## 1 Introduction  
Engagement is the ability to spend attentional resources on task-related stimuli and ignore external interference [1]. As a fundamental aspect of cognition, engagement ability plays a crucially important role in the operational environment [2]. Engagement helps us to ignore interference and focus our awareness, which is necessary for learning, working, and building normal relationships [3, 4, 5]. Being a participant in numerous and heterogeneous daily tasks, everyone endeavors to improve their efficiency with high engagement [6, 7, 8]. In highly professional scenarios in particular, such as clinical operations [9], aircraft piloting [10] and aerial work [11], engagement level monitoring is very important and related to life safety [12]. The disability of being engaged in current tasks and dealing with mental workload may lead to severe accidents [13]. Moreover, measuring engagement is of great clinical application. For example, measuring engagement can help to diagnose psychological diseases, such as attention deficit hyperactivity disorder (ADHD), which is a common disease in children [14]. Furthermore, engagement level influences the reliability of psychological tests [15]. Monitoring the engagement level can measure the credibility of psychological tests and therefore serves as an auxiliary means in other psychological treatments. In this way, it becomes more and more significant to recognize and measure engagement level [16, 17]. Psychologists have made attempts to design various self-reporting questionnaires and scales in order to reflect the engagement level of subjects more accurately [18, 19, 20, 21]. However, these subjective tools are delayed and sometimes uncertain due to indistinct memory and dishonesty. Unlike subjective tools, physiological signals can be collected simultaneously with the execution of the current task and can reflect the engagement level more accurately without subjective interference [22; 23]. Therefore, researchers have started to recognize engagement level and workload through physiological signals. In [24], physiological signals, including electrocardiogram (ECG), skin conductivity (SC), and respiration (RESP) signals, are collected and combined with the Self-Assessment Manikin to detect the cognitive load. [PERSON] et al. [25] decomposed ECG signals using an S-transform algorithm to detect engagement and attention state. [PERSON] et al. [22] introduced the implementation of a low-density hybrid system for engagement recognition, in which wireless electroencephalography (EEG), ECG, electrooculogram (EOG), and near-infrared spectroscopy (NIRS) are utilized. This study focuses on EEG-based engagement recognition. Existing studies in neuropsychology have revealed the direct correlation between EEG signals and a variety of cognitive behaviors, including engagement level [26; 27; 28], and established EEG-based engagement recognition. The key to decoding engagement level using EEG signals is to extract the most representative features to realize engagement level classification. The most widely used feature in engagement level classification is spectral power. [PERSON] et al. [29] predicted engagement utilizing power spectral density (PSD) features. The PSD features in \(\delta\) (1-4 Hz), \(\theta\) (4-8 Hz), \(\alpha\) (8-13 Hz), and \(\beta\) (13-30 Hz) were extracted as features to feed into classifiers to predict engagement level. Similarly, 1 Hz bin PSD features were utilized by [PERSON] et al. and fed into deep models for engagement assessment [23]. Relative band power of \(\delta\), \(\theta\), \(\alpha\), and \(\beta\) bands were calculated, and \(P_{\beta}/(P_{\alpha}+P_{\theta})\) was taken as an EEG index by [PERSON] et al. [30]. The four features were analyzed under different tasks. Researchers in [31] extracted relative PSDs from differential EEG channels and fed them into a linear DFA to realize binary engagement classification for subjects who ranged from 67 to 93 years old.