## 2 Materials and Methods
### Feature Extraction  
In this study, various power spectral features in the frequency domain and features calculated by combinations of electrodes were extracted from the constructed EEG signals. The extraction of prominent statistical characteristics is important for emotion recognition. The physiological signals, e.g., EEG, are characterized with high complexity and non-stationarity, and power spectral density (PSD) [20; 21; 22] from different frequency bands is the most well-known applicable statistical feature in the task of emotion analysis. This benefits from the assumption that EEG signals are stationary for the duration of a trail [50]. Many studies in neuroscience and psychology [51] suggest that these five frequency bands are closely linked to psychological activities, including the emotion activity: Delta (1 Hz-3 Hz), Theta (4 Hz-7 Hz), Alpha (8 Hz-13 Hz), Beta (14 Hz-30 Hz), and Gamma (31-50 Hz). The fast Fourier transform (FFT) can be applied using discrete Fourier transform (DFT) [52], while the common alternatives are short-time Fourier transform (STFT) [53; 54]. PSD features are extracted from the above five frequency bands using 256-point STFT and a sliding 0.5 s Hanning window with 0.25 s overlapping along 1 s epoch for each EEG channel.  
Differential entropy (DE) [55; 56] is a measurement of the complexity of a continuous random variable by extending the Shannon entropy concept [57]. These studies by [PERSON] et al. [47; 48] and [PERSON] et al. [56] introduced DE for emotion classification using EEG low/high-frequency patterns.  
The original formula of DE is defined as  
\[h(X)=-\int_{X}f(x)\log(f(x))dx, \tag{1}\]  
and DE when a random variable \(X\) obeys the Gaussian distribution \(N(\mu,\,\sigma^{2})\) can be simply given as:  
\[h(X)=-\int_{-\infty}^{+\infty}\frac{1}{\sqrt{2\pi\sigma^{2}}}\exp\frac{(x-\mu )^{2}}{2\sigma^{2}}\log\frac{1}{\sqrt{2\pi\sigma^{2}}}\exp\frac{(x-\mu)^{2}}{ 2\sigma^{2}}dx=\frac{1}{2}\log 2\pi e\sigma^{2}, \tag{2}\]  
where \(\pi\) and \(e\) are constants. According to [55], given a certain frequency band, DE equals to the logarithmic spectral energy for a fixed-length EEG recording. Thus, the DE features are calculated in the five frequency bands as for the PSD features.  
In the literature [58; 59], the asymmetric brain activity between the left and right hemispheres is of high relation with emotions. In the studies [47; 48], the differential asymmetry (DASM) and rational asymmetry (RASM) features were defined as the differences and ratios of the DE features of hemisphere asymmetric electrodes. Here, 14 pairs of asymmetric electrodes are selected to calculate DASM and RASM: Fp1-FP2, F7-F8, F3-F4, T7-T8, P7-P8, C3-C4, P3-P4, O1-O2, AF3-AF4, FC5-FC6, FC1-FC2, CP5-CP6, CP1-CP2, and PO3-PO4. The DASM and RASM features are given as  
\[\text{DASM}=\text{DE}(X_{left})-\text{DE}(X_{right}), \tag{3}\]  
and  
\[\text{RASM}=\text{DE}(X_{left})/\text{DE}(X_{right}) \tag{4}\]  
respectively. Due to the studies suggested in [58; 59], the emotional states are closely linked to the spectral differences of brain activity between frontal and posterior brain regions. The definition of differential caudality (DCAU) features [47; 48] was also adopted in this paper to characterize the spectral asymmetry in frontal-posterior direction. The DCAU features are given as the differences between 11 pairs of frontal-posterior electrodes: FC5-CP5, FC1-CP1, FC2-CP2, FC6-CP6, F7-P7, F3-P3, Fz-Pz, F4-P4, F8-P8, Fp1-O1, Fp2-O2. The formulation of DCAU is defined as  
\[\text{DCAU}=\text{DE}(X_{ frontal})-\text{DE}(X_{posterior}). \tag{5}\]  
The dimensions of the PSD, DE, DSAM, RASM, and DCAU features are 160 (32 channels * 5 bands), 160 (32 channels * 5 bands), 70 (14 pairs of electrodes * 5 bands), 70 (14 pairs of electrodes * 5 bands), 55 (11 pairs of electrodes * 5 bands), respectively. For simplicity, the above-extracted features were used directly and separately as input for the introduced and compared recognition methods.