## 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 [PERSON] 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, \(\delta\) waves and \(\theta\) waves dominate brain activity, whereas \(\alpha\) and \(\beta\) wave activities gradually increase throughout childhood. In the field of nonlinear dynamics analysis, in 2006, the work of [PERSON] 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, [PERSON] 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, [PERSON] 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, [PERSON] 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 EEGbackground 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.