## 3 Methods
### Multiband Four-Dimensional Feature Construction
Treating all channel data of a single frequency band as a whole, such that \(\chi^{i}_{S}\) is transformed into \(\left\{\mathrm{p}_{1}^{\theta},\mathrm{p}_{1}^{\alpha},\mathrm{p}_{1}^{\beta},\mathrm{p}_{1}^{\gamma}\right\}\), where \(\mathrm{p}=\left\{\mathrm{p}_{1},\mathrm{p}_{2},\ldots,\mathrm{p}_{M}\right\}\) denotes all channel data of a single frequency band, the arrangement order is shown in Figure 3. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Frequency Band** & **Frequency Range** & **Brain States** & **Awareness** \\ \hline \(\delta\) & 1–4 & Extreme fatigue and deep sleep states & Sleep mode \\ \(\theta\) & 4–8 & Light sleep, frustrated state & Low \\ \(\alpha\) & 8–13 & Awake, quiet, and eyes closed state & Medium \\ \(\beta\) & 13–30 & Active thinking, mental tension, anxiety, concentration state & High \\ \(\gamma\) & 30–50 & Multimodal sensory stimulation, mentally active state & High \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Emotional states correspond to different frequency band information. Figure 3: Channel alignment order. After data enhancement, our focus shifts to emotion recognition at the segmentation level, and considering that human emotion changes are temporally dynamic, the window segmented signal \(X_{\text{S}}^{i}\) is segmented into equal-length frames of 0.5 s. Using 0.5 s data per channel as the vector components that constitute a single frame window, \(X_{\text{S}}^{i}\) will be converted into a sequence containing 2u frame vectors, \(X_{\text{S}}^{i}=\left\{\left\{\text{P}_{\text{i}}^{10},\text{P}_{\text{i}}^{1 \alpha},\text{P}_{\text{i}}^{18},\text{P}_{\text{i}}^{17}\right\},\ldots, \left\{\text{P}_{\text{i}}^{j0},\text{P}_{\text{i}}^{j\alpha},\text{P}_{\text{i }}^{j\beta},\text{P}_{\text{i}}^{j\gamma}\right\}\right\}\) (\(i=1,2,\ldots,\text{n}_{\text{j}}=1,2,\ldots,2\text{u}\)). Considering the information complementarity between different features, the DE and PSD features of all channels within each frame window are extracted in this paper [16]. DE is a derivative of [PERSON]'s concept of information entropy over a continuous probability distribution, which is a good method to describe internal EEG information. A specific length of EEG that approximately obeys the Gauss distribution \(\text{N}(\text{u},\text{o}_{\text{i}}^{2})\) is calculated as:  
\[\text{DE}=-\int_{-\infty}^{+\infty}\frac{1}{\sqrt{2\pi\text{o}_{\text{i}}^{2} }}\text{e}^{-\frac{(\kappa-\text{n})^{2}}{2\text{o}_{\text{i}}^{2}}}\log( \frac{1}{\sqrt{2\pi\text{o}_{\text{i}}^{2}}}\text{e}^{-\frac{(\kappa-\text{n} )^{2}}{2\text{o}_{\text{i}}^{2}}})\text{dx}=\frac{1}{2}\log(2\pi\text{e} \text{o}_{\text{i}}^{2}) \tag{6}\]  
where \(\sigma\) is the variance in the sequence signal. PSD is a physical quantity that characterizes the relationship between the power energy of a signal and its frequency and is often used to study random vibration signals, which can describe the activation level and emotional complexity of EEG signals. It is calculated as:  
\[\text{P}(\text{w})=\frac{1}{\text{MU}}\left|\sum_{n=0}^{\text{M}-1}x_{\text{N }}^{i}(\text{n})\text{d}(\text{n})\text{e}^{-\text{jwn}}\right|^{2} \tag{7}\]  
where \(x_{\text{N}}^{i}(\text{n})\) is the sampled data in segment i, \(\text{d}(\text{n})\) is the selected window function, M is the length of each segment, and U is the normalization factor. The final two sets of features obtained both include a two-dimensional vector sequence of four frequency bands, where the frame vectors \(\hat{\text{f}}_{\text{i}}^{\text{Y}}\) and \(\text{g}_{\text{i}}^{\text{jY}}\) retain the same arrangement as \(\text{p}_{\text{i}}^{\text{jY}}\).