WSEL: EEG feature selection with weighted self-expression learning for incomplete multi-dimensional emotion recognition

Venue: acmmm_org_ACMMM_2024_Conference
Published: 2024-04-08 16:16:40

Abstract: Due to the small size of valid samples, multi-source EEG features with high dimensionality can easily cause problems such as overfitting and poor real-time performance of the emotion recognition classifier. Feature selection has been demonstrated as an effective means to solve these problems. Current EEG feature selection research assumes that all dimensions of emotional labels are complete. However, owing to the open acquisition environment, subjective variability, and border ambiguity of individual perceptions of emotion, the training data in the practical application often includes missing information, i.e., multi-dimensional emotional labels of several instances are incomplete. The aforementioned incomplete information directly restricts the accurate construction of the EEG feature selection model for multi-dimensional emotion recognition. To wrestle with the aforementioned problem, we propose a novel EEG feature selection model with weighted self-expression learning (WSEL). The model utilizes self-representation learning and least squares regression to reconstruct the label space through the second-order correlation and higher-order correlation within the multi-dimensional emotional labels and simultaneously realize the EEG feature subset selection under the incomplete information. We have utilized two multimedia-induced emotion datasets with EEG recordings, DREAMER and DEAP, to confirm the effectiveness of WSEL in the partial multi-dimensional emotional feature selection challenge. Compared to nine state-of-the-art feature selection approaches, the experimental results demonstrate that the EEG feature subsets chosen by WSEL can achieve optimal performance in terms of six performance metrics.

Main paper: 
 introduction: 
 Electroencephalogram (EEG) is a portable, non-traumatic technology for measuring brain activity that can react quickly to a range of affective states [32, 42] . EEG-based emotion recognition has received a lot of interest lately in the field of multimedia-induced affective computing because of its high temporal resolution and affordability [6, 9, 23] . Various types of feature extraction approaches, such as non-stationary index (NSI) [19] , rational asymmetry (RASM) [26] , higherorder crossing (HOC) [33] , etc., have been used to analyze the non-stationary and nonlinear EEG signals in order to correctly represent different affective states.The quantity of electrodes accessible for emotion recognition is rapidly increasing due to the development of EEG signal collecting equipment, and a large number of EEG features could be extracted from the electrodes [3, 40] . However, owing to the relatively limited number of EEG samples, the related features are often high-dimensional and always consist of redundant, irrelevant, and noisy information, which may significantly decrease the emotion recognition performance [39] . Feature selection is an effective means to choose noteworthy features and exclude irrelevant information from the original features, which retains the original neural representation information of the EEG features and enhances the transparency and interpretability of the emotion recognition model [13] .The EEG feature selection algorithms could be broadly divided into three types based on feature subset assessment and search mechanism: filter, wrapper, and embedded approaches [12] . The filter techniques consider the statistical characteristics of the EEG data to evaluate the significance of EEG features in affective computing. However, the feature selection performance is often unsatisfactory with these techniques, regardless of the learning algorithm [53] . Several studies have attempted to utilize wrapper techniques to address the issue. In many cases, the wrapper techniques could achieve better prediction performance than the filter techniques [12] due to the fact they employ the learning outcomes of a particular classifier as the evaluation index for the EEG feature subset. Nevertheless, the wrapper approaches often require lots of trials and incur significant computing costs [53] . Recently, researchers have been paying close attention to embedded approaches as a potential substitute approach to deal with the filter problem. The search for EEG feature subsets can be integrated into the optimization problem using embedded techniques. The effectiveness of the embedded techniques on the EEG-based emotion recognition task has been demonstrated [44, 45] .Current EEG feature selection research relies on the completeness of the data. However, the training data in the practical application often includes missing information, such as partial dimensions of emotion labels from several samples, owing to the open acquisition environment, subjective variability, and border ambiguity of individual perceptions of emotion. The above incomplete information directly restricts accurate modelling for the relationship between the EEG and the multi-dimensional emotional labels.To address the issue, we propose a novel EEG feature selection model with weighted self-representation learning (WSEL) for incomplete multi-dimensional emotion recognition. The model could reconstruct the label space through the second-order correlation and higher-order correlation within the multi-dimensional labels and simultaneously select the informative and redundant EEG feature subsets under the partial multi-dimensional information.Furthermore, the following are the primary contributions to our work:• This study proposes an incomplete multi-dimensional emotion feature selection method. The method embeds the process of EEG feature selection into an extended weighted self-representation model, which is able to suppress the effect of missing labeling data on model construction and introduce second-order and higherorder correlations within multi-dimensional emotion labels to recover missing labels. • In order to copy the optimization problem of WSEL, an efficient and straightforward alternative scheme is proposed to ensure convergence and obtain an optimal solution. • To confirm the effectiveness of WSEL in the incomplete multi-dimensional emotion feature selection challenge, two multimedia-induced emotion datasets with EEG recordings and multi-dimensional emotional labels, DREAMER and DEAP, have been implemented. Compared to nine state-of-the-art feature selection approaches, the experimental outcomes demonstrate that the EEG feature subsets chosen by WSEL can achieve the best emotion recognition performance on six evaluation metrics. 
notations and related works 2.1 notations and definitions: 
 This section provides a concise summary of the definitions of the norms and symbols adopted throughout the work. Vectors are represented by lowercase strong letters (x, y ...), whereas matrices are represented by capital letters (𝑋, 𝑌 ...). The mathematical notation for the transpose is represented by an uppercase superscript 𝑇 . The operator denoted by ⊙ represents the Hadamard product. The trace of a matrix is represented as Tr. The Frobenius norm and 𝑙2,1 norm of a matrix 𝑋 are represented as:EQUATION‖𝑋‖2,1EQUATION𝑋 ∈ R 𝑑×𝑛 is an EEG feature matrix, and each row represents a feature vector x 𝑑 ∈ R 1×𝑛 . 𝑌 ∈ {-1, 1} 𝑛×𝑘 is a multi-dimensional emotional label matrix. The variables 𝑑, 𝑛, and 𝑘 correspond to the quantities of features, samples, and dimensions, respectively. The vector 1𝑛 = (1, 1 . . . , 1) 𝑇 ∈ R 𝑛×1 is defined as a column vector consisting of all elements being equal to one. The symbol 𝐼𝑛 ∈ R 𝑛×𝑛 represents an identity matrix.Emotion representation models fall into two categories: discrete emotion models and dimensional emotion models, depending on how emotions are depicted. Discrete emotion models utilize several basic discrete categories to characterize emotions. For example, there are six basic discrete categories, namely happiness, sadness, fear, anger, disgust, and surprise [34] . Complex emotion categories are composed of combinations of the basic discrete categories. However, the representation approach cannot scientifically describe the nature of emotions or effectively quantify emotional states from a computational perspective [1] .In order to solve the difficulties faced by the discrete model, the dimensional affective model maps affective states as points on a multi-dimensional space, and the affective states are distributed in different locations in the space based on different dimensions, and the distances between the locations reflect the differences and associations between different affective states [1] . Compared with the discrete emotion model, the dimensional emotion model has the advantages of a wide range of characterization and the ability to describe the emotional evolution process [8] . Commonly used dimensional models include the Valence-Arousal (VA) model [35] and the Valence-Arousal-Dominance (VAD) model [29] .The EEG feature selection techniques may be categorized into three groups based on their interaction with classification models: filter-based, wrapper-based, and embedded-based methods [53] .Filter-based methods assess the significance of EEG features based on specific criteria. The discriminatory EEG features that score highly are subsequently chosen, such as ReliefF [49] , information gain [4] , maximum relevance minimum redundancy [2, 41] , conditional mutual information maximization [47] , etc. However, the aforementioned filterbased methods may overlook a number of helpful features that, when paired with other features, are discriminative because learning models are neglected [36] .Using random or sequential search, wrapper-based approaches "wrap" features into candidate EEG feature subsets. A learning or prediction model then assesses the performance of these candidate EEG feature subsets. Several popular wrapper-based techniques, including the evolutionary computation algorithm [30] and the ReliefF-based genetic algorithm [18] , have been proposed or employed for EEG-based affective computing. Nevertheless, the computational complexity of wrapper-based techniques is often significant because of the iterative nature of feature subset searches [37] .In order to address the shortcomings of filter-based or wrapper-based feature selection techniques, embedded-based methods have been put forward [24] . These methods integrate feature selection into the training model process and assess the relative significance of individual EEG features while optimizing learning models. Because of its completeness in statistics theory and efficacy for data analysis, least squares regression is a popular statistical analysis model for embedded-based feature selection approaches [5, 31, 43, 44] . Least square regression (LSR)-based embedded feature selection algorithms seek to learn a projection matrix 𝑊 and then rank the feature significance by {‖𝑤 1 ‖2, ..., ‖𝑤 𝑑 ‖2|} [46] . The discriminative EEG feature subsets can be chosen according to their significance. 
problem formulation: 
 This section proposes a unique EEG emotional feature selection approach to acquire non-redundant and relevant feature subsets for incomplete multi-dimensional affective computing.The WSEL framework is defined as follows:EQUATIONwhere the projection matrix and coefficient matrix are represented by the variables 𝑊 and 𝑈 , respectively. 𝛾 and 𝜆 are both tradeoff parameters. The basic feature learning function, weighted self-expression learning function, and global feature redundancy learning function are denoted by the symbols 𝐹 , 𝐶, and Ω, respectively. The next sections will introduce the definitions of 𝐹 , 𝐶, and Ω.LSR is employed to estimate the correlation between the EEG feature matrix 𝑋 and the self-expression matrix 𝑌 𝑈 .To perform EEG feature selection, the projection matrix 𝑊 is constrained by 𝑙2,1-norm. The term 𝐹 (𝑋, 𝑊, 𝑌, 𝑈 ) could be expressed as follows:EQUATIONin which 𝑏 ∈ R 𝑘×1 is a bias vector, 𝑊 ∈ R 𝑑×𝑘 is the projection matrix, 𝑈 ∈ R 𝑘×𝑘 is the coefficient matrix, and 𝛿 (𝛿 > 0) is a tradeoff parameter.To describe the dimension-missing information, the element 𝑃𝑖,𝑗 of an indicator matrix 𝑃 is defined as follows: Then, 𝑃 is introduced into the self-expression learning function as follows:𝑃𝑖𝑗 = {︃ 1 if 𝑖-thEQUATIONVia high-order label correlations among the multi-dimensional emotion labels, each dimension can be represented by all the dimensions. In order that each label is reconstructed by the most directly relevant labels, the self-expression coefficient matrix 𝑈 is imposed with a 𝑙2,1-norm constraint.Afterwards, a graph-based manifold regularizer is implemented to maintain consistency of the local geometry structures between the self-expression space 𝑌 𝑈 and the original multi-dimensional label space 𝑌 [14] . A graph Laplacian matrix 𝐿𝑌 ∈ R n×𝑛 is indicated by the notation 𝐿𝑌 = 𝐺 -𝑆. The affinity graph for 𝑌 is represented by 𝑆, and the elements of the diagonal matrix 𝐺 can be obtained by 𝐺𝑖𝑖 = ∑︀ 𝑛 𝑗=1 𝑆𝑖𝑗. A heat kernel has been employed to generate the affinity graph 𝑆. The similarity value of two labels, 𝑦𝑖. and 𝑦𝑗., is represented by the element 𝑆𝑖𝑗. 𝑆𝑖𝑗 is defined as follows:𝑆𝑖𝑗 = ⎧ ⎨ ⎩ exp (︂ - ‖𝑦𝑖.-𝑦𝑗.‖ 2 𝜎 2)︂ 𝑦𝑖. ∈ 𝒩𝑞 (𝑦𝑗.) or 𝑦𝑗. ∈ 𝒩𝑞 (𝑦𝑖.) 0 otherwise (7) The symbol 𝜎 represents the graph construction parameter, whereas 𝒩𝑝 (𝑦𝑗) denotes the set of the top 𝑞 closest neighbours of the label 𝑦𝑗..Ultimately, by including the graph-based manifold regularizer in the weighted self-expression learning, the formulation of the term 𝐶 can be expressed as follows:EQUATIONwhere 𝛽 and 𝜂 represent tradeoff parameters.In addition, we introduce a global feature redundancy matrix 𝐴 to evaluate the correlations among all the EEG features. The value of 𝐴 could be obtained via the following calculation:EQUATIONwhere 𝑓𝑖 ∈ R 𝑛×1 and 𝑓𝑗 ∈ R 𝑛×1 are 𝑖-th and 𝑗-th centralized features of two types of EEG features 𝑥𝑖 and 𝑥𝑗 (𝑖, 𝑗 = 1, 2, ..., d). 𝑓𝑖 and 𝑓𝑗 can be computed as follows:EQUATION)where 𝐻 = 𝐼n -1 𝑛 1𝑛1𝑛 𝑇 . Eq. ( 9) can be changed toEQUATION𝐹 is defined as 𝐹 = [𝑓1, 𝑓2, ..., 𝑓 𝑑 ].Let 𝑍 be a diagonal matrix such that each diagonal element 𝑍𝑖,𝑖 = 1 ‖𝑓 𝑖 ‖ (𝑖 = 1, 2, ..., d). Since the matrix 𝑂 is positive semi-definite and 𝐴 = 𝑂 ⊙ 𝑂, the resulting global feature redundancy matrix 𝐴 is both non-negative and positive semi-definite [38] . Therefore, the global feature redundancy learning function Ω can be defined as:EQUATIONBy combining Eq. ( 4), Eq. ( 8), and Eq. ( 12) together, the proposed WSEL can be formulated as follows:min EQUATION 
optimization strategy: 
 Taking the partial derivative of Eq. ( 13) with respect to 𝑏 and setting it equal to zero, we can solve for 𝑏 using the equation𝑏 = 1 𝑛 (︀ 𝑈 𝑇 𝑌 𝑇 1𝑛 -𝑊 𝑇 𝑋1𝑛 )︀. By replacing the aforementioned equation in Eq. ( 13), the optimization problem will be transformed to minEQUATIONThe alternatively iterative update technique is adopted to derive solutions for the two variables (𝑊 and 𝑈 ) in Eq. ( 14). The technique is presented as follows:When 𝑈 is fixed and we remove the irrelevant terms, we obtain the following function about 𝑊 :EQUATIONBy taking the partial derivative of ℒ (𝑊 ) w.r.t.𝑊 , we could getEQUATION)where 𝐷 is a diagonal matrix and the element of 𝐷 is calculated by 𝐷𝑖𝑖 =1 2 √ 𝑊 𝑇 𝑖 𝑊 𝑖 +𝜖 (𝜖 → 0).Hence, the optimal solution 𝑊 can be updated as follows:𝑊 = (𝑋𝐻𝑋 𝑇 + 𝜇𝐴 + 𝛿𝐷) -1 (𝑋𝐻𝑌 𝑈 ) (17)When 𝑊 is fixed, by introducing a Lagrange multiplier Ψ for 𝑈 ≥ 0, we have the following Lagrange function: Then, the partial derivative of ℒ (𝑈 ) w.r.t.𝑈 in Eq. ( 18) is calculated as:EQUATIONEQUATION)where 𝑉 is a diagonal matrix and the element of 𝑉 is calculated by 𝑉𝑖𝑖 =1 2 √ 𝑈 𝑇 𝑖 𝑈 𝑖 +𝜖 (𝜖 → 0).Based on the Karush-Kuhn-Tucker complementary condition Ψ𝑖𝑗𝑈𝑖𝑗 = 0, the update rule for 𝑈 is Update 𝑊 via 𝑊 = (𝑋𝐻𝑋 𝑇 + 𝜇𝐴 + 𝛿𝐷) -1 (𝑋𝐻𝑌 𝑈 );EQUATIONUpdate 𝑈 via Eq. (20); 7: until Convergence; 8: return 𝑊 for EEG feature selection. 9: Sort the EEG features by ‖𝑤𝑖‖2;Algorithm 1 provides the specific optimization steps for Eq. ( 13). The scores of each EEG feature in the incomplete multi-dimensional emotion recognition task can be evaluated by 𝑊 . Ultimately, the optimal EEG feature subset with non-redundant and informative features is obtained. 
experimental details: 
 This section introduces experimental details, including dataset description, EEG feature extraction, and experimental setup.Comprehensive experiments are conducted on two EEG datasets with multi-dimensional labels to assess the performance of WSEL, including DEAP [17] and DREAMER [15] . The VAD paradigm is employed in the databases to describe human emotions. During the multimedia stimulation, EEG signals were concurrently recorded. A detailed description of the experimental setup can be found in [15] and [17] . Table 1 presents basic information for the two datasets.The experiments used a band-pass filter with a cutoff frequency of 1-50 Hz to remove noise from the EEG recordings. Subsequently, artifacts related to eye movement and muscle activities were suppressed using independent component analysis. It should be mentioned that EEG feature extraction was performed on the whole trial as a sample. As stated differently, trials were not divided into many parts in order to expand the sample size of the experiments.Based on earlier studies on EEG emotional feature extraction and analysis [13, 45] , thirteen types of EEG features were extracted for the multi-dimensional affective computing task, such as C0 complexity [54] , NSI [19] , differential asymmetry (DASM) [28] , HOC [33] , spectral entropy(SPE) [48] , RASM [26] , shannon entropy(SHE) [25] , DE [7] , absolute power (𝐴𝑃 ), the absolute power ratio of the theta band to the beta band (𝐴𝑃 𝛽 /𝐴𝑃 𝜃 ) [16] , the amplitude of the Hilbert transform of intrinsic mode functions (AHTIMF), the instantaneous phase of the Hilbert transform of intrinsic mode functions (IPHTIMF) [13] , and function connectivity (FC). The comprehensive descriptions of the thirteen EEG features can be found in [7, 13, 44] . The dimensions of the thirteen EEG feature types are presented in Table 2 .Nine advanced feature selection methods are compared in order to fully assess the performance of WSEL in the multidimensional affective computing task. The compared techniques include multi-label feature selection using multi-criteria decision making (MFS-MCDM) [10] , multi-label graph-based feature selection (MGFS) [11] , PMU [20] , global relevance and redundancy optimization (GRRO) [50] , scalable criterion for large label set(SCLS) [22] , feature selection with orthogonal regression (FSOR) [45] , global redundancy minimization in orthogonal regression (GRMOR) [44] , FIMF [21] , and feature selection method via manifold regularisation (MDFS) [51] .The EEG recordings were divided into low and high values depending on the self-assessed score of each affective dimension. The threshold value for this category was established at five. Multi-label k-nearest neighbor (ML-KNN) [52] was implemented as a base classifier. The values for the number of nearest neighbors and smooth were set to 10 and 1, respectively. Seventy percent of the participants were chosen randomly to be used as training sets, while the remaining thirty percent were designated as test sets. A cross-subject experiment setup was implemented. In order to mitigate any bias, a total of 50 separate and unbiased experiments were carried out, and the average outcome was regarded as the ultimate measure of affective computing.The research applied six performance metrics for evaluating the effectiveness of multi-dimensional emotion recognition. These metrics include two label-based evaluation metrics, macro-F1 and micro-F1, as well as four example-based evaluation metrics: average precision, coverage, ranking loss, and hamming loss. The detailed information on the above metrics could be found in [51] . 
experimental results and discussion 6.1 performance comparison in incomplete multi-dimensional emotion recognition: 
 We employed the strategy in [27] to simulate the incomplete multi-label setting, eliminating certain ratios of labels from each dimension as missing data. With a step of 10% , the missing ratio was set between 10% and 50%. By using the aforementioned feature selection methods, almost 10% of all EEG features were selected. The tradeoff parameters (𝜆, 𝛽 𝜂, 𝜇, and 𝛿) were tuned from 10 3 to 10 3 with a step of 10 1 . Fig. 2 and Fig. 3 show the comparative results on the DEAP and DREAMER datasets. The horizontal axis of each figure represents the missing ratio of multi-dimensional labels, while the vertical axis represents the results of each performance metric. The results of WSEL are shown in Fig. 2 and Fig. 3 as the red line. As seen in Fig. 2(a-c ) and Fig. 3(a-c ), the multi-dimensional emotion recognition performance ability improves with decreasing values. Furthermore, as shown in Fig. 2(d-f ) and Fig. 3(d-f ), the multi-dimensional emotion recognition performance ability improves with increasing values. Compared with the results of the other nine methods, WSEL almost maintains the best performance with various missing ratios. Table 3 provides a summary of the quantitative comparative results across the six multi-label performance metrics. ↑ denotes a larger result being better, and ↓ denotes the contrary. Overall, the results in Fig. 2 , Fig. 3 , and Table 3 prove that the EEG feature subset chosen by the WSEL method has the best incomplete multi-dimensional emotion recognition performance.To further validate the effectiveness of the weighted selfrepresentation learning module for label reconstruction, the proportion of the number of successfully recovered emotional labels with various missing rates is summarized in Table 4 . As shown in Table 4 , the proposed method is able to effectively recover more than 60% of the missing labels through the weighted self-representation learning module, which in turn provides richer multi-dimensional emotional label information for the basic feature learning module. The Nemenyi test is applied as a specific post-hoc test to complete the multi-dimensional emotion recognition performance comparison, and the WSEL is implemented as the control method. The outcomes of the Nemenyi test in terms of six performance metrics are shown in Fig. 4 . WSEL outperforms the other nine approaches on all performance metrics, as Fig. 4 illustrates. This indicates that the WSEL method could achieve highly competitive multi-dimensional emotion recognition performance with incomplete label information.To determine the contributions of each module in the proposed EEG feature selection model, we carried out ablation experiments. There are three important modules in WSEL, and we only sequentially removed each module. Table 5 illustrates that the weighted self-expression model plays a key role in recovering missing labels by efficiently capturing high-order correlation information within incomplete multi-dimensional emotional labels. Other modules play roles in maintaining the local geometry structures and removing redundant information. Additionally, the computational time cost of all the methods was compared. The implementation was made in MAT-LAB (MathWorks Inc., Novi, MI, USA) and run under Microsoft Windows 11 × 64 on a computer with an Intel Core i5-124000HQ 2.5 GHz CPU and 16.00 GB of RAM. The average computational time results are shown in Table 6 . As seen in Table 6 and Table 4 , the proposed method is able to obtain the optimal performance of incomplete multi-dimensional emotion recognition with relatively little computational cost. Finally, we conduct a convergence speed analysis of the proposed iterative optimization algorithm. Fig. 5 shows the convergence curves of the objective value on the DEAP and DREAMER. The tradeoff parameters (𝜆, 𝛽 𝜂, 𝜇, and 𝛿) are all fixed at 10. As seen in Fig. 5 , the WSEL algorithm converges rapidly in a small number of iterations, demonstrating the potency of our iterative optimization strategy. 
conclusions and future work: 
 An embedded EEG feature selection framework under incomplete multi-dimensional emotion information is proposed, which selects discriminative EEG features and reconstructs the multi-dimensional emotion label space by simultaneously merging weighted self-expression learning and global feature redundancy learning in the least squares regression model. Furthermore, a simple and effective substitute strategy is also proposed to copy the optimization problem of WSEL. The experimental results have demonstrated the effective performance of WSEL.Although the proposed method can recover missing emotional labels to a certain extent (more than 60%), its recovery rate is not particularly satisfactory, especially in real brain computer interface-based emotion recognition applications. It is an interesting topic to improve the recovery rate of missing labels. In the future, we will focus on researching novel strategies to improve the recovery rate of missing labels for incomplete multi-dimensional affective computing. 
 
 Appendix:  


Decision: The paper presents a novel EEG feature selection model with weighted self-expression learning (WSEL) aimed at addressing the problem of incomplete multi-dimensional emotional labels in EEG emotion recognition. The model's effectiveness is validated using two datasets, DREAMER and DEAP, and compared against nine state-of-the-art feature selection approaches, showing superior performance in six performance metrics.

Reviewer KZD6's and reviewer xq6x's concerns have been resolved. Reviewer sSZj's concerns have been partially resolved, with some contradictions and a suggestion for improving data presentation. For the final version, please address the contradictions highlighted by Reviewer sSZj regarding the use of subjective labels and improve data presentation as suggested. Additionally, ensure that Reviewer r3sa's concerns are adequately addressed to enhance the overall quality and clarity of the paper.

Reviews: review: paper_summary: paper_summary: This paper presents a novel EEG feature selection model with weighted self-representational learning (WSEL) for incomplete multi-dimensional emotion recognition. The label space is successfully reconstructed under the incomplete information. Extensive experiments validate the model on two publicly available datasets, and its performance is compared with nine state-of-the-art feature selection approaches.
strength_weakness: strength_weakness: 1、An embedded feature selection method for EEG signals is proposed. 
2、The consideration of incomplete information in practical applications for EEG analysis is an important aspect for extending affective brain-computer interface (aBCI) techniques into real-world applications.
limitations: limitations: 1、The paper template does not meet the requirements of ACM MM 2024. 
2、In Fig. 1, there are some typos, such as "Incmoplete" and "Redunancy". 
3、An incorporation of a graph-based manifold regularizer is adopted based on the label space. The regularization effect should be thoroughly examined, especially when the emotional labels are limited. 
4、The rationale for calculating global feature redundancy learning based on correlation should be explained.
5、Additional discussions on the impact of hyperparameters should be included in the discussion section.
paper_summary: paper_summary: The paper introduces an EEG feature selection model called Weighted Self-Expression Learning (WSEL) for incomplete multi-dimensional emotion recognition. The primary goal of this model is to address the challenges posed by high-dimensional multi-source EEG features and the limited size of valid samples. WSEL performs feature selection and optimization by learning and utilizing the intrinsic structure and correlations within the data, which can suppress the influence of missing label data on model construction. The method has been tested on two well-known public datasets: DREAMER and DEAP.
strength_weakness: strength_weakness: - The proposed method, WSEL, embeds the EEG feature selection process into the extended weighted self-expression model, adopting High-Order Correlation to capture complex relationships among multiple variables, not limited to simple linear relationships.

- An effective and easy alternative is proposed to ensure convergence and obtain an optimal solution for Multi-Dimensional Emotion Recognition.

- Validated using two multimedia-induced affective datasets, DREAMER and DEAP, the WSEL-selected EEG feature subset performed best on all six performance indicators compared to nine existing feature selection methods.
limitations: limitations: #### **Major**:

- **Novelty**: The mathematical equations remind me of some current feature selection methods that were not included in the authors’ comparison study and other main contexts, such as IMUFS (Huang et al., IEEE TKDE, 2023) and the Joint Self-Expression Module (Yuan et al., PRCV 2020). Could the authors step-by-step explain their unique contributions compared to such methods to prove their novelty, both from a global conceptual perspective and with detailed mathematical explanations?

- The accurate recovery rates of missing labels vary irregularly with the missing ratio, rather than showing a negative correlation. Specifically, the highest recovery rate (69.08%) occurred at a 20% missing ratio. How did the authors consider their model’s unexpected degeneration when only 10% of the labels were missing?

- Since the motivation for this work, as stated at the beginning of the abstract, is to address overfitting, showing a comparison of training and testing loss under the conditions of no feature selection and with feature selection would be intuitive to indicate the power of the proposed methods.

- WSEL models involve multiple matrix operations and higher-order correlation calculations, which can be computationally expensive on large-scale datasets. How do the authors consider the computational efficiency of their method on large-scale datasets? The authors should interpret the reasons for the inferiority of the proposed method in terms of computational timing cost compared with models like MGFS, MFS, and FIMF, as well as discuss what causes the magnitude jump in the computational time of these models like PMU, FSOR, and GRMOR.

- The authors only show their own model’s convergence performance in Figure 5, which does not fully demonstrate the potency of the optimization strategy. Including the convergence curves of other models in the same panel could provide stronger evidence.

- The proposed WSEL algorithm introduces many weight parameters (e.g., \(\lambda, \gamma, \delta, \beta, \eta, \mu\)), which may require precise fine-tuning to balance the contributions of different components when applied to new datasets. Improper selection of these parameters may lead to degraded model performance.


#### **Minor**:

- To enhance readability, placing the citation next to the name of the method being compared would be better.

- For written rigor, the abbreviations of the six metrics used in Table 3 should be defined in advance, such as Hamming Loss (HL), Ranking Loss (RL), Coverage (CV), Average Precision (AP), Macro-F1 (MA), and Micro-F1 (MI).
paper_summary: paper_summary: The manuscript utilizes EEG data to implement emotion recognition.
strength_weakness: strength_weakness: Aiming at the problems of feature dimension catastrophe and incomplete multi-dimensional labeling information, the manuscript conducts multi-dimension emotion recognition research under incomplete labels and proposes a EEG feature selection method. Extensive experiments are conducted on two publicly available datasets to demonstrate the effectiveness of the method.
limitations: limitations: However, the innovation of the manuscript is somewhat weak and the experimental results are puzzling. The manuscript needs further improvement. The detailed comments are as follows:
1) From my point of view, the Figure 1 and Section 3 are confusing. As can be seen in Figure 1, EEG feature learning first implements global feature redundancy learning to obtain the EEG feature matrix X and redundancy matrix A. Then, the EEG feature subset is extracted by basic feature learning for multidimensional emotion recognition. However, in Section 3, basic feature learning is introduced first, then weighted self-expression learning, and finally global feature redundancy learning, which makes it difficult to understand the flow of the proposed model.
In addition, for Figure 1, the manuscript proposes a WSEL architecture, which consists of three sections, one of which is WSEL. Does WSEL represent the model framework or one of the methods?
2) Among the nine advanced feature selection methods, is there a method proposed for incomplete multi-dimensional labels?
3) Legends are missing in Figures 2 and 3. Figure 2 shows the emotion classification performance with different missing ratios. It is suggested to analyze the reason why the classification performance is almost unchanged in the case of larger missing ratios.
4) Table 2 does not indicate under which condition the emotion recognition results were obtained. It is recommended to compare with the following studies and describe their relevance and differences with the manuscript :
[1] Embedded EEG Feature Selection for Multi-Dimension Emotion Recognition via Local and Global Label Relevance,  IEEE Transactions on Neural Systems and Rehabilitation Engineering, vol. 32, pp. 514-526, 2024. (18 January 2024)
5) Table 4 exhibits the proportion of the number of successfully recovered emotional labels with various missing rates. Why when the missing rate is 40% and 50%, the accurate recovery rate of the label is higher than that of the missing rate is 10%?
6) The English should be improved, there are a number of problems with sentence grammar and structure and formatting errors, such as Eq. (13), (18) and (19).
paper_summary: paper_summary: This paper addresses the issue of incomplete labels that may arise in open scenes in EEG emotion recognition, enhancing feature selection methods. The approach includes three modules: basic feature learning, weighted self-expression learning, and global feature redundancy learning to accomplish the feature selection process. Specific optimization strategies are proposed, and the methods show state-of-the-art performance on two different multimodal emotion datasets.
strength_weakness: strength_weakness: 1. Innovation: Compared to previous FSOR and GRMOR models, the WSEL module proposed in this paper is a significant innovation. It is used to describe and reconstruct multidimensional missing label information, providing a solution to the specific problem of missing labels.
2. Writing Clarity: The modules and descriptions in Figure 1 align well and are clearly articulated. Detailed descriptions are provided for different methods through formulas. Additionally, pseudocode is provided to explain the steps.
3. Review: The review of the three methods—filter, wrapper, and embedded—is thorough.
4. Significance: The explosion of feature volume is a significant issue in EEG emotion recognition. This paper further provides a solution to the problem of missing labels in open scenes, which is expected to promote the development of relevant sub-communities.
5. Experimental Validation: Analyses are conducted on various evaluation matrices, showing state-of-the-art performance.
limitations: limitations: 1. Copyright Issue with Figures: The experimental scene diagram from the DEAP dataset homepage is pasted in Figure 1 (not affecting the model architecture). It is suggested that the authors consider potential copyright issues to avoid potential disputes.
2. Reproducibility: It is hoped that the authors will further open-source the code to promote development in related fields.