# A Novel Approach for Emotion Recognition Based on EEG Signal Using Deep Learning
## 3 Material and Methods
### Feature Extraction Methods
#### 3.2.2 Variation Mode Decomposition  
VMD performs time-frequency decomposition like EMD, by decomposes the signal into \(k\) discrete number of sub-signals [36]. It has been developed to overcome the limitations arising in EMD [37]. Since VMD does not use a recursive approach, it obtains IMFs with a concurrent approach. Furthermore, it is an adaptive approach, and it converts the signal into a certain number of IMFs with the relevant center frequencies. IMFs are the AM-FM (amplitude modulated frequency modulated) signals, and they can be calculated using the Equation (2) [37].  
\[uk(t)=A_{k}(t)\cos(_{k}(t)) \tag{2}\]  
where \({}_{k}(t)\) represents the non-decreasing function and the derivative of the \({}_{k}(t)\) (instantaneous frequency) and should be more than or equal zero. \(A_{k}(t)\) represents the amplitude and it is more than or equal zero as well. Finally, \(uk(t)\) specifies the sub-signals. IMF also allows non-discontinuous and discontinuous signals like the sawtooth. After calculating the mode, the bandwidth of the mode is determined based on [PERSON]'s rule, as in Equation (3) [37].  
\[BW_{FM}=2(\Delta f+f_{FM}) \tag{3}\]  
where \(BW\) refers to the practical bandwidth, \(\Delta f\) represents the maximum deviation, and \(f_{FM}\) shows the carrier frequencies. In addition, Equation (4) is used to calculate the total practical IMF bandwidth, and Equation (5) is used to calculate the VMD method.  
\[BW_{AM-FM}=2(\Delta f+f_{FM}+f_{AM})) \tag{4}\]  
\[\underset{u_{k},u_{k}}{\text{min}}\left\{\sum_{k}\|\phi_{t}\Big{[}\Big{(} \Big{(}\delta(t)+\frac{j}{\pi t}\Big{)}*u_{k}(t)\Big{)}e^{-j\text{m}_{k}t} \Big{]}\|^{2}_{2}\!\!,\!\!  
IMFs. Compared to EMD, the VMD method was found to be more effective against noisy signals [38]. When the literature is reviewed, it is seen that VMD is used effectively in the biomedical field at least as much as EMD. Emotion recognition [22], EMG-based signal studies [30], and diagnosis of lung disease [31] can be given as examples. The effective use of the VMD method in the biomedical field has enabled us to use this method in this study. Figure 4 shows the IMFs of the EEG signal used in this study, obtained by VMD.  
Statistical features were extracted from a total of 14 IMFs obtained in EMD and VMD. These statistical features are the maximum value, the minimum value, and the average value. We believe that the features obtained by using statistical methods give acceptable results and are still used in the signal processing field. There are several types of statistical methods, such as min, max, average, median, standard deviation, etc. We selected three of them (maximum, minimum, and average). The maximum and minimum values show the start and endpoints of the identified EEG signals, with the maximum and minimum value showing the maximum amplitude and minimum amplitude values of the samples of the EEG data. These values are required to compare the highest and lowest peak signals in different mental states. In the region selected for sample data, the peak-to-peak (P-P) shows the difference between the value of the maximum amplitude and the minimum amplitude. Average computes the average amplitude value of the EEG data samples collected between endpoints in the selected region. Equation (6) is used to extract the mean value of the EEG signal [39]:  
\[Avg=\frac{1}{n_{e}-n_{s}}\sum_{i=n_{s}}^{n_{e}-n_{s}}X_{iEEG} \tag{6}\]  
where \(n_{s}\) refers to the starting point of the signal, \(n_{e}\) refers to the endpoint of the signal. Besides, \(n_{e}-n_{s}\) represents to the total number of samples, and variable \(i\) refers to the values on the horizontal axis.