## 3 Method
### JMI-Based Greedy Feature Selection Algorithm (JMI-Score)  
In the task of emotional feature classification and recognition, it is necessary to perform feature dimensional reduction processing on the obtained high-dimensional features, and to avoid overfitting caused by too high dimensional. Therefore, a greedy feature selection algorithm based on JMI is proposed here to select features, as shown in the Algorithm 1, the specific steps of the Joint Mutual Information (JMI)-based greedy feature selection algorithm proposed in this paper are shown below. JMI Introduction  
The mutual information is a measure \(X\) and \(Y\) between two (possibly multidimensional) random variables, which quantifies the amount of information about one random variable obtained through another random variable. The mutual information is given by the following equation:  
\[I(x,y)=\sum_{j=1}^{N}\ \sum_{j=1}^{M}\ p\big{(}x_{i},y_{j}\big{)}\log\frac{p \big{(}x_{i},y_{j}\big{)}}{p(x_{i})p\big{(}y_{j}\big{)}}, \tag{4}\]  
\(x_{i},y_{j}\) are the \(X\), \(Y\) components, and with \(N\) and \(M\) values, respectively. JMI provides the best trade-offs in terms of accuracy, stability, and flexibility based on two assumptions:  
1. After removing a feature given the removed feature itself, any unselected feature is conditionally independent of the union of the selected features: \[p\big{(}x_{k};x_{s/i}\mid x_{i}\big{)}=p\big{(}x_{k}\mid x_{i}\big{)}p\big{(}x _{s/i}\mid x_{j}\big{)},\] (5)
2. Any unselected feature is conditionally independent of the union of selected features after removing any feature of a given class label and the removed feature itself: \[p\big{(}x_{k};x_{s/i}\mid x_{i},y\big{)}=p\big{(}x_{k}\mid x_{i},y\big{)}p \big{(}x_{s/i}\mid x_{i},y\big{)},\] (6)  
Assuming the above two, the JMI score of the feature \(x_{k}\) is obtained according to the mutual information formula,  
\[J_{JMI}(X_{k})=\text{argmax}\left(\sum_{X_{j}\in S}\ I\big{(}X_{k}X_{j};Y\big{)} \right), \tag{7}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Signal** & **Feature Group** & **Description of the Extracted Features** \\ \hline \multirow{4}{*}{ECG} & \multirow{4}{*}{Time Domain} & R, P, Q, S, T (mean, max, min, std), IBI (mean, max, min, Peaks, std, kurtosis, skewness), HRV (mean, std, kurtosis, skewness), RR interval mean, RR interval std \\  & Frequency Domain & PSD-VLF, PSD-LF, PSD-HF, TP, pLF, pLF, LFHF, LFHF, nHF, nLF \\  & \multirow{4}{*}{NonLinear} & \multirow{4}{*}{\begin{tabular}{} \end{tabular} } & \multirow{4}{*}{\
\begin{tabular}{} \end{tabular} } \\  & & & \\ \hline \multirow{4}{*}{GSR} & \multirow{4}{*}{
\begin{tabular}{} \end{tabular} } & Mean, Max, Min, Std, 1 Diff (abs, mean, std), 2 Diff (abs, Mean, std), kurtosis, skewness, SCR RiseTime, SCR Width (mean, max, min, std), Skin Conductance (Mean, Max, Min, Std, 1 Diff, 2 Diff), \\  & & & \\ \cline{1-1}  & & & \\ \cline{1-1}  & & & \\ \cline{1-1}  & & & \\ \cline{1-1}  & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of extracted features. This is the information between the target \(Y\) and the joint random variables \(X_{k}X_{j}\), defined by pairing the candidate \(X_{k}\) with each of the previously selected features \(X_{j}\). The candidate feature \(X_{k}\) that maximizes this mutual information is selected and added to the feature subset \(S\). The maximum joint mutual information is defined as: Let \(F=\{f_{1},f_{2},\ldots\ldots,f_{N}\}\) be the full feature set, let \(S\) is a subset of the selected features. Let \(f_{i}\in F-S\), \(f_{s}\in S\).Max\(J\)\(MI\) is the maximum value of the joint mutual information shared with the class label \(C\) by the candidate feature \(f_{i}\) when each feature in the subset \(S\) is individually connected, therefore \(\underset{s=1,2,\ldots,k}{max}I(f_{i},f_{s};C)\). ```
Input: All feature sets \(F=\{f_{1},f_{2},\ldots\ldots,f_{N}\}\), Classification Tags C, Number of features \(D\), Simple classification model model Selected feature set subscript \(S\). JMI-Score (\(F\), \(C\), model, \(S\), \(D\)):
1.