, and preserving key structural information of the graph. The latter provides high-quality input for the spectral clustering algorithm.

Further, we analyze the graph embeddings using a clustering algorithm to generate pseudo-labels, a crucial step within the semi-supervised learning framework. Pseudo-labels not only guide subsequent model optimization but also serve as a self-feedback mechanism, enhancing the model’s learning and recognition of clustering structures.

Finally, through the repeated training of the graph attention autoencoder, we perform further clustering analysis on data integrated with pseudo-labels and evaluate the clustering outcomes to verify the model’s performance.

3.1. Encoder

3.1.1. Time Frequency Feature Fusion for EEG Graph Structure

To enable the graph attention autoencoder to learn deeper graph embedding representations, we initially transform EEG signals into a specialized graph structure. This step aims to adapt to the Laplacian-enhanced graph attention autoencoder, ensuring the EEG signal characteristics can be effectively understood and utilized by the encoder. To enrich the feature representation of nodes, we fuse the original time domain features and frequency domain features of EEG signals to constitute the node’s feature representation.

Each EEG signal is processed and converted into a graph structure A with rich features Z, including:

(1) Node: Each EEG channel serves as a node in the graph, and the node’s feature, denoted by Z, is derived by integrating a segment of the original EEG time series signal with frequency domain features calculated from the same segment. Frequency domain features are obtained through the Fast Fourier Transform (FFT) that computes the power spectral density, band power, and peak frequency for the δ (0.5–4 Hz), θ (4–8 Hz), α (8–13 Hz), and β (13–30 Hz) bands.

These frequency attributes are carefully chosen because they disclose vital details of the frequency domain pertinent to epilepsy, highlighting shifts in energy distribution across distinct frequencies and modifications in the main frequency elements. Previous research has shown significant differences in EEG background waves across different age groups in the frequency domain, particularly in the early stages of child development, where δ and θ waves dominate brain wave activity and later on, α and β waves gradually strengthen.

(2) Edge: Using the correlation between the channels calculated using the wavelet coherence algorithm to establish edges between nodes. The connection can only be established if the correlation between channels is greater than a pre-set threshold. The structure of the graph is represented by the adjacency matrix representation of the edges as A.

As mentioned earlier, analyzing EEG data solely from a time series perspective is often insufficient, as it may overlook important inter-channel spatial relationships inherent in EEG recordings. These spatial relationships can provide crucial insights into brain functional connectivity. Recent studies have confirmed this viewpoint by employing various correlation analysis methods, such as Multiscale Entropy (MSE), Phase Locking Value (PLV), and Euclidean Distance [26,27].

We choose wavelet coherence to measure the similarity or synchrony between two signals at specific times and frequencies. Compared to simple wavelet transforms, wavelet coherence considers the relationship between two signals by calculating the product of their wavelet transforms and integrating over a certain time window, thus assessing the coherence level of two signals at specific times and frequencies. The calculation method is as follows:

$$W_x\left(t,f\right)={\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}x\left(u\right)·{\theta }_{t,f}^{\mathrm{*}}\left(u\right)du$$

(1)

$${CW}_{xy}\left(t,f\right)={\int }_{t-\frac{\theta }{2}}^{t+\frac{\theta }{2}}{W}_x\left(\tau ,f\right)·W_y^{*}\left(\tau ,f\right)$$

(2)

where $W_x(t,f)$ represents the wavelet transform value of signal $x\left(u\right)$ at time $t$ and frequency $f$. $x\left(u\right)$ denotes the original signal, where $u$ is the time variable, and ${\theta }_{t,f}\left(u\right)$ is the wavelet function, dependent on time $t$ and frequency $f$.

${CW}_{xy}(t,f)$ represents the wavelet coherence between two signals $\mathrm{x}$ and $\mathrm{y}$ at time $t$ and frequency $f$. $W_x(\tau ,f)$ and $W_y(\tau ,f),\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{p}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{l}\mathrm{y},$ represent the wavelet transform values of signals $x$ and $y$ at time $\tau$ and frequency $f$. $\theta$ is the width of the window.

3.1.2. Laplacian-Enhanced Graph Attention Autoencoder

To effectively characterize the EEG signal’s graph structure A and the node feature matrix Z, this study employs a variant of the modified graph attention network [28] as the graph attention autoencoder (GAAE). Its core innovation lies in the integration of a hierarchical graph attention strategy with the Laplacian filter (see Figure 2). By learning the hidden representation of each node through its neighboring nodes, node features are integrated with the graph structure into a latent representation. This method not only precisely evaluates the importance of neighboring nodes but also introduces the Laplacian filter to the front end of the graph attention autoencoder, smoothing node features and reducing data noise. This strategy reflects local similarity while preserving global structural information. It significantly enhances the consistency and continuity of the feature space, providing more suitable input for the spectral clustering algorithm and markedly improving the overall performance of spectral clustering.

The calculation of the Laplace matrix and its filter is as follows:

The graph’s Laplacian matrix L is obtained by subtracting the adjacency matrix A from the diagonal degree matrix D formed from each node’s degree.

$$L=D-A$$

(3)

Here, each element $d_i$ of the degree matrix $D$ is the sum of the weights of the edges adjacent to node $i$ calculated as $d_i={\sum }_{j=1}^N{w}_{ij}$, where $w_{ij}$ represents the connection weight between node $i$ and node $j$. $\mathrm{A}$ is the adjacency matrix of the EEG graph structure.

Subsequently, we apply the Laplacian filter to each node’s feature vector, calculating the new feature matrix $Z^{\prime }$

$$Z^{\prime }=\sigma \left(LZ\right)$$

(4)

where $Z$ is the original node feature matrix, and $\sigma$ is a non-linear activation function.

After completing the computation and application of the Laplacian matrix, these optimized node features are used for learning graph embeddings. Initially, the feature of a single node $i$ is represented through the action of the Laplacian filter as $z_i^0$.

These node features, unprocessed by the graph attention layer, are fed into the graph attention autoencoder, initiating the learning process for graph embeddings.

The graph attention autoencoder aims to update features by considering the contributions between nodes. Specifically, the feature representation $z_i^{l+1}$ of node $i$ at the $l+1$ layer is calculated as follows:

$$z_i^{l+1}=\sigma \left(\sum _{j\in N_i}{\alpha }_{ij}{W}_{z_j^l}\right)$$

(5)

where $N_i$ represents the set of neighboring nodes of node $i$, ${\alpha }_{ij}$ is a weight computed through the attention mechanism, representing the importance of neighboring node $j$ to node $i$. $\sigma$ is a non-linear function.

The computation of the attention coefficient ${\alpha }_{ij}$ involves two key steps: evaluation based on attribute importance and the consideration of topological structure. First, from an attribute perspective, ${\alpha }_{ij}$ is calculated through a parameterized single-layer feedforward neural network that utilizes the feature vectors of nodes $i$ and $j$:

$$c_{ij}={\overrightarrow{\alpha }}^T\left[W_{x_i}||W_{x_j}\right]$$

(6)

where $\left|\right|$ represents the concatenation of vectors, and $\overrightarrow{\alpha }$ a is a weight vector learned.

Further, considering the graph’s topological structure, we measure the topological relevance between nodes by computing a proximity matrix $M$ up to t-order neighbors.

$$M=\frac{B+B^2+\cdots +B^t}{t}$$

(7)

$B$ is the transition matrix, where $B_{ij}=1/d_i$, and $d_i$ is the degree of node $i$. $M_{ij}$ thus reflects the topological relevance of node j to node $i$.

Taking into account both attribute and topological weights, the final attention coefficient ${\alpha }_{ij}$ is normalized among all neighboring nodes using the Softmax function.

$${\alpha }_{ij}=\frac{\exp \left(LeakyReLU\left(c_{ij}\right)\right)}{{\sum }_{r\in N_i}\exp \left(LeakyReLU\left(c_{ir}\right)\right)}$$

(8)

We take $x_i=z_i^{\left(0\right)}$ as the input and refine the feature representation by stacking two graph attention layers, ultimately obtaining a low-dimensional graph embedding for each node. This process not only encodes the node’s attribute information but also integrates structural information, achieving a deep understanding and representation of graph data.

3.1.3. Decoder

In the decoder section, we have decided to employ a decoder focused on graph structure reconstruction. This decision is based on two core considerations. Firstly, by optimizing the error loss before and after graph structure reconstruction, we can facilitate encoder self-feedback, enhancing the model’s adaptability. Secondly, and more importantly, we aim to build a joint loss function by integrating the graph structure reconstruction loss and the spectral clustering loss, thus enhancing the overall performance of the model.

Considering the latent embeddings have effectively integrated the key information of node content and graph structure, we selected a decoder based on the inner product to predict the connection probabilities between nodes. This decoder was chosen for its efficiency and flexibility:

$${\widehat{A}}_{ij}=sigmoid\left(z_i^T{z}_j\right)$$

(9)

where ${\widehat{A}}_{ij}$ is a reconstructed adjacency matrix, whose elements predict the probability of links existing between nodes. To minimize reconstruction error, we utilize the mean squared error formula to calculate the difference between the actual adjacency matrix $A_{ij}$ and ${\widehat{A}}_{ij}$ to minimize the reconstruction error.

$$L_{recon}=\frac{1}{n^2}{\sum }_{i=1}^n{\sum }_{j=1}^n{{(A}_{ij}, {\widehat{A}}_{ij})}^2$$

(10)

This loss function ensures that the model, during its learning process, is capable not only of reconstructing the graph’s structure but also of accurately capturing and simulating the complex interrelations among nodes within the graph.

3.2. Spectral Clustering

As an efficient method of graph-theoretic clustering, spectral clustering relies on the spectral properties of a graph for effective data grouping [29]. In the encoding part of our model, we particularly emphasize the role of the Laplacian matrix in elucidating the structural characteristics of graphs. The Laplacian filter integrated into the encoder not only smooths the features between adjacent nodes, thereby preserving vital information, but also enhances the representation of inter-node relationships. This process results in graph embeddings that are suitable for spectral clustering, offering a rich feature space. The spectral clustering algorithm follows the following process.

(1) Construction of the Similarity Matrix:

We first construct a matrix that reflects the similarity between samples. In this process, for the graph embeddings generated by the graph attention autoencoder, we calculate the similarity between nodes using the Gaussian kernel function, defined as follows:

$$s_{ij}=exp\left(-\frac{{\left||z_i-z_j|\right|}^2}{{2\sigma }^2} \right)$$

(11)

where $\sigma$ is the bandwidth parameter of the Gaussian kernel, determining the rate of similarity decay. $S_{ij}$ denotes an $n\times n$ similarity matrix, where each element of $s_{ij}$ represents the similarity between nodes $i$ and $j$.

(2) Computation of the Laplacian Matrix:

Subsequently, we construct the graph’s adjacency matrix $W_{ij}$, i.e., $S_{ij}$= $W_{ij}={\left[s_{ij}\right]}_{n\times n}$, and calculate the degree $d_i={\sum }_{j=1}^N{s}_{ij}$ of each sample point, forming the degree matrix $D=diag(d_1,...d_n)$. The Laplacian matrix is defined consistent with the method using the Laplacian filter described earlier:

$$L=D-W$$

(12)

(3) Computation of Eigenvectors and “Soft-Cutting”:

To partition the data into $k$ clusters, we compute the eigenvectors corresponding to the $k$ smallest eigenvalues of the Laplacian matrix $L$ and combine them into the feature matrix $H^{\prime }={\left[{h^{\prime }}_{ij}\right]}_{n\times k^{\prime }}$. This step is seen as “soft-cutting” the graph, providing appropriate feature representation for subsequent clustering.

K-means Clustering and Mapping Back to the Original Dataset:

Finally, we perform K-means clustering on the feature matrix $H^{\prime }$ to obtain the final clustering results. These results represent the clustering of the original sample space and provide the possibility for further analysis of EEG background waves across different clusters.

3.3. Multi-Objective Optimization Encoders

The core of this method lies in utilizing the representative cluster center labels identified in step 4, as shown in Figure 3, to guide the graph attention encoder in generating more discriminative graph embeddings. Furthermore, by adopting a multi-objective optimization strategy that jointly optimizes the decoder’s graph reconstruction loss and clustering loss, the model precisely reconstructs the graph structure while generating graph embeddings that are more suitable for clustering analysis, achieving a multi-objective optimized encoder. Figure 3 below illustrates this process.

3.3.1. Semi-Supervised Learning Optimization

In the semi-supervised learning phase, we employ an iterative feedback mechanism to optimize the encoder. In the first round of iteration, the model takes unlabeled data from all subjects as input and generates pseudo-labels by marking the center of each clustering result. In subsequent iterations, these pseudo-labels are used as supervisory signals to finely tune the encoder, producing more discriminative graph embeddings.

Pseudo-Label Feedback: The pseudo-labels are updated based on the clustering results obtained after each iteration and are fed back to the encoder as additional supervisory information. This process not only strengthens the model’s learning of the clustering structure but also enhances its understanding of the intrinsic distribution of the data.

The overall semi-supervised training process is shown in Figure 3. In step 1, we prepare all unlabeled subject samples after pretreatment and then feed the unlabeled samples into the GAAE. In step 2, the embedded representation of the EEG graph structure is obtained using the GAAE. Step 3 involves performing spectral clustering with the obtained EEG-embedding representations. Step 4 consists of extracting cluster center samples and generating pseudo-labels for some subjects from various clustering centers. Step 5 includes retraining the model using the unlabeled samples and the samples with updated pseudo-labels. Steps 2 to 5 are iterated multiple times, and upon reaching the maximum number of iterations, the final clustering results are produced.

3.3.2. Joint Loss Optimization

To achieve effective optimization, we introduce a joint optimization strategy of clustering loss and graph reconstruction loss, which aims to find a model configuration that achieves efficient graph structure reconstruction and accurate node clustering simultaneously.

Clustering loss: Calculated based on the output of spectral clustering, where each node is represented by a pseudo-label indicating its cluster center. Using the K-means algorithm as the final step of spectral clustering, the clustering loss is defined as follows:

$$L_{cluster }={\sum }_{i=1}^n{\left||z_i-{\mu }_{ci}|\right|}^2$$

(13)

where $z_i$ represents the embedding of node $i$, ${\mu }_{ci}$ is the center of the cluster to which the node belongs, and $\mathrm{n}$ is the total number of nodes.

Graph reconstruction loss: Defined by comparing the difference between the adjacency matrix of the original graph and that of the reconstructed graph. Mean Squared Error (MSE) is used to quantify this difference:

$$L_{recon}=\frac{1}{n^2}{\sum }_{i=1}^n{\sum }_{j=1}^n{{(A}_{ij}, {\widehat{A}}_{ij})}^2$$

(14)

where $A_{ij}$ and ${\widehat{A}}_{ij}$ represent the elements of the original and reconstructed graph’s adjacency matrices, respectively.

Joint Optimization: Joint loss is minimized by the following equation:

$${L_{total }=L}_{cluster }+\lambda L_{recon}$$

(15)

where $\mathsf{\lambda }$ is used to balance the impact of reconstruction loss.

Parameters are updated through the gradient descent based on $L_{total }$. This involves calculating the gradients of the joint loss and using these gradients to update the parameters of the encoder and the decoder.

4. Experiments

4.1. Dataset and Preprocessing

This study utilized the dataset provided by the Cuban Human Brain Mapping Project (CHBMP) [30], comprising 282 participants defined as “functionally healthy,” aged between 18 to 68 years, with an average age of 31.9 years. The sample population was gender-balanced and included detailed demographic information such as gender, hand preference, and educational background.

Through stringent health criteria, 282 participants were selected from 2019 potential candidates, excluding any individuals with known diseases or brain functional impairments. The CHBMP dataset includes high-density resting-state EEG recordings in different conditions (closed eyes, open eyes, and hyperventilation), MRI data including anatomical T1-weighted images and diffusion-weighted imaging. Additionally, the dataset incorporates results from cognitive assessment tools like the Mini-Mental State Examination (MMSE) and the Wechsler Adult Intelligence Scale (WAIS-III), offering a comprehensive neurocognitive profile for the study.

From the original dataset, 193 participants were selected for in-depth analysis. Through data cleaning, denoising, and standardization processes, we ensured the quality and consistency of the preprocessed data. Notably, for EEG data, multiple signal processing techniques were employed, such as filtering, artifact removal, and amplitude normalization, to reduce external interference and system errors.

Through preprocessing, we constructed a clean dataset comprising 193 participants aged between 18 to 68 years, laying a solid foundation for subsequent study.

4.2. Baseline Methods

We aimed to explore and evaluate the effectiveness of different clustering algorithms in performing age-clustering tasks with EEG signals. We compared the total of ten clustering algorithms, covering methods reliant on a single information source (either node attributes or graph structure) and those integrating both types of information.

Methods based on the single information source:

• K-means: A foundational method for many clustering approaches [31,32].
• Spectral clustering: Utilizes eigenvalues for dimensionality reduction followed by clustering.
• GraphEncoder [33]: Trains stacked sparse autoencoders to obtain representations.
• DeepWalk [34]: A structure-based representation learning method.
• DNGR [35]: Uses stacked denoising autoencoders, encoding each vertex into a low-dimensional vector representation.

Methods based on graph structure and attributes:

• ● GAE: A graph-based autoencoder model for learning low-dimensional representations of nodes in a graph.
• ● VGAE [15]: A variational version of GAE, introducing variational inference to learn probabilistic distributions of nodes.
• ● ARVGE [36]: A graph-embedding method that integrates variational autoencoders and adversarial training, learning low-dimensional robust representations of graph nodes by introducing adversarial regularization.
• ● AGC [21]: An adaptive graph-clustering method that integrates structural and content information for node clustering.

Note that some of the above-mentioned methods, including GraphEncoder, DeepWalk, DNGR, GAE, VGAE, and ARVGE, are actually representation-learning methods; our approach is first to utilize these methods to get representations from graph data, followed by applying the representation to spectral clustering.

4.3. Evaluation Metrics and Parameter Settings

Use four evaluation metrics to measure the performance of clustering results: Accuracy (ACC), Normalized Mutual Information (NMI), Adjusted Rand Index (ARI), and F-score. These metrics collectively provide a comprehensive evaluation framework to assess the quality of clustering results from various angles, with better-performing clustering algorithms expected to score higher across these metrics.

Baseline Settings:

For the baseline algorithms, parameters were carefully chosen, and implementation details were strictly followed as recommended in their respective original papers, ensuring each algorithm could be compared in its best state.

Parameter Settings:

For our proposed method, the encoder was designed with a hidden layer of 256 neurons and an embedding layer of 16 neurons.

The experiments began with preprocessing described in Section 4.1. The data were then fed into various clustering algorithms, yielding clustering results analyzed across the specified metrics.

Through these rigorous evaluation processes and multi-faceted performance metrics, our goal was to accurately identify clustering methods that are capable of revealing the relationship between EEG background waves and age changes.

4.4. Experimental Results

• Model Comparison

The experimental results are shown in

Table 1. EEG age clustering experiment results on the CHBMP dataset.

Method	Dataset	ACC	NMI	ARI	F-Score
K-means	CHBMP	0.524	0.302	0.261	0.415
Spectral	CHBMP	0.374	0.245	0.208	0.324
GraphEncoder	CHBMP	0.311	0.103	0.163	0.208
DNGR	CHBMP	0.432	0.188	0.176	0.231
DeepWalk	CHBMP	0.453	0.311	0.226	0.291
GAE	CHBMP	0.591	0.371	0.347	0.408
VGAE	CHBMP	0.608	0.347	0.398	0.402
ARVGE	CHBMP	0.621	0.397	0.328	0.426
AGC	CHBMP	0.681	0.424	0.402	0.503
SGAAE-AC	CHBMP	0.754	0.479	0.423	0.663

. The results demonstrated that our proposed SGAAE-AC method performed exceptionally well on CHBMP datasets, especially in terms of ACC, NMI, ARI and F-score.

Methods solely relying on a single information source displayed ACC values between 0.311 (GraphEncoder) and 0.524 (K-means) on the CHBMP dataset. Our SGAAE-AC method, integrating structural and content information, achieved a remarkable ACC of 0.754, significantly surpassing these methods. Among strategies incorporating graph structure and attributes, performance improved progressively from GAE to AGC, with AGC reaching 0.681 and ARVGE 0.621 in ACC. Yet, SGAAE-AC stands out even among these, delivering superior results across various metrics through optimized information use and strategic enhancements.

The SGAAE-AC model outperformed the leading AGC method by 0.073 in ACC, thanks to its innovative use of label feedback from clustering to refine graph embeddings, reducing misclassifications and boosting ACC. Improvements in NMI and ARI by 0.055 and 0.021, respectively, over AGC, are credited to SGAAE-AC’s simultaneous optimization of graph reconstruction and clustering loss, enhancing feature representation’s relevance and the model’s self-learning capabilities. Moreover, the F-score benefits from precise data portrayal and efficient classification, further elevated by the Laplacian filter’s role in enhancing local and global information coherence, thus improving the model’s ability to discern EEG patterns by age, which is reflected in a higher F-score.

2.

Experimental Parameter Adjustments

Our research adjusted the hidden layer dimensions of the graph attention autoencoder from 16 to 512 neurons and the number of attention heads from 1 to 8.

We can see from Figure 4a,b a stable improvement in clustering performance when the dimension of the hidden layer increased from 128 to 256 neurons. However, further increases in the number of embedding layer neurons showed some performance fluctuations. Notably, despite fluctuations, the overall ACC and NMI scores remained at a high level. As for the number of attention heads, a stable improvement in clustering performance was observed when increasing from 1 to 2 heads. However, further increases led to a downward trend in performance.

These observations suggest that selecting appropriate dimensions for the embedding layer and the number of attention heads is crucial for optimizing model performance, especially with complex graph structure data. Excessive neurons or attention heads might lead to performance degradation, likely due to overfitting or increased model complexity. Hence, our research emphasizes the importance of finding an optimal parameter balance in model design.

3.

Ablation experiment

To ensure the rigor of our experimental results, we conducted ablation studies to explore the impact of the optimization module on our model’s parameters.

Table 2. Ablation experiment.

Model Variants	CHBMP
	ACC	NMI	ARI	F-Score
GAAE and spectral clustering	0.654	0.424	0.332	0.503
+Laplacian filtering	0.660	0.430	0.336	0.621
+Joint optimization	0.692	0.467	0.402	0.653
+Semi-supervised learning	0.754	0.479	0.423	0.663

shows the results of this experiment, and Figure 5 uses t-SNE dimensionality reduction [37] to display changes in learned embeddings for the EEG age-clustering task within the CHBMP dataset across different training configurations.

Original Signal Scatter: Figure 5a depicts the distribution under original conditions.

Laplacian Filter: Figure 5b shows clearer clustering tendencies among different age groups after incorporating the Laplacian filter in the encoder.

Encoder with Joint Loss Optimization: Figure 5c further displays the embedding effect after the joint optimization of graph reconstruction loss and clustering loss, where the clustering of each age group is more pronounced, indicating the effectiveness of the joint optimization strategy in enhancing clustering outcomes.

Semi-supervised Learning Approach: Figure 5d reveals the evolution of embeddings with semi-supervised learning, where boundaries between clusters are clearer and nearly non-overlapping, showcasing the significant impact of semi-supervised learning methods on improving embedding quality and clustering performance.

4.5. Result Analysis

In our research, we divided EEG data into four age groups, a choice driven by the understanding that too many groups could weaken our analysis by reducing the sample size in each, making it harder to spot meaningful trends. This division mirrors practices in neuroscience and psychology, which often explore changes across similar age spans. Moreover, our model’s flexibility allows users to specify the number of clusters based on their actual needs, making it a versatile tool for various studies.

The clustering model effectively divided the EEG background wave data into four distinct age groups: 18–25, 25–35, 35–50, and over 50 years old. We calculated comprehensive frequency domain features such as the log-average spectrum for all participants within each age interval, subsequently analyzing EEG background wave activity.

4.5.1. Pattern Analysis

The log-average spectrum is a method for processing PSD, simplifying spectral analysis through logarithmic treatment and making subtle variations more recognizable. This technique allows for a comprehensive and clear presentation of a signal’s frequency domain characteristics, such as frequencies, peak values’ total power and band power, serving as a powerful tool for in-depth signal understanding.

Figure 6 shows the log-average spectrum across different frequency bands for each age group, measured on 19 electrodes.

Our study reveals distinct differences in brain activity between young and older adults; older individuals exhibit lower frequencies and power in the $\delta$, $\theta$, and $\alpha$ bands, while $\beta$ band power is comparatively higher.

1. Young Adulthood (18–25)

Specifically, individuals aged 18 to 25 displayed an average $\alpha$ frequency of around 10.5 Hz, alongside robust power within the alpha band. In contrast, for those aged 50 and above, the peak α frequency decelerated to an average of 9.56 Hz, with diminished band power. Notably, there is an overall reduction in alpha band power with advancing age. The close association of $\alpha$ waves with cognitive functions such as attention, learning, and memory indicates that the brain is undergoing rapid development at this stage, marking the transition from immaturity to maturity.

2. Middle Age (25–50)

In individuals aged 25 to 35, EEG recordings indicate subtle shifts, characterized by a slight decline in $\theta$ and $\alpha$ wave activities. However, between the ages of 35 and 50, these changes become more pronounced, with a continued decrease in $\theta$ and $\alpha$ activities and a noticeable increase in $\beta$ wave activity.

3. Senior Years (50+)

In individuals aged 50 and above, both the frequency and power of θ waves significantly decrease, indicating a downward trend in θ wave resting-state activity from ages 18 to 68. Overall, the amplitude of brainwaves, specifically the total power, markedly reduces, with diminished α wave activity, leading to a general slowdown in brain activity. Studies have shown that the power of alpha waves is closely related to attention, memory processing, and overall cognitive health. The reduction in alpha wave power in older adults may reflect a general decline in these cognitive functions. Conversely, reduced alpha activity may signal heightened experience levels, enabling seniors to transition between engagements more efficiently and swiftly. This discovery is supported by Klimesch GEER and colleagues’ research (2021) [38]. These changes in older adults compared to younger adults may reflect a reallocation of neural resources and an ability to adapt to environmental changes. Additionally, alpha synchrony may help in deselecting a stronger but currently irrelevant neural ensemble, allowing the weaker but relevant ensemble to be boosted, as suggested by research on neural oscillatory synchronization [39].

We observed an increased relative power of β waves in older adults. This could stem from their wealth of life experiences, wherein a single input may trigger a cascade of “pretrained” memories. A study indicates that beta activity is related to attentional top–down modulation, which is crucial for processing memories and experiences. Beta synchrony is associated with the selection of relevant neural ensembles, further supporting the idea that increased beta activity in older adults might reflect their extensive life experiences [39]. Additionally, the concept of reminiscing and its therapeutic benefits are well-documented, highlighting how reflecting on past experiences can activate memory networks and enhance cognitive functioning [40].

Another study showed a phenomenon associated with motor control and inhibitory activity within the motor cortex. Barry and De Blasio’s hypothesis (2017) [41] suggests that the increase in β wave activity in the elderly might represent the additional processing resources required to maintain responsiveness to environmental changes.

4.5.2. Electrodes Attention Analysis

The Standard 10–20 system EEG electrode layout and brain region division map, as presented in Figure 7, is foundational for understanding the variations in electrode attentiveness across the different frequency bands depicted in Figure 8.

To delve into the model’s attention allocation patterns across different frequency bands, we performed a row-wise averaging of the model’s attention weight matrix and normalized the results to a range of 0 to 10. This process enabled us to quantitatively assess the GAAE’s degree of attention to interactions between EEG electrodes across different frequency bands.

In the δ band, the model particularly focuses on the frontal lobe electrodes Fp1 and Fp2, closely related to frontal lobe activity. In the θ band, attention is mainly on the occipital (O1, O2) and frontal (F3, F4) regions, possibly reflecting these areas’ unique roles in this frequency band. $\alpha$ band’s attention distribution is more concentrated, especially in the posterior temporal (T5) and occipital regions, closely related to age-associated brain activity. As for the $\beta$ band, the model shows broad attention, covering multiple areas from the mid-temporal (T3, T4) to posterior temporal (T5, T6), emphasizing the close relationship between beta band EEG signals and age.

Overall, the model’s attention in the $\alpha$ and $\beta$ bands was significantly higher than in the $\delta$ and $\theta$ bands. This observation aligns with existing research, confirming that delta and theta bands dominate brain electrical activity in young ages. As people grow older, activity in the $\alpha$ and $\beta$ bands increases, especially from adolescence to middle age, showing a significant upward trend [3,4,5,6]. These insights not only enrich our understanding of age-related changes in brain electrical activity but also provide new perspectives for future neuroscience research.

5. Conclusions

This study introduces an innovative approach for EEG age clustering, named SGAAE-AC, to reveal the relationship between EEG background waves and age. This method is tailored for EEG data through an improved graph construction technique, which, by integrating graph attention autoencoders with Laplacian filters, enhances the model’s capability in brain signal representation and the accuracy of clustering outcomes. Furthermore, SGAAE-AC employs a multi-objective optimization scheme and a semi-supervised learning paradigm, which further enhances the accuracy and robustness of EEG age clustering without the need for true labels. Extensive experiments have demonstrated that this model outperforms other methods across all the evaluation metrics, including ACC, NMI, ARI and F-score, showcasing its advancement and effectiveness in the field of EEG age clustering.

The significance of this study lies in its capability to capture the dynamic changes in EEG background waves across different age stages. It not only provides new tools for the analysis of EEG signals but also offers scientists new perspectives for exploring age-related changes in brain function and unveiling the fundamental laws of human cognitive development.

In our future projects, we plan to utilize larger and more diverse datasets to train the model. This will enable the model to learn a wider range of EEG features, potentially enhancing its accuracy and ability to generalize. Leveraging the unique capabilities of our model in EEG feature extraction and representation, we will also explore research opportunities, such as brain age prediction based on EEG signals.