## 1 Introduction
Researchers in [22] extracted multi-modal physiological signals, including EEG, ECG, and NIRS signals, in which the maximum power, the power density integral power, and the relative power of \(\delta\), \(\theta\), \(\alpha\), and \(\beta\) bands were extracted as features. Then, the features were selected using a correlation-based feature selection (CFS) method and classified with the k-nearest neighbor (KNN) method. However, only information in the frequency domain is utilized in these methods, which fails to exploit the underlying information related to engagement level in EEG signals. Therefore, it is significant to improve the engagement recognition accuracy by integrating information from different domains and extracting representative features to realize classification. For the spatial domain, the common spatial pattern (CSP) [32] method is one of the most popular and powerful spatial filtering methods in the motor imaginary (MI)-based brain-computer interface (BCI). The purpose of the CSP is to find spatial filters so that the variance of the filtered data is maximized for one class and minimized for the other class. However, due to the sensitivity of the CSP to noise, many extensions of CSP-based methods have emerged to improve its effectiveness. In [33], an L1 norm-based CSP is introduced, in which the L1 norm is in place of the L2 norm to figure out the spatial filter estimation in order to improve the robustness of the CSP. [PERSON] et al. [34] proposed an integrated theoretical framework of a regularized CSP (RCSP) and specifically designed four RCSP algorithms, among which the optimal RCSPs are a CSP with Tikhonov regularization and weighted Tikhonov regularization. Recently, a correlation-based CSP (CCSP) based on temporal correlation was designed to improve the performance of the CSP [35]. In this study, the CCSP algorithm was adopted to extract spatial features. For the frequency domain, the combination of a filter bank and a CSP is a simple way to combine the information in the frequency domain with that in the spatial domain [36]. A set of filter banks was designed, and their effectiveness was compared to select the optimal filter bank. In addition, for the phase domain, both amplitude and phase information were considered to utilize the potential information embedded in the EEG signals. Therefore, this paper proposes an engagement recognition using a multi-domain feature extraction method based on correlation-based common spatial patterns (MDCCSPs), which presents three contributions:  
* Firstly, an engagement recognition method based on a correlation-based CSP is proposed, in which the temporal correlation is utilized as a prior to improve the effectiveness. Specifically, the original CCSP is extended into three versions by replacing various correlation coefficients ([PERSON]'s linear correlation coefficient, [PERSON]'s correlation coefficient [37], and [PERSON]'s correlation coefficient). * Secondly, this study integrates information from spatial, frequency, and phase domains to fully exploit the potential of EEG data. A filter bank is combined with the original CCSP to extract features in the frequency domain and the spatial domain. Besides, the Hilbert transform is applied to obtain the amplitude and phase angle of EEG signals. Multi-domain features are integrated and fed into an SVM to realize engagement recognition. * Thirdly, the proposed method is validated and compared with existing methods on an open dataset composed of 29 subjects. Experimental results show that it offers an efficient way to recognize the level of engagement, which is validated by its outperformance. The rest of the article is arranged as follows. The proposed engagement recognition method using the multi-domain feature extraction method based on correlation-based common spatial patterns is described in detail in Section 2. In Section 3, the experimental setups are presented, and the results are analyzed. Then, a discussion is provided in Section 4. Finally, Section 5 summarizes the whole article.