## 3 Materials and Methods
### Feature Extraction Methods
#### 3.3.4 Location Domain  
Location-domain features would be obtained from voltage measurements at various locations on the scalp and their differences or ratios among left and right sites. Differential asymmetry (DASM) and rational asymmetry (RASM) may capture some aspects of the asymmetry between the two sides. These features are based on the premise that certain cognitive and emotional processes are lateralized, meaning that they are more dominant in one hemisphere of the brain than the other. Table 1 shows the mathematical expressions and the parameters of the feature extraction methods in the time, frequency, time-frequency, and location domains implemented in this research. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Method** & **Mathematical Expression** & **Description** \\ \hline Time domain & & \\ \hline Maximum (Max) & \((X_{i}\in\mathbb{C})\) & (1) & \(X_{i}\) is the maximum element of \(\mathbb{C}\) if any other component of that set is less than or equal to \(X_{i}\). \\ \hline Mean & \(norm=\frac{1}{N+1}\frac{N}{\sum_{i=1}^{N}X_{i}}\) & (2) & \\ \hline Standard deviation (Stddev) & \(siddev=\sqrt{\frac{N}{\sum_{i=1}^{N}X_{i}}}(X_{i}-norm)^{2}\) & (3) & In Equations (2)–(6), \(X_{i}\) represent the data (EEG signal), where \(i=1,\ldots,N\), and \(N\) is the total number of samples (experiments). \\ \hline Skewness & \(skewness=\frac{\sum_{i=1}^{N}X_{i}-norm^{2}/N}{(siddev)}\) & (5) & \\ \hline Kurtosis & \(kurtosis=\frac{\sum_{i=1}^{N}X_{i}-norm^{4}/N}{(siddev)^{2}}\) & (6) & \\ \hline Mean of absolute values of the first difference & \(AFD_{N}=\frac{1}{N+1}\sum_{i=1}^{N-1}|X(i+1)-X(i)|\) & (7) & In Equations (7) and (8), \(X_{i}\) represents the data (EEG signal), where \(i=1,\ldots,N\), and \(N\) is the total number of samples (experiments). \\ \hline The mean of absolute values of the second difference of normalized (ASD,N 0) & \(ASD_{N}=\frac{1}{N+1}\sum_{i=1}^{N-2}|X(i+2)-X(i)|\) & (8) & \\ \hline Shannon entropy (ShEn) & \(ShEn=-\frac{N}{\sum_{i=1}^{N}P(X)\log P(X)}\) & (9) & \(X\) represents the EEG signal, \(P\) is the occurrence probability for the values in \(X\), and \(N\) is the total number of experiments. \\ \hline Approximate entropy (ApEn) & \(APEn(X,m,r)=1\) & (10) & \(X\) represents the EEG signal, \(m\) is the size of the vector, \(r\) is the tolerance value, \(N\) is the total number of experiments, and \(C_{i}^{m}\) is the vector self-similarity. \\ \hline Sample entropy (SampEn) & \(SampEn(X,m,r)=\log^{\mathcal{O}r}(r)-\mathcal{O}^{n+1}(r)\) & (11) & Self-similarity of the pairs of vectors \(u(i)\) and \(u(j)\) with a tolerance of \(r\). If the signals are self-similar, then \(\mathcal{O}^{n}\) (\(t\)) is high. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mathematical expressions and a brief description of the feature extraction methods. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Method** & **Mathematical Expression** & & **Description** \\ \hline Permutation entropy (PerEn) & \(PE(X)=\frac{\sum_{i=1}^{M}p(\pi_{i})\log p(\pi_{i})}{\log p(\pi_{i})}\) & (12) & \(f(u(i|j,\pi_{k})=1\) when \(u(i|j,\pi_{k})\) and \(\pi_{k}\) have the same pattern, else is 0, and the pattern is defined by the order of \(u(i|j,\pi_{k})\) that corresponds to each element. The occurrence probability of each pattern category is \(p(\pi_{k})\). \\ \hline Energy (Eng) & \(Eng=\sum_{m=1}^{N}|X(n)|^{2}\) & (13) & \(X(n)\to 0\) as \(n\rightarrow\pm\infty\), where \(X(n)\) is the EEG signal. \\ \hline Average power (Avg) & \(Avg=\lim\limits_{N\to 0}\frac{1}{N}\frac{N}{\sum_{i=-1}^{M}|X(n)|^{2}}\) & (14) & \(N\) is the number of samples taken for the computation, and \(X(n)\) is the EEG signal. \\ \hline Root mean square (EMS) & \(RMS=\sqrt{\frac{1}{N}\sum_{i=1}^{N}X^{2}(n)}\) & (15) & \(N\) is the number of samples taken for the computation, and \(X(n)\) is the EEG signal. \\ \hline Line length (LinLen) & \(LL=\frac{N}{\sum_{i=1}^{N}|X(i-1)-X(i|)|}\) & (16) & \(X\) is the EEG signal, \(N\) is the number of samples in the signal, and \(i\) is the data index.