## 3 WFBRCSP Methods
### Weight Assignment for Band-Specific Mutual Information  
The weighted filter bank allows for selective processing of different frequency bands of the signal. By combining information from multiple frequency bands, it can improve the algorithm's robustness to noise and artifacts. Although EEG signals exhibit subject-specific characteristics, there may still be some similarity in the EEG responses between different subjects during motor imagery tasks, especially in task-related brain regions and common signal patterns (e.g., \(\alpha\) waves, \(\beta\) waves). In traditional RCSP methods, when adding the data from source domain subjects to the covariance matrix, the data from all source domain subjects are typically added with equal weights. Mutual information-based weight allocation, by weighting the data from certain subjects for regularization, can avoid the negative impact of data with a weak correlation to the target subject on the model, thereby enhancing classification performance. Mutual information maximization (MIM) is an information-theoretic optimization criterion designed to measure the statistical dependence between two random variables. In this study, mutual information maximization is applied in the subject-weighting strategy, specifically manifested as:  
1. Calculating mutual information:  
For each frequency band, the mutual information between the target subject's data and the source domain subject's data is calculated to quantify their correlation in the time domain. The mutual information of each frequency band for a given source domain subject is then accumulated to obtain the total mutual information;  
Figure 1: The block diagram of weighted filter bank and regularization common spatial pattern method. 2 Subject weight allocation:  
Based on the mutual information maximization criterion, higher weights are assigned to source domain subjects with high correlation, while lower weights are given to source domain subjects with low correlation, thereby adaptively enhancing the contribution of more specific subjects. First, the EEG signals of the target subject and all of the source domain subjects are divided into sub-bands using a 5 th-order Butterworth filter with frequency bands of 4-8 Hz, 8-12 Hz, \(\ldots\), 36-40 Hz [20]. Given the EEG signals \(X_{i}\) and \(Y_{j}(i\
eq j)\) of the target subject \(i\) the and source domain subjects \(j\) for a specific task \(c\) within a certain frequency band \(B\), the mutual information is defined as:  
\[I_{B}^{c}(X_{i},Y_{j})=\sum_{x_{i}\in X_{i}}\sum_{y_{j}\in Y_{j}}p_{B}^{c}(x_{i },y_{j})\log(\frac{p_{B}^{c}(x_{i},y_{j})}{p_{B}^{c}(x_{i})p_{B}^{c}(y_{j})}) \tag{1}\]  
where \(P_{B}^{c}(x_{i},y_{j})\) is the joint probability distribution of the target subject \(i\) and source domain subject \(j\) for the class \(c\) task in frequency band \(B\), \(p_{B}^{c}(x_{i})\), and \(p_{B}^{c}(y_{j})\) are the marginal probability distributions of the target subject \(i\) and source domain subject \(j\) for class \(c\) task in frequency band \(B\), respectively. The total mutual information of the source domain subject is obtained by accumulating the mutual information between the source domain subject \(j\) and the target subject \(i\) across all classification tasks and all sub-bands:  
\[I(X_{i},Y_{j})=\sum_{c\in\{1,2\}}\sum_{B\in\Omega}I_{B}^{c}(X_{i},Y_{j}) \tag{2}\]  
The subject with the maximum mutual information is used as the reference. The total mutual information between all source domain subjects, and the target subject \(i\) is then normalized to ensure that the weight values of the source domain subjects lie within the range \(0\leq w_{j}\leq 1\).