## 3 Methods
### Extension of Symbolic Aggregate Approximation
Then, the mean value of each subsequence is calculated. Since the normalized sequence follows Gaussian distribution, the corresponding probability distribution is divided into equal areas. For the time series \(B=b_{1},b_{2},b_{3},\cdots,b_{n}\), \(n\) represents its length and the number of segments is \(\omega\), then the segmented time series could be expressed as \(B^{\prime}={b_{1}}^{\prime},{b_{2}}^{\prime},{b_{3}}^{\prime},\cdots,{b_{ \omega}}^{\prime}\) in terms of Equation (2). \[{b_{i}}^{\prime}=\frac{\omega}{n}\sum_{ \begin{subarray}{c}\mu(i-1)\\ \omega\end{subarray} +1}^{\frac{\mu i}{\omega}}b_{j} \tag{2}\]  
In view of the statistical table in reference [32; 33], the region of sequence \(B^{\prime}\) is segmented and judged. After that, different regions are represented by symbols so that the values are serialized into symbol sequences, respectively. The breakpoints \(\beta\) that divide the distribution space into \(\alpha\) equiprobable regions are determined by a lookup table that could be seen in Table 3.  
As Table 3 illustrates, the values of \(\beta_{i}\) (\(i=1,2,3,4\)) are defined by means of a statistical table that divides the Gaussian curve into equal areas. Each area is delimited by the interval \([\beta_{i-1},\beta_{i}]\). (3) Each subsequence segment is encoded with a symbol. Finally, the region corresponding to the mean of each subsequence is found, and the character corresponding to the region is used to replace the subsequence. After PAA, the equal size segments and their average values are obtained, and then the maximum and minimum values are defined in each segment. This means the time series is represented by the mean value and two additional values (the maximum and the minimum in the subsegment). These segments are described in Figure 4. \begin{table}
\begin{tabular}{c c c c} \hline \hline \(\alpha\) & \(\beta\) & \(3\) & \(4\) & \(5\) \\ \hline \(\beta_{1}\) & \(-0.43\) & \(-0.67\) & \(-0.84\) \\ \(\beta_{2}\) & \(0.43\) & \(0\) & \(-0.25\) \\ \(\beta_{3}\) & \(0.67\) & \(0.25\) \\ \(\beta_{4}\) & & & \(0.84\) \\ \hline \hline \end{tabular} Note: The breakpoint from \(3\) to \(5\) is given in Table 3[31].  
\end{table} 
Table 3: The value table of break point. For any given segment \(B^{\prime}_{i}\) in a time series, \(S_{k}\) and \(E_{k}\) are the start and end position on the time segment \(B^{\prime}_{i}\), respectively. The middle position \(p_{mid}\) of the time segment \(B^{\prime}_{i}\) could be calculated by Equation (3):  
\[P_{\text{mid}}=\frac{S_{k}+E_{k}}{2} \tag{3}\]  
\(S^{\prime}_{1}\), \(S^{\prime}_{2}\), and \(S^{\prime}_{3}\) are assumed to be the first, second, and third symbols in the \(k\)th (\(k\leq\omega\)) subsection. The \(p_{\text{max}}\), \(p_{\text{min}}\), and \(p_{\text{mid}}\) denote the maximum, minimum, and average value in the \(k\)th subsection on the \(x\)-axis, respectively. At the same time, \(S^{\prime}_{\text{max}}\), \(S^{\prime}_{\text{min}}\), and \(S^{\prime}_{\text{mid}}\)  
Figure 3: Diagram of the preprocessing of characteristic signals like ECG, EDA, and RESP. (**a**) Diagram of ECG filtering results, (**b**) Diagram of EDA filtering results, (**c**) Diagram of RESP filtering results. are supposed to be the maximum, minimum, and average characters in the \(k\) segment, respectively. The sequence of strings in the \(k\)th segment can be calculated by Equation (4):  
\[(s_{1}^{\prime},s_{2}^{\prime},s_{3}^{\prime})=\left\{ \begin{array}{lcl}(s_{ \max}^{\prime},s_{\min}^{\prime},s_{\min}^{\prime})&if&p_{\max}<p_{\min}\\ (s_{\min}^{\prime},s_{\min}^{\prime},s_{\max}^{\prime})&if&p_{\min}<p_{\min} \\ (s_{\min}^{\prime},s_{\max}^{\prime},s_{\min}^{\prime})&if&p_{\min}<p_{\max} <p_{\min}\\ (s_{\max}^{\prime},s_{\min}^{\prime},s_{\min}^{\prime})&if&p_{\max}<p_{\min} <p_{\min}\\ (s_{\min}^{\prime},s_{\max}^{\prime},s_{\min}^{\prime})&if&p_{\min}<p_{\max} <p_{\min}\\ (s_{\min}^{\prime},s_{\min}^{\prime},s_{\max}^{\prime})&otherwise\end{array} \right.